# Why is the potential energy of an ideal gas 0?

Why Is the Potential Energy Of an Ideal Gas 0?
C O N T E N T S:

KEY TOPICS

• For the following reasons, ideal gas particles have no potential energy.(More…)
• For now, you can just think of internal energy as the total kinetic plus potential energy of the particles comprising a physical system, and heat as thermal energy transferred to the system from the environment or vice versa.(More…)
• This chapter covers the following topics: kinetic and potential energy, chemical and thermal energy, energy units, het and work and their interconversion,temperature and its meaning, measuring temperature, temperature scales,absolute temperature, heat capacity, specific heat.(More…)

POSSIBLY USEFUL

• Since Δ U isolated system 0, ΔU system -ΔU surroundings and energy is conserved.(More…)
• Work done on a gas results in an increase in its energy, increasing pressure and/or temperature, or decreasing volume.(More…)

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KEY TOPICS

For the following reasons, ideal gas particles have no potential energy. [1] Stagnation density 0 When stagnation enthalpies are used, the energy balance for a single-stream, steady-flow device When the fluid is approximated as an ideal gas with constant specific heats SPEED OF SOUND AND MACH NUMBER Speed of sound (or the sonic speed): The speed at which an infinitesimally small pressure wave travels through a medium. [2] The ideal gas is a special case in which the molar internal energy is a function only of temperature. [3] While studying thermodynamics, I read that the internal energy of an ideal gas is a function of temperature only. [3] Levine, Ira N. “Thermodynamic internal energy of an ideal gas of rigid rotors.” [4] Then internal energy of an ideal gas is total kinetic energy of its molecules. [1] The average kinetic energy is nothing else than the temperature of the ideal gas. [3] In general, the internal energy is a function of two intensive properties, in this case T and V. But, in the case of an ideal gas, the equation of state is such that the second term in this equation is identically equal to zero. (Substitute PRT/V to confirm this). [3] For an adiabatically expanding ideal monatomic gas which does work on its environment (W is positive), internal energy of the gas should decrease. [5]

Boyle’s law : The observation that the pressure of an ideal gas is inversely proportional to its volume at constant temperature. [5] For an ideal gas, the product of pressure and volume (PV) is a constant if the gas is kept at isothermal conditions. [5]

The value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant. [5] The reason is that the atoms of an ideal gas are non-interacting point particles. [3] For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in for an ideal gas. [5]

The ideal gas law can be considered to be another manifestation of the law of conservation of energy. [6] We already know that the internal energy of an adiabatic process of an ideal gas depends only on the temperature of the system. [7] Note that $dU nC_VdT$ for any process as the internal energy depends only on the temperature of the system of ideal gas. [7]

In Section 1.6, we derived the equation of state for an ideal gas utilizing only the average kinetic energy of the molecules, which was determined from a root-mean-square molecular speed. [8]

What that means is that there?s no potential energy resulting from electrostatic forces between the gas particles, so the internal energy is entirely kinetic. [9]

One gram of water at zero °Celsius compared with one gram of copper at zero °Celsius do NOT have the same internal energy because even though their kinetic energies are equal, water has a much higher potential energy causing its internal energy to be much greater than the copper’s internal energy. [4] Eating increases the internal energy of the body by adding chemical potential energy. [5] In essence, metabolism uses an oxidation process in which the chemical potential energy of food is released. [5] This process is the intake of one form of energy–light–by plants and its conversion to chemical potential energy. [5]

During collision kinetic energy does convert in to potential energy, but almost within no time the collision is over and effectively molecules have kinetic energy ONLY. It is because of this situation, in kinetic theory calculations,( in collisions), we do not consider kinetic energy – potential energy transformations. [1]

The first term is the kinetic energy (and is the same for the ideal gas), while the second term is a potential energy (and is zero for the ideal gas). [10]

To do this, consider the limit as a ? 0, that is, the case of the old ideal gas. [8] The gas is called an ideal gas, in which case the relationship between the pressure, volume, and temperature is given by the equation of state called the ideal gas law. [6] To make this more concrete, supposing your system is an ideal gas obeying the relationship PV nRT, where P pressure, V volume, n the number of moles of your gas, R is the gas constant, and T temperature. [9] The ideal gas law can be expressed either as P V N k T P V N k T, where N is the number of atoms or molecules and k is the Boltzmann constant, or as P V n R T P V n R T, where n is the number of moles and R is the universal gas constant. [6] Step 4 Determine whether the number of molecules or the number of moles is known, in order to decide which form of the ideal gas law to use. [6] I could get into the details of where the Ideal Gas Law fails, and the other models (like Van Der Waals) that scientists have developed to try and account for problems of attractive forces existing between molecules, or the volume of the molecules themselves — but you can learn all of that in a physical chemistry class. [11] Note that absolute pressure and absolute temperature must be used in the ideal gas law. [6] When the fluid is approximated as an ideal gas with constant specific heats T0 is called the stagnation (or total) temperature, and it represents the temperature an ideal gas attains when it is brought to rest adiabatically. [2] If a plot of volume versus temperature is linear, the gas is behaving as an ideal gas. [6] We can write the first law of thermodynamics for adiabatic process of ideal gas as \ We replace $dT$ in the above equation by differentiating ideal gas equation and solving for $dT$. [7] The gas constant R is used in the Ideal Gas Law and Nernst Equation. [12] The Ideal Gas Law combines Boyle’s Law, Charles’ Law, and Avogadro’s Law in one simple, memorable formula: PVnRT. The major flaw in this formula is so obvious in its name that it’s almost funny when you finally realize it — the law only fits data for ideal gases. [11] The ideal gas law describes the behavior of real gases under most conditions. [6] We used an isothermal process with an ideal gas, and one of the assumptions of the ideal gas model is a lack of intermolecular interactions between the particles comprising the gas, which is not the case with real gases. [9]

For now, you can just think of internal energy as the total kinetic plus potential energy of the particles comprising a physical system, and heat as thermal energy transferred to the system from the environment or vice versa. [9] The Maxwell- Boltzmann distribution has been recognized to be valid for the solid state too, including the potential energy of position and the internal energy of molecules ( Langmuir, 1920 ). [8] Quantum effects constrain individual molecules to discrete allowed energy levels, and a more detailed statistical thermodynamic approach would account for rotational and vibrational energy modes, in addition to translational and potential energy, and would even entail different microstate-counting methods for fermions vs bosons ( Stowe 2008 ). [9] Energy balance (with no heat or work interaction, no change in potential energy If the fluid were brought to a complete stop, the energy balance becomes Stagnation enthalpy: The enthalpy of a fluid when it is brought to rest adiabatically. [2] The MD technique, in solving the classical equations of motion for a system of atoms interacting according to a potential energy force field, provides a means of examining the time evolution of a molecular system and the various conformational and momentum changes that occur. [8] We know from our study of fluids that pressure is one type of potential energy per unit volume, so pressure multiplied by volume is energy. [6] Gases have particles that are spread apart, giving them lots of potential energy, like when the ball is lifted a long way above the earth. [13] State or phase is a measure of the potential energy of the particles. [13] To escape from a planet, an object of mass m must have a kinetic energy ( mu 2 /2) that is greater than its gravitational potential energy. [8]

Potential energy of gas in gravitational field (K&K 5.3) Consider a column of atoms each of mass $$M$$ at temperature $$T$$ in a uniform gravitational field $$g$$. [10] Neither of them accounts for the potential energy created when gas molecules move apart in ascent or closer together in descent along a declining density gradient with height. [14] That is the mechanism behind the gas laws and the quantity of the latter is vastly greater than simple gravitational potential energy. [14]

It describes the case that you have a system of particles (e.g., our ideal gas) in contact with a heat bath (i.e., it can exchange energy with a large reservoir of particles at a given temperature), and you can exchange particles with the heat bath. [15] Small white boards What kind of interactions might exist in a real gas that are ignored when we treat it as an ideal gas? Answer Repulsion and attraction! $$\ddot\smile$$ Atoms will have a very high energy if they sit on top of another atom, but atoms that are at an appropriate distance will feel an attractive interaction. [10] The ideal gas is unique in that its energy is independent of its density. [10] Now we could integrate to find the work, but the easy approach is to find the heat from $$T_H\Delta S$$, and then use the First Law to find the work. \ Now using the First Law. \ This tells us that the photon gas does work as it expands, like the ideal gas does, but unlike the ideal gas, the work done is considerably less than the heat absorbed by the gas, since its internal energy increases significantly. [10] One would be to use the ideal gas law combined with the internal energy $$\frac32NkT$$ and to make use of energy conservation. [10] Since for a monatomic ideal gas $$U\frac32NkT$$, keeping the internal energy fixed means the temperature also remains fixed, there won’t be any heating and the temperature will certainly stay fixed. [10] We can find the internal energy from $$FU-TS$$ now that we know the entropy. \ which looks like the monatomic ideal gas internal energy plus a correction term, which depends on the density of the fluid. [10]

This fix performs grand canonical Monte Carlo (GCMC) exchanges of atoms or molecules with an imaginary ideal gas reservoir at the specified T and chemical potential (mu) as discussed in (Frenkel). [16] As an alternative to specifying mu directly, the ideal gas reservoir can be defined by its pressure P using the pressure keyword, in which case the user-specified chemical potential is ignored. [16] In contrast to the concentration dependence, the temperature-dependence of the ideal gas chemical potential will be almost entirely incorrect. [10]

We can start by solving for the Fermi energy of a fermi gas, which is equal to the chemical potential when the temperature is zero. [10] This energy serves as the external chemical potential, and allows us to solve for the properties of the gas by setting the total chemical potential equal everywhere, and solving for the internal chemical potential, which we can relate to the concentration. [10]

Find the chemical potential of an ideal monatomic gas in two dimensions, with $$N$$ atoms confined to a square of area $$AL^2$$. [10]

Use the ideal gas law to calculate pressure change, temperature change, volume change, or the number of molecules or moles in a given volume. [17] The ideal gas law can be derived from basic principles, but was originally deduced from experimental measurements of Charles? law (that volume occupied by a gas is proportional to temperature at a fixed pressure) and from Boyle?s law (that for a fixed temperature, the product is a constant). [17] The ideal gas law may be used to more accurately determine surface temperatures of planets with thick atmospheres than the S-B black body law, if a density term is added; and if kg/m is used for density instead of gms/m, the volume term V may be dropped. [14] The atmosphere will adjust to that temperature by changing it’s volume and density, and the ideal gas law equation will balance. [14] You could still use his Equation 5 version of the Ideal Gas Law to calculate the temperature from the other variables, regardless of whether or not the atmosphere is heated by nuclear reactors. [14]

The “other? 33 Kelvin cannot be provided by the greenhouse effect, because if it was, the molar mass version of the ideal gas law could not then work to accurately calculate planetary temperatures, as it clearly does here. [14] The variables of density and temperature and mean near-surface atmospheric molar mass would simply readjust to the new reality and the Ideal Gas Law would still be satisfied. [14] Holmes says that if you know the pressure and molar density, then temperature is accurately “modeled” by the ideal gas law. [14] From that height, say 10 km, down to the surface, the temperature rises according to the ideal gas law, giving us the “greenhouse effect”. [14] Ok Venus, it doesn’t work, the CO2 at the surface is supercritical and the Ideal Gas Law equation of state doesn’t apply. [14] At earth conditions, the ideal gas law is a very accurate equation of state. [14]

In the ideal gas model, the volume occupied by its atoms and molecules is a negligible fraction of The ideal gas law describes the behavior of real gases under most conditions. (Note, for example, that is the total number of atoms and molecules, independent of the type of gas.) [17] I’ll just use $$N$$ for the number of each gas type. \ We can rewrite this to look like a single ideal gas with the geometric mean of the two $$n_Q$$ s, with twice the volume and number: \ So the total initial entropy would be just twice the individual entropy if the two gasses had the same mass. [10]

The cylinder contains an ideal gas of atoms of mass $$M$$ at temperature $$T$$. [10] The ideal gas law is generally valid at temperatures well above the boiling temperature. [17] If this paper was correct then the temperature of the earth would remain at 33K since that is apparently what the ideal gas law would predict. [14] Whether the planet is warmed by the sun or by internal radioactivity or whether the warming is increased by GHGs is NOT determinable from the fact that the atmospheres obey the Ideal Gas Law. [14] Planetary atmospheres generally obey the Ideal Gas Law, duh, why wouldn’t they ? and no, that doesn?t mean that you can diagnose or rule out heating processes simply because the atmosphere obeys the Ideal Gas Law. [14] Your claim, that because atmospheres follow the Ideal Gas Law that THEREFORE the effect of CO2 is vanishingly small doesn’t pass the laugh test. [14] As I understand the theory and Willis’ argument, the Ideal gas law would be upheld REGARDLESS of whether or not Green House Gas heating is real, because if it is happening the warmer atmosphere expands and rebalances the equation. [14] All that Robert Holmes has shown is that the atmospheres of various planets obey, to a good approximation, the Ideal Gas Law. [14] What? In fact, it would be a huge shock if planetary atmospheres did NOT generally obey the Ideal Gas Law. [14] The planet would assuredly get warmer ? but the atmosphere wouldn?t stop obeying the Ideal Gas Law. [14] Atmospheres follow both the Boltzmann curve AND the ideal gas law. [14] State the ideal gas law in terms of molecules and in terms of moles. [17] How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large typically is. [17] The Ideal Gas Law is upheld regardless of where the heat comes from. [14] Small groups Solve for the heat capacity at constant pressure of the ideal gas Answer \ This one requires one (small) step more. [10] Small groups Solve for the heat capacity at constant volume of the ideal gas Answer \ This one is relatively easy. [10] Your thought experiment of adding a bunch of nuclear reactors to create heat doesn’t really address the same claim (at least as I understand it) yes the gases would be hotter, and yes they would adjust to still be a nearly ideal gas, but having greenhouse gases or not would make no difference to the eventual equilibrium. [14] Ideal gas law does give T out if put among others, density and pressure in. [14] We define the universal gas constant and obtain the ideal gas law in terms of moles. [17] Over at the Notrickszone, there’s much buzz over a new paper entitled Molar Mass Version of the Ideal Gas Law Points to a Very Low Climate Sensitivity, by Robert Holmes. [14] This formula then may be known as the molar mass version of the ideal gas law. [14] Note that the first term is just what we get from the ideal gas law. [10] The formula used is the molar version of the ideal gas law. [14] The engine itself (our ideal gas in this case) returns to its original state after one cycle, so it doesn’t have any changes. [10] “and no, that doesn?t mean that you can diagnose or rule out heating processes simply because the atmosphere obeys the Ideal Gas Law.” [14] One-dimensional gas (K&K 3.11) Consider an ideal gas of $$N$$ particles, each of mass $$M$$, confined to a one-dimensional line of length $$L$$. [10] It looks shockingly like the entropy of a 3D ideal gas, right down to the quantum length scale (which is no longer a quantum density), commonly called the “thermal de Broglie wavelength.” [10]

This chapter covers the following topics: kinetic and potential energy, chemical and thermal energy, energy units, het and work and their interconversion,temperature and its meaning, measuring temperature, temperature scales,absolute temperature, heat capacity, specific heat. [18] Without convection, heat conduction will make the temperature of the atmosphere uniform more than molecules gaining/losing potential energy as a result of losing/gaining altitude will make the lower atmosphere warmer and the upper atmosphere colder. [14] The source of the energy is the SUN. The heat energy from the sun is converted into the potential energy of mass when it goes up, rises by e.g. water molecules in rising air. [14] All that potential energy returns as kinetic energy (heat) when air descends and recompresses along the density gradient. [14] The total heat capacity is the sum of contributions from the kinetic energy and from the potential energy. [10] The kinetic energy has only half the magnitude of the potential energy and works against it; the total bond energy is their sum. [18] Performance of work involves a transformation of energy ; thus when a book drops to the floor, gravitational work is done (a mass moves through a gravitational potential difference), and the potential energy the book had before it was dropped is converted into kinetic energy which is ultimately dispersed as thermal energy. [18] The potential energy of a mass does not have a temperature, the mass only has energy by virtue of its place (height above a datum). [14] If we have two solids of equal mass held at the same height above the surface of the Earth, even if one mass is cold and one mass is hot, they both have the same potential energy. [14] Isn’t the potential gravitational energy a function of proximity to the source, especially for the distances being discussed here? Surely there is less gravitational potential energy for molecules in the stratosphere than there is for molecules in the troposphere or at the surface. [14] It?s actually the other way around, RW: the higher the molecule is above the planet?s surface, the greater is its gravitational potential energy. [14] This potential energy decrease is sufficient to enable H 2 + to exist as a discrete molecule which we can represent as + in order to explicitly depict the chemical bond that joins the two atoms. [18] The intramolecular potential energy of the inserted molecule may cause the kinetic energy of the molecule to quickly increase or decrease after insertion. [16] When that molecule falls, that gravitational potential energy is converted back into kinetic energy. [14] At this stage is is worth motivating the virial theorem from mechanics, which basically says that the magnitude of the average potential energy of a bound system (which is bound by a power law force) is about the same as the average of its kinetic energy. [10] Sure, it can ‘generate’ potential energy for something (in this case air), but that’s only turned into kinetic energy by falling toward it. [14] Since the planet has gravity, this rising air is merely converting kinetic energy into gravitational potential energy. [14] Air moving upward against gravity trades kinetic energy (speed) for potential energy. [14] This fall causes the descending upper air to loose potential energy and to thereby gain heat by adiabatic auto compression so maintaining the observed lapse rate in the tropospheric winter air above the South Pole. [14] Ah so once air is convected into the upper atmosphere it has no gravitational potential energy. [14] For locations inside a planet?s atmosphere, a molecule?s gravitational potential energy can be calculated as the simple product of the molecule?s mass (m), the acceleration due to gravity (g) and its altitude or “height” (h) above a baseline referent (normally sea level); i.e. mgh. [14] Any mass rising vertically upwards in a gravitational field is slowed down by the force of gravity, the mass loses kinetics but it gains potential energy as it rises. [14] If an object of mass m is raised off the floor to a height h, its potential energy increases by mgh, where g is a proportionality constant known as the acceleration of gravity. [18] We can distinguish between external chemical potential, which is basically ordinary potential energy, and internal chemical potential, which is the chemical potential that we compute as a property of a material. [10] At the instant it strikes the surface, the potential energy you gave supplied to the book has now been entirely converted into kinetic energy. [18] This makes sense in that the thing that is holding a bound state together is the potential energy, while the thing that is pulling it apart is the kinetic energy. [10] Now let the object fall; as it accelerates in the earth’s gravitational field, its potential energy changes into kinetic energy. [18] We will consider just one atom, but now with gravitational potential energy as well as kinetic energy. [10] If energy is then used to get further away, that’s the kinetic energy returned to potential energy, rinse & repeat. [14] For that energy to be included in the total potential energy of the system (the quantity used when performing GCMC exchange and MC moves), you MUST enable the fix_modify energy option for that fix. [16] The full_energy option means that the fix calculates the total potential energy of the entire simulated system, instead of just the energy of the part that is changed. [16] The exponential is going to be very close to one, and we can use a power series approximation for it. \ The first term is our equipartition term: $$\frac12kT$$ each for the kinetic and potential energy. [10] As the body rises away from the surface it will slow down and lose velocity as its distance away from the planet increases and therefore its potential energy increases. [14]

POSSIBLY USEFUL

Since Δ U isolated system 0, ΔU system -ΔU surroundings and energy is conserved. [4] If ?U is negative for a few days, then the body metabolizes its own fat to maintain body temperature and do work that takes energy from the body. [5] Not the answer you’re looking for? Browse other questions tagged thermodynamics energy pressure temperature ideal-gas or ask your own question. [3] The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system. [5] The first law of thermodynamics is a version of the law of conservation of energy, specialized for thermodynamical systems. [5] The 1st law of thermodynamics explains human metabolism: the conversion of food into energy that is used by the body to perform activities. [5] The law of conservation of energy can be stated like this: The energy of an isolated system is constant. [5] When the volume is reduced the average interparticle distance is reduced, and therefore, because of the presence of $U$, the energy will change even if $T$ is kept constant. [3] From a combination of the first and second laws of thermodynamics, we find that we an express the change in internal energy per mole between any two closely neighboring thermodynamic equilibrium states of a single phase fluid of constant composition (including non-ideal gases) by the equation: $$dUC_vdT-\left dV$$where V is the molar volume. [3] The 1st law of thermodynamics states that internal energy change of a system equals net heat transfer minus net work done by the system. [5] Internal Energy : The first law of thermodynamics is the conservation-of-energy principle stated for a system where heat and work are the methods of transferring energy for a system in thermal equilibrium. [5] According to the first law of thermodynamics, heat transferred to a system can be either converted to internal energy or used to do work to the environment. [5]

To a first approximation, the can will not expand, and the only change will be that the gas gains internal energy, as evidenced by its increase in temperature and pressure. [5] For an ideal, the product of pressure and volume (PV) is a constant if the gas is kept at isothermal conditions. (This is historically called Boyle’s law. ) However, the cases where the product PV is an exponential term, does not comply. [5] Isobaric process is one in which a gas does work at constant pressure, while an isochoric process is one in which volume is kept constant. [5] If a gas is to expand at a constant pressure, heat should be transferred into the system at a certain rate. [5] An isobaric expansion of a gas requires heat transfer to keep the pressure constant. [5]

Work Done by Gas During Expansion : The blue area represents “work” done by the gas during expansion for this isothermal change. [5]

If we are interested in how heat transfer is converted into work, then the conservation of energy principle is important. [5] Anabolism uses up the energy produced by the catabolic break down of your food to create molecules more useful to your body. [5] The body stores fat or metabolizes it only if energy intake changes for a period of several days. [5]

Therefore, from the first law, $\Delta E0$: the energy is unchanged. [3] Considering the body as the system of interest, we can use the first law to examine heat transfer, doing work, and internal energy in activities ranging from sleep to heavy exercise. [5] Heat transferred out of the body (Q) and work done by the body (W) remove internal energy, while food intake replaces it. (Food intake may be considered as work done on the body. ) (b) Plants convert part of the radiant heat transfer in sunlight to stored chemical energy, a process called photosynthesis. [5] Our body loses internal energy, and there are three places this internal energy can go–to heat transfer, to doing work, and to stored fat (a tiny fraction also goes to cell repair and growth). [5] As shown in Fig 1 heat transfer and doing work take internal energy out of the body, and then food puts it back. [5]

It is usually formulated by stating that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, minus the amount of work done by the system on its surroundings. [5] An isolated system cannot exchange heat or work with its surroundings making the change in internal energy equal to zero. [4] Here ?U is the change in internal energy U of the system, Q is the net heat transferred into the system, and W is the net work done by the system. [5]

The internal energy of a system is identified with the random, disordered motion of molecules; the total (internal) energy in a system includes potential and kinetic energy. [4] For many systems, if the temperature is held constant, the internal energy of the system also is constant. [5] If you eat just the right amount of food, then your average internal energy remains constant. [5]

Therefore, no matter how much you decrease the volume of the box: since they don’t interact, the energy will remain the same if the temperature (average kinetic energy) is unchanged. [3]

?UQ?W. Note also that if more heat transfer into the system occurs than work done, the difference is stored as internal energy. [5] There are three places this internal energy can go–to heat transfer, to doing work, and to stored fat. [5]

An isothermal process is a change of a system, in which the temperature remains constant: ?T 0. [5] The distribution is valid for atoms or molecules constituting ideal gases. [19]

Work done on a gas results in an increase in its energy, increasing pressure and/or temperature, or decreasing volume. [6] The gas constant is equivalent to the Boltzmann constant, just expressed in units of energy per temperature per mole, while the Boltzmann constant is given in terms of energy per temperature per particle. [12] When we cause a solid to melt into a liquid, or liquid to boil into a gas, we’ve added energy to the system through heat. [13] The energy can be changed when the gas is doing work as it expands–something we explore in Heat and Heat Transfer Methods –similar to what occurs in gasoline or steam engines and turbines. [6] The temperature of the gas is proportional to the average kinetic energy of the molecules. [11] He developed the concept of the mole, based on the hypothesis that equal volumes of gas, at the same pressure and temperature, contain equal numbers of molecules. [6] The value of the gas constant ‘R’ depends on the units used for pressure, volume and temperature. [12] The motion of atoms and molecules–at temperatures well above the boiling temperature–is fast, such that the gas occupies all of the accessible volume and the expansion of gases is rapid. [6] Because the forces between them are quite weak at these distances, the properties of a gas depend more on the number of atoms per unit volume and on temperature than on the type of atom. [6]

It is important to emphasize that because the greenhouse effect originates in radiative transfer processes in the earth-atmosphere system, the net effect of a greenhouse gas such as CO 2 on the temperature of the atmosphere depends on the altitude and temperature. [8] The temperature of the gas establishes the speed distribution of the molecules of a given gas (1.7a). [8] This emission process depends not only on the concentration of the gas but very sensitively on the temperature since this determines the population of the excited states that emit ( Eq. (A) ). [8] In Figure 13.20, the pressure of one mole of gas is held fixed at 10 5 Pa, while the temperature is varied and the pressure measured. [6] The advantage of f ( T ) is that the plot becomes, per any ambient temperature, always the same, irrespective of the molecular mass m of the individual gas species ( Fig. 9.1(b) ). [8]

Overall, then, there is absorption of infrared terrestrial radiation by the greenhouse gases, collisional deactivation to convert this energy to heat, and emission of infrared radiation but at the lower temperatures characteristic of higher altitudes. [8] This energy goes into increasing the pressure of air inside the tire and increasing the temperature of the pump and the air. [6] Temperature is a measure of the kinetic or movement energy of the particles. [13] This leads to smaller total energy emission out to space compared to what would be the case for a higher temperature. [8] A Maxwell- Boltzmann distribution of thermal energy is imparted on the system for a particular temperature to obtain initial atomic velocities, and then Newton?s equation is evaluated for each time step, usually 1 fsec. [8]

The central peak (Q-branch) corresponds to a pure vibrational transition (? J 0), and the envelope of lines at lower (P-branch) and higher (R-branch) wavenumbers correspond to ? J 1, the spread in these envelopes reflecting the rotational energy dependence E R ? J ( J + 1). [8] Simultaneously there is emission of infrared radiation from the Boltzmann distribution of molecules in excited states, which leads to a negative energy component. [8] Atomic species are more likely to occur high in the atmosphere where molecules encounter photons having sufficient energy to break molecular bonds. [8]

Note that here again I am using the convention in which positive q represents thermal energy transferred in to the system from the environment, and positive w represents positive work done on the system by an external force. [9] Those might be the parts of an engine, but in thermodynamics we’re usually talking about particles that are near to each other so that energy can transfer between them. [13] Whatever it is, the particles contained inside the system have a certain amount of total energy. [13]

X-rays are also generated when the electron beam hits the samples surface and can be converted into voltage in relation to the intensity of their emission by an X-ray microanalyser via the process of energy dispersive X-ray (EDX) analysis, thereby providing detailed quantitative information as to the samples elemental composition ( Fig. 10.3 ). [8]

Since temperature is proportional to the average molecular kinetic energy of a system, constant temperature implies constant internal energy for processes involving ideal gasses. [9] In thermodynamics, temperature is an average property describing a system; however, in this case, it will be useful to extend to each molecule the concept of individual temperature (e.g. cold, mild and hot) according to Eqn (9.4) relating temperature with kinetic energy. [8] In practice, this means that collisions between molecules occur sufficiently frequently to ensure that the internal energy levels are redistributed according to the local kinetic temperature. [8] Heat simply refers to the thermal energy transferred across the system boundary, and internal energy refers to the total energy (kinetic plus potential) of the system. [9] The internal energy of such a system is equal to the sum total of all the kinetic energies and potential energies of all the particles inside it. [13] To be exact, the internal energy of the system is the total of the kinetic or movement energy of the particles and the potential or position energy of the particles. [13]

I should probably mention that in this case that the work done by the system would be perfectly off-set by the heat absorbed by the system, and thus the total change in internal energy ?E would equal zero. [9] In rapid expansion of a natural process the system does work spending its internal energy and cools down. [7]

During a stagnation process, the kinetic energy of a fluid is converted to enthalpy, which results in an increase in the fluid temperature and pressure. [2] To be exact, temperature is the average kinetic energy of the particles in a substance. [13] The above assumes LTE, i.e., that the populations of the vibrational and rotational energy levels are characterized by the same temperature as the mean kinetic energy. [8] Increase in temperature means the increase in internal energy and decrease in temperature means the decrease in internal energy. [7] When you look at the temperature and state of a system, those are two clues that tell you about the internal energy that it contains. [13] Perhaps counter-intuitively, while it?s true that internal energy is a state function, the change in a system?s internal energy is the sum of two path-dependent functions. [9]

That’s because internal energy is a term that is used commonly in thermodynamics. [13]

This increased energy can also be viewed as increased internal kinetic energy, given the gas?s atoms and molecules. [6] This general distribution, known as the Maxwell- Boltzmann distribution, is referred to as an increasing series of small intervals composed of molecules characterized by the same kinetic energy or the same thermal level. [8]

The Maxwell law of molecular velocities f ( v ) is a particular case of the Boltzmann distribution of energy levels, if one equals to ? the kinetic energy E c. [8]

Maxwell introduced this law for the velocities of particles of a fluid ( Maxwell, 1868 ), e.g. a gas or a liquid solution in thermal equilibrium, and gives the probability f ( v ) d v that the velocity v will be found in the infinitesimal range v to v + d v and gives the frequency of occurrence of the specific value v for the chosen velocity component v x, v y, v z per each direction x, y, z. [8] We have calculated the angle at which the gas isotherm issues from the point P 0, Z 1 whose critical value of the compressibility factor is denoted by Z c. [8] In an atmosphere with convective mixing, the various species of gases are well mixed, allowing determination of a specific gas constant for the mixture. [8] This is clearly going to be a function of the concentrations of absorbing gases, their infrared absorption cross sections, the flux of terrestrial radiation, and the total gas pressure, which determines the rate of collisional deactivation. [8] We will primarily use the term molecule in discussing a gas because the term can also be applied to monatomic gases, such as helium. [6] Figure 13.17 Atoms and molecules in a gas are typically widely separated, as shown. [6]

Units for the gas constant vary, depending on other units used in the equation. [12] Some people assume the symbol R is used for the gas constant in honor of the French chemist Henri Victor Regnault, who performed experiments that were first used to determine the constant. [12] Chemistry and physics equations commonly include “R”, which is the symbol for the gas constant, molar gas constant, or universal gas constant. [12] It is the universal gas constant divided by the molar mass (M) of a pure gas or mixture. [12]

In the case of a classical gas, we always consider the three-dimensional volume. [8]

Figure 1.5 shows that a d DL value corresponding to two Debye lengths (i.e., a mean potential volume extending two Debye lengths from each surface) leads to a strict equality of the mean potential model and the Poisson-Boltzmann model in the case of monovalent ions, as long as the diffuse layers from each surface do not interact. [8] If the diffuse layers overlap, a mean potential model applied to the entire pore volume has the tendency to underestimate the mean anion concentration. [8] A much simpler mean potential model (often improperly referred to as a Donnan model) can be used. [8]

The additional degeneracy factor ( J + 1), representing the increased number of states available at higher rotational quantum numbers, ensures that the most probable rotational quantum number is not J 0 but some higher number, and increases with increasing temperature (indicated by the outward displacement of the peaks of the P- and R-branches in Figure 3 ). [8] We know the initial pressure P 0 7 10 5 Pa P 0 7 10 5 Pa, the initial temperature T 0 18 C T 0 18 C, and the final temperature T f 35 C T f 35 C. [6] Therefore, if the volume doubles, the pressure must drop to half its original value, and P f 0. 50 atm. [6]

The stagnation state is indicated by the subscript 0 Isentropic stagnation state: When the stagnation process is reversible as well as adiabatic (i.e., isentropic). [2] Since, on a planetary scale, pressure only depends on atmospheric mass & gravity, the Gas Law essentially represents a single equation with 2 unknowns temperature and air density. [14] Your assertion that ” temperature is determined by the interplay of pressure and density, with some influence from molar mass” is physically INCORRECT. My point is further supported by the fact that your model (which is basically an inverted form of the Gas Law equation) contains NO solar radiation. [14] Both use the gas law and molar mass in the equations and confirm that the atmosphere’s temperature, pressure, and density are primarily governed by the basic physics. [14] A law through which one can arrive at the temperature by the measurement of just three gas parameters, pressure, density and molar mass, for diverse places such as Venus, Earth (anywhere in the troposphere). [14]

If we insulate the box, the temperature of the gas will drop due to the First Law (i.e. energy conservation). [10] Now I’ll put in the density of states. \ Now we can just solve for the Fermi energy! \ This is the energy of the highest occupied orbital in the gas, when the temperature is zero. [10] We have a hot place (where the temperature is $$T_H$$, which has lost energy due to heating our engine as it expanded in step 2), and a cool place at $$T_C$$, which got heated up when we compressed our gas at step 4. [10] The energy can be changed when the gas is doing work as it expands–something we explore in Chapter 14 Heat and Heat Transfer Methods –similar to what occurs in gasoline or steam engines and turbines. [17] That is after all exactly the definition of a greenhouse gas one which can radiate energy in the thermal infrared range of wavelengths (or if you prefer a gas with an emissivity significantly greater than zero at these wavelengths). [14] Energy of a relativistic Fermi gas (Slightly modified from K&K 7.2) For electrons with an energy $$\varepsilon\gg mc^2$$, where $$m$$ is the mass of the electron, the energy is given by $$\varepsilon\approx pc$$ where $$p$$ is the momentum. [10] Entropy, energy, and enthalpy of van der Waals gas (K&K 9.1) In this entire problem, keep results to first order in the van der Waals correction terms $$a$$ and \$b. [10]

Question If we view the liquid and solid here as two separate systems that are in equilibrium with each other, what can you tell me about those two systems? Answer They must be at the same temperature (since they can exchange energy), they must be at the same pressure (since they can exchange volume), and least obvious they must be at the same chemical potential, since they can exchange molecules. [10] If the energy remains the same, merely switching from potential to kinetic and back, how can that affect the temperature? The only way is to add more energy (the sun) or retard cooling (theoretically by ghg). [14] Except for radiant energy that is transmitted through an electromagnetic field, most practical forms of energy we encounter are of two kinds: kinetic and potential. [18]

Specifically, we now have three extensive variables that the internal energy depends on, as well as their derivatives, the temperature, pressure, and chemical potential. [10]

I’ve tried to tell Willis many times that the conduction/convection explanation for the surface temperature enhancement is entirely consistent with his observations and that his observations are themselves a product of the effect of atmospheric pressure on the ocean surface due to the way that surface pressure affects the amount of energy taken up by the phase change from liquid to vapour in evaporation. [14] How can I rationalize this procedure? Two ways: 1) Multiplying all three quantities is the only way to get the units to come out in “joules”. 2) The amount of energy required increases with the mass, the temperature change, and the heat capacity, so all three factors must be multiplied. [18] The heat capacity tells us how many joules of energy it takes to change the temperature of a body by 1 C°. [18] Heat, you will recall, is not something that is “contained within” a body, but is rather a process in which energy enters or leaves a body as the result of a temperature difference. [18] In this case we will involve no external work at all, only energy and entropy flows at three temperatures, since the work done is all generated from heat. [10] No energy loss at the cold junction no heat engine and no work output which in this case means no wind and no water elevated to higher altitude by evaporation and rainfall. [14] The atmosphere is in effect the working fluid of a heat engine converting thermal energy into mechanical work (wind, elevating water to levels above sea level etc). [14] The only way the atmosphere can lose energy at this altitude is by radiation to space but the only components of the atmosphere that can radiate energy at these temperatures (thermal infrared) are the greenhouse gases. [14] I figure the bottom of an atmosphere has a higher temperature than the rest of it because there are more molecules (all of them, being hotter than absolute zero, bounding about with some energy) for my thermometer to interact with, i.e. to experience some energy transfer from. [14] Maintaining convective overturning within an atmosphere suspended off the surface against gravity requires energy, that energy cannot be radiated to space if convection is to continue and that energy causes a surface temperature rise above that predicted by the S-B equation. [14] Surface temperature of the sun (K&K 4.2) The value of the total radiant energy flux density at the Earth from the Sun normal to the incident rays is called the solar constant of the Earth. [10] Convection is a process by which air rises vertically upward, specifically for this case air that has been warmed by contact with an illuminated surface that is converting solar energy to heat. [14] In the tropics, the water vapor level at the surface has far more stored energy in latent heat of evaporation, than the deserts do, why they cool so much at night, this effect is enabled by air temps nearing dew point, and desert dew points are so low, and then when it gets there there isn’t a lot of wv available to condense, in the tropics, it’s never ending. [14] There is nowhere for that energy to go it would heat the surrounding air which would make it too hot for the water vapour to condense in the first place. [14] The specific heat of water is 4.18 1J K -1 g -1 and its temperature increased by 3.0 C°, indicating that it absorbed (10 g)(3 K)(4.18 J K -1 g -1 ) 125 J of energy. [18] Jer0me you are confusing heat with temperature; heat is energy, temperature is the effect heat has on a mass under specific conditions. [14] If an object such as a mass of air can become non-uniform in temperature from mere thermal agitation, this means thermal agitation causing a source of usable energy (a temperature difference), and I don’t buy that. [14] As we saw before (when working with the radiation pressure of a vacuum?) the pressure is given by the thermal average value of the derivative of the energy eigenvalues. \ The usual challenge here is that fixed temperature is not the same thing as fixed entropy. [10] When a warmer body is brought into contact with a cooler body, thermal energy flows from the warmer one to the cooler until their two temperatures are identical. [18] You can think of temperature as an expression of the “intensity” with which the thermal energy in a body manifests itself in terms of chaotic, microscopic molecular motion. [18] At the end, both samples of water will have been warmed to the same temperature and will contain the same increased quantity of thermal energy. [18] Everyone knows that a much larger amount of energy is required to bring about a 10-C° change in the temperature of 1 L of water compared to 10 mL of water. [18] It will be so huge that we can treat it using classical thermodynamics, i.e. we can conclude that the above equation applies, and we can assume that the temperature of this huge system is unaffected by the small change in energy that could happen due to differences in the small system. [10] The greater the value of C, the the smaller will be the effect of a given energy change on the temperature. [18] This energy supplements losses from the surface which are driving lower temperatures, driving WV to condense, it’s just more energy is released that it takes to cool that molecule that same amount if it didn’t have to condense to cool. [14] Chem1 energy heat and temperature (Part 3 of 6 lessons on Essential background ) introduces the fundamentals of chemical energetics for a course in General Chemistry. [18] Because this effect is a temperature effect, and the energy barrier of all that stored latent heat that has to be radiated to cool. [14] They will ALSO do this if GHG’s increase global temperature by slowing the rate of energy (heat) release. [14] Molecules are vehicles both for storing and transporting energy, and the means of converting it from one form to another when the formation, breaking, or rearrangement of the chemical bonds within them is accompanied by the uptake or release of energy, most commonly in the form of heat. [18] If it is claimed that CO2 by absorbing infrared photons and then giving the energy to Nitrogen and Oxygen molecules in collisions heats the atmosphere then CO2 will actually reduce convection lowering the tropopause. [14] An dense atmosphere contains more heat, ie, it takes the same energy transfer longer to warm it up. [14] Work is the transfer of energy by any process other than heat. [18] Equalizes when systems are in contact. ( intensive ) Energy Challenging. measure work and heat (e.g. by measuring power into resistor). ( extensive ) \ Entropy ( extensive ) Measure heat for a quasistatic process and find \ Derivatives Measure changes of one thing as the other changes, with the right stuff held fixed. [10] It’s a little annoying to do it this way, because I could have just used energy conservation and the fact that my system is a cycle to say that the total work must be equal and opposite to the total heat. [10] A heat engine has taken in energy as heat and used a portion of it to do work. [20] A transfer of energy to or from a system by any means other than heat is called work. [18] Energy is measured in terms of its ability to perform work or to transfer heat. [18] You can think of heat and work as just different ways of accomplishing the same thing: the transfer of energy from one place or object to another. [18] Chapter 8 covers heat and work, which you learned about during Energy and Entropy. [10] Energy conservation tells us that \ where I’ve taken the usual convention (for this kind of problem) where all signs are positive, so $$Q_C$$ is the magnitude of heat drawn from the inside, $$W$$ is the work done, and $$Q_H$$ is the amount of heat dumped in the room. [10] The energy inputs to the heat pump are our work $$W$$ and the heat from the cool side $$Q_C$$. [10] Heat and work are both measured in energy units, but they do not constitute energy itself. [18] Heat and work are best thought of as processes by which energy is exchanged, rather than as energy itself. [18]

Pressure tells us how the energy changes when we change the volume, i.e. how much work is done. [10] You might want a dimension check: work (which is an energy) is $$dW pdV$$ which will remind you that pressure is energy per volume. [10] Small groups Work out (or write down) the energy eigenstates for a particle confined to a cubical volume with side length $$L$$. [10] Now to find the amount of work we had to do, we just need to use energy conservation (i.e. the First Law). [10] Because the second derivative of the entropy is always negative, the first derivative is monotonic, which means that the temperature (which is positive) will always increase if you increase the energy of the system and vice versa. [10] To find the entropy at temperature $$T$$ we need first to consider the energy eigenstates of this system. [10] For this reason, we also like to define other properties of electrons at the Fermi energy: momentum, velocity (technically speed, but it is called Fermi velocity), and even “temperature”. \ The text contains a table of properties of metals at the Fermi energy for a number of simple metals. [10] The only source of energy that can maintain the higher air temperatures at 4m and above is the heating of descending air from aloft by tropospheric adiabatic auto compression. [14] If we allow the temperature to be negative, then higher energy states will be more probable than lower energy states. [10] These latter two forms of thermal energy are not really “chaotic” and do not contribute to the temperature. [18] Temperature, by contrast, is not a measure of quantity; being an intensive property, it is more of a “quality” that describes the “intensity” with which thermal energy manifests itself. [18] This is the major form of thermal energy under ordinary conditions, but molecules can also undergo other kinds of motion, namely rotations and internal vibrations. [18] An internal combustion engine converts the chemical energy stored in the chemical bonds of its fuel into thermal energy. [18] The reactants H 2 and O 2 contain more energy in its chemical bonds than does H 2 O, so when they combine, the excess energy is liberated, given off in the form of thermal energy, or “heat”. [18] When two bodies are placed in thermal contact and energy flows from the warmer body to the cooler one,we call the process heat. [18] Heat is the quantity of thermal energy that enters or leaves a body. [18] The warmer body loses a quantity of thermal energy Δ E, and the cooler body acquires the same amount of energy. [18] Just because there are greenhouse gases. i.e. gases which can radiate energy in the thermal infrared range of wavelengths, and which are necessary to cool the earth, it doesn’t mean that the supposed greenhouse effect of 33degC is real far from it. [14] It would mean that the pressure at each level of the atmosphere makes no difference whatsoever, so that the surface temp under 19,000 pounds/square yard, receiving energy from the sun as well as from the surface heating, would be exactly the same as the temp under 500 pounds/square yard pressure much higher up. [14] The atmospheric cycle is driven by energy input at the surface (from sunlight absorbed by Earths surface and from there coupled to the atmosphere) plus energy loss at the tropopause to space by green house gases. [14] If most of the heat were transfer within the atmosphere were to take place via radiation and the timescales of heat transfer were too short for conduction to be the primary mechanism for heat distribution, you’d have a clear energy difference between infrared active gases and non active gases. [14] This warmed surface transfers energy to the atmosphere that releases this energy eventually to space. [14] Energy loss to space is by radiation from the surface (atmospheric window) and the atmosphere. [14] Since air is a very poor conductor of heat the amount of cooling of the air above would be minimal and the air above would not descend since by definition it would have to be hotter than the air below if it was to cool pass energy to the surface). [14] There is no insolation at the South Pole in winter and so no radiant energy to heat the ice surface and cause buoyancy driven atmospheric convection. [14] It’s purely the inputs/outputs that change that and not some mythical heat pump pumping energy from space down to the ground. [14] Now we can do a change of variables into an energy variable: \ And now putting all these things into our integral we find \ And now our integral is in a form where we can finally make use of the delta function! If we had not transformed it in this way (as I suspect is a common error), we would get something with incorrect dimensions! $$\ddot\frown$$ \ And that is the density of states for a non-relativistic particle in 3 dimensions. [10] Kittel gives a method for finding the density of states which involves first integrating to find the number of states under a given energy $$\varepsilon$$, and then taking a derivative of that. [10] The density of states is the number of orbitals per unit energy at a given energy. [10] This is just the probability of the state being at energy $$\epsilon$$, which is \ The average number in this state is equal to the probability. [10] This provides our stepping stone to go from a microcanonical picture where all possible microstates have the same energy (and equal probability) to a canonical picture where all energies are possible and the probability of a given microstate being observed depends on the energy of that state. [10] This makes it sharply peaked, provided $$kT\ll \varepsilon_F$$, which can justify evaluating the density of states at the Fermi energy. [10] To find the energy, of course, we need the Fermi-Dirac function times the density of states. [10] The net energy flux density in vacuum between the two planes is $$J_U\sigma_B\left(T_h^4-T_c^4\right)$$, where $$\sigma_B$$ is the Stefan-Boltzmann constant used in (26). [10] When the mol keyword is used, the full_energy option also includes the intramolecular energy of inserted and deleted molecules, whereas this energy is not included when full_energy is not used. [16] If this is not desired, the intra_energy keyword can be used to define an amount of energy that is subtracted from the final energy when a molecule is inserted, and subtracted from the initial energy when a molecule is deleted. [16] For molecules that have a non-zero intramolecular energy, this will ensure roughly the same behavior whether or not the full_energy option is used. [16] Changing pressure alters the amount of energy needed to break the bond between water molecules. [14] Atoms and molecules are the principal actors-out of thermal energy, but they possess other kinds of energy as well that play a major role in chemistry. [18] Hang on a minute. I thought the back radiation downwards from the CO2 molecules was trillions of little ping pong ball like photons and that these photons carried energy and when they pinged into the surface of the earth that energy was given up and the molecules of the earth were heated up. [14] The chemical bonds in the glucose molecules store the energy that fuels our bodies. [18] By convention, the energy content of the chemical elements in their natural state (H 2 and O 2 in this example) are defined as “zero”. [18] Quantum concentration (K&K 3.8) We need to start by finding the formula for the ground state energy of a particle in a box. [10] Consider a system that may be unoccupied with energy zero, or occupied by one particle in either of two states, one of energy zero and one of energy $$\varepsilon$$. [10] Why does this bosonic system look like a simple harmonic oscillator? Since the particles are non-interacting, we have the same set of energy eigenvalues, which is to say an equally spaced series of states. [10] Quantum mechanically, the wave function for the entire state with $$N$$ atoms will separate and will be a product of states \ and the energy will just be a sum of different energies. [10] For other systems, of course, this will not be the case, but this will be true for any system in which the energy states are symmetrically arranged around zero. [10] It turns out that in many cases (particularly for solids) we can represent a given excited state of the many-body system as a sum of the energy of a bunch of non-interacting quasiparticles. [10] By default, this option is off, in which case only partial energies are computed to determine the energy difference due to the proposed change. [16] Fortunately, this is pretty easy to resolve: permuting the labels doesn’t change the energy, so we have a largish degenerate subspace in which to work. [10] Although work can be completely converted into thermal energy, complete conversion of thermal energy into work is impossible. [18] Energy fluctuations (K&K 3.4) Consider a system of fixed volume in thermal contact with a resevoir. [10] Boltzmann, of course, did not know this, and assumed that there were an infinite number of microstates possible within any energy range, and would strictly speaking interpret $$g(E)$$ in terms of a volume of phase space. [10] Let’s consider how we maximize entropy when we allow not just microstates with different energy, but also microstates with different number of particles. [10] We want to solve this purely classically, since we don’t know how to solve the energy eigenvalue equation with interactions between particles included. [10] We can say that 100 g of hot water contains more energy ( not heat !) than 100g of cold water. [18] When you warm up your cup of tea by allowing it to absorb 1000 J of heat from the stove, you can say that the water has acquired 1000 J of energy — but not of heat. [18] Nigil, Water vapor regulates how how cold the surface gets late at night by converting WV to water and using the stored energy to supplement about 35W/m^2 at this site in Aus. [14] Simplified: solar energy is thermalized in the surface (mostly water). [14] The intimate connection between matter and energy has been a source of wonder and speculation from the most primitive times; it is no accident that fire was considered one of the four basic elements (along with earth, air, and water) as early as the fifth century BCE. [18] I’m thinking that gravity is doing something to the air mass in such a way that the Sun’s energy is used a certain way. [14] The total system energy before and after the proposed GCMC exchange or MC move is then used in the Metropolis criterion to determine whether or not to accept the proposed change. [16] Let us now examine the multiplicity of our combined system, making $$B$$ be our large system: \ We can further find the probability of any particular energy being observed from \ where we are counting how many microstatesstates of the combined system have this particular energy in system $$A$$, and dividing by the total number of microstates of the combined system to create a probability. [10] We must hold the total probability to 1, and we must fix the mean energy to be $$U$$. [10] Gravity provides the means by which energy can be extracted from the higher mass. [14] You could have assumed a uniform mass density, and then argued that the actual energy must be of a similar order of magnitude. [10] If we define the velocity as $$c\hat k$$ where $$c$$ is the speed of light and $$\hat k$$ is its direction, the power flux (or intensity) in the $$\hat z$$ direction will be given by the energy density times the average value of the positive $$\hat z$$ component of the velocity. [10] There are continually fluctuations going on, as energy is going back and forth between your system and the environment, and the process of measurement (which is slow) will end up measuring the average. [10] Since this whole process is adiabatic the trip itself does nothing to the energy balance of the atmosphere. [14]

You will recall from earlier science courses that energy can take many forms: mechanical, chemical, electrical, radiation (light), and thermal. [18] Find an expression for the thermal average energy of the system. [10] This is the problem with using averages for somethings, remember in this case, we get a much larger burst of energy for part of the day, and then it decays. [14] In the case of the water mill we are using gravity to extract energy from, ultimately, the Sun. [14]

Solar energy provides the energy to lift the air in the first place. [14] Our Gibbs sum will just have this one additional term in it. \ The separation now comes about because we can now separate the first orbital from the second, and the energy and number are both the sum of value for the first orbital plus the value for the second orbital. [10] The above assumes that $$g(E)$$ is a differentiable function, which means that the number of microstates must be a continuous function of energy! This highlights one of the distinctions between the microcanonical approach and our previous (cannonical) Gibbs approach. [10]

This is a bit of a contradiction you’ll need to get used to: we treat our systems as non-interacting, but assume there is some energy transfer between them. [10] Do we really need a greenhouse effect to determine the temperature of an atmosphere? One thing that GHGs do is absorb surface radiation and transfer that energy to the atmosphere as kinetic energy. [14] Convection will always run at a rate that ensures the surface is at the required temperature to both radiate to space at the same rate as radiation comes in from space AND leaves enough additional surface kinetic energy (heat) to keep the atmosphere suspended in hydrostatic equilibrium against the downward force of gravity. [14] Gravity causes the basic lapse rate by distributing the energies of the molecules that make up the atmosphere in such a way that the faster-moving molecules will tend to be located towards the bottom and the slower-moving ones will tend to be located towards the top. Since temperature corresponds with average kinetic energy, this implies that a temperature-gradient corresponding with altitude, or a “lapse rate” in other words, is created in the atmosphere. [14] Temperature is a measure of the average kinetic energy of the molecules within the water. [18] Then they can describe what happens if you squeeze more molecules to that volume of gas all with the same average kinetic energy because that volume is at sea level rather than above sea level. [14] For instance, when defining a macrostate of a given gas or liquid, we could specify the internal energy, the number of molecules (or equivalently mass), and the volume. [10] Small groups Solve for the internal energy at zero temperature of a Fermi gas. [10] An irreversible expansion into vacuum will do no work (since it moves nothing other than the gas itself), which means that it will not change the internal energy (unless energy is transfered by heating). [10] Gas surrounding this surface collides with the surface and heat is converted into kinetic energy in the gas. [14] The convection due to the small (very small) amount of ‘heat’ from an IR photon being ‘absorbed’ then that energy passed as kinetic energy to nitrogen and oxygen molecules is unlikely to cause those larger gas molecules to convect in a way sufficient to measurably ‘raise the tropopause’ in the way that the storms formed by th powerful hydrologic cycle do. [14] The kinetic energy of the electrons is the $$U$$ of the Fermi gas, which in class we showed to be \ where $$m$$ is the mass of the electron. [10]

This method requires a gas constant and the knowledge of only three gas parameters; the average near-surface atmospheric pressure, the average near surface atmospheric density and the average mean molar mass of the near-surface atmosphere. [14] In effect Helium gas escapes from the Earth because the temperatures found in the Earth?s upper atmosphere are too high for the mass of our planet to retain this low molecular weight (and therefore high average velocity) gas. [14] Maxwell starts by saying (page 300, para. 2) that vertical columns of gas in thermal equlibrium have equal temperature throughout but then states (p 300, para. 5) ‘This result is by no means applicable to the case of our atmosphere. [14] The motion of atoms and molecules (at temperatures well above the boiling temperature) is fast, such that the gas occupies all of the accessible volume and the expansion of gases is rapid. [17] If you were to replace the vacuum tube inside a thermos with three gases (CO2, H2O, N2) which one would cause the thermos to lose heat fastest at temperatures where none of the gases would condense? The non conductive and non infrared active gas or one of the infrared active but conductive gases? My money would be on H2O, the most conductive gas. [14] If you know the pressure and molar density, the temperature is specified whether the gas is ideal or not. [14] Ideal or not, it takes only two variables to completely describe the thermodynamic state of a gas. [14]

Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be and atmospheric pressure. [17] Its major difference happens because of the difference between a gas and a liquid, which means that there is no temperature low enough that there will not be a gas in equilibirum with a solid at low pressure. [10] Where is the solar heating in your equation? In other words, what controls the air density in your model? In the real atmosphere, gas volume (thus density) is controlled by pressure and solar heating. [14] If gas is at 1 atm pressure it will warm up to be over 100 C. And if air is half density at Earth sea level pressure, it will be cooler. [14]

At the temperatures of earth’s air, CO2 is not a condensing gas. [14] In a gas of different types of molecules all at the same temperature, the speeds of the heavier molecules will generally be _________ the speeds of the lighter molecules. [20] Solid surfaces are therefore more efficient thermal radiators than gases because it is the process of flexure that determines if a gas molecule can intercept and emit infrared radiation, something that only polyatomic molecules can achieve. [14] We will primarily use the term “molecule” in discussing a gas because the term can also be applied to monatomic gases, such as helium.) [17] M should typically be chosen to be approximately equal to the expected number of gas atoms or molecules of the given type within the simulation cell or region, which will result in roughly one MC move per atom or molecule per MC cycle. [16] Unlike the motion of a massive body such as a baseball or a car that is moving along a defined trajectory, the motions of individual atoms or molecules are random and chaotic, forever changing in magnitude and direction as they collide with each other or (in the case of a gas,) with the walls of the container. [18] This fix cannot be used to perform GCMC insertions of gas atoms or molecules other than the exchanged type, but GCMC deletions, and MC translations, and rotations can be performed on any atom/molecule in the fix group. [16] Every N timesteps the fix attempts both GCMC exchanges (insertions or deletions) and MC moves of gas atoms or molecules. [16] Move and deletion attempt candidates are selected from gas atoms or molecules within the region. [16] Note that very lengthy simulations involving insertions/deletions of billions of gas molecules may run out of atom or molecule IDs and trigger an error, so it is better to run multiple shorter-duration simulations. [16] Atoms and molecules in a gas are typically widely separated, as shown. [17] It would mean the structure and behavior of the gas molecules is not as important as just their mass. [14] For a low mass and therefore low escape velocity planet orbiting close to the heat source of sun, the lighter molecular weight atmospheric gas will more easily achieve escape velocity, even when the heavier atmospheric gas will not and so will be retained. [14] However the heat is mostly transferred from the surface to the gas by radiation (and evaporation for latent heat). [14] Clearly the existing greenhouse gas theory for Earth predicts that E1 will have a much higher (33K?) surface temperature than E2 Because of GHGs. [14] You could surmise that solid surfaces inside the greenhouse are warmed by solar radiation, these solid objects warm the air due to molecular collisions (oh boy look gas IS conductive), and this air then rises and is replaced by cooler air. [14] Adding a greenhouse gas to an atmosphere raises the tropopause. [14] One issue in the outer solar system is atmospheres tending to have methane, which is a greenhouse gas. [14] He links the Poisson Relationship (the Gas Laws) to both experiments and the real atmosphere. [14] More importantly, the gas law relationship really only works for true adiabatic processes when you are talking about compression/expansion cycles. [14] The amount of work in this case is not equal and opposite to the amount of work done when the gas was adiabatically expanded. [10]

Expand a gas to twice its original volume at fixed temperature $$T_H$$. [10] The Fermi gas is more exciting (and more. thermal?) when the temperature is not precisely zero. [10] This animation depicts thermal translational motions of molecules in a gas. [18]

The second term mu_ex is the excess chemical potential due to energetic interactions and is formally zero for the fictitious gas reservoir but is non-zero for interacting systems. [16] How do we find out what the density (or equivalently, volume) of the liquid and solid are? You already know that the pressure, temperature and chemical potential must all be equal when two phases are in coexistence. [10] When you look at the phase diagram in its usual pressure versus temperature representation, you can now think of the lines as representing the points where two chemical potentials are equal (e.g. the chemical potential of water and ice). [10] Conditions for coexistence You should remember that when two phases are in coexistence, their temperatures, pressures, and chemical potentials must be identical, and you should be able to make use of this. [10] Essenhigh RH. Prediction of the standard atmosphere profiles of temperature, pressure, and density with height for the lower atmosphere by solution of the (S? S) integral equations of transfer and evaluation of the potential for profile perturbation by combustion emissions. [14] The gravitational potential is a constant process of compression and expansion based around the average temperature of the atmosphere. [14] If used with the fix nvt command, simulations in the grand canonical ensemble (muVT, constant chemical potential, constant volume, and constant temperature) can be performed. [16] We can once again find the expression we found last week, where \ We can solve for the chemical potential \ Thus it decreases as volume increases or as the temperature increases. [10] Particles spontaneously flow from high chemical potential to low chemical potential, just like heat flows from high temperature to low. [10] To find the heat capacity more carefully, we could set up this integral, noting that the Fermi-Dirac function is the only place where temperature dependence arises: \ where in the last stage I assumed that the chemical potential would not be changing significantly over our (small) temperature range. [10] Derive an expression for the ensemble average occupancy $$\langle N\rangle$$, when the system composed of this orbital is in thermal and diffusive contact with a resevoir at temperature $$T$$ and chemical potential $$\mu$$. [10] What defines a spontaneous change of molecule number? A difference in total chemical potential! So this difference must be zero. [10] Chemical energy refers to the potential and kinetic energy associated with the chemical bonds in a molecule. [18] A molecule rises, trading kinetic energy for gravitational potential. [14]

If an air mass of uniform temperature should become non-uniform in temperature without a net gain or loss of kinetic energy of its molecules, then its entropy would decrease. [14] All molecules at temperatures above absolute zero are in a continual state of motion, and they therefore possess kinetic energy. [18] The Carbon Dioxide molecules will move much more slowly that the Helium atoms do because their greater mass means that the kinetic energy of motion for the CO2 molecule is carried by a particle with 11 times the mass of the Helium atom. [14] In this problem, we showed that the density $$n_Q$$ is basically the same as the density of a single particle that is confined enough that its kinetic energy is the same as the temperature. [10] There will be a value of the concentration for which this zero-point quantum kinetic energy is equal to the temperature $$kT$$. (At this concentration the occupancy of the lowest orbital is of the order of unity; the lowest orbital always has a higher occupancy than any other orbital.) [10]

The First Law tells us that the heat is equal to the change in internal energy, provided no work is done (i.e. holding volume fixed), so \ which is a nice equation, but can be a nuisance because we often don’t know $$U$$ as a function of $$T$$, which is not one of its natural variables. [10] In the latter two cases, we would also invoke the First Law, to argue that the work done to the system must equal the change in internal energy plus the energy added to it by heating. [10]

The internal energy change is thus \ So the system is losing energy (thus doing work) as we adiabatically expand it down to lower temperature. [10] How do we find the heat capacity? We can work out a rough equation for the internal energy change (relative to zero), and then take a derivative. [10] Since the internal energy doesn’t change, the heat and work are opposite. [10]

Since this is an adiabatic process there is no heat transfer, so the only source of energy for that work is the internal energy of the parcel of air. [14]

Answer At high temperatures, $$\beta\hbar\omega \ll 1$$, which means \ So far this doesn’t tell us much, but from it we can quickly tell the high temperature limits of the entropy and internal energy: \ The entropy increases as we increase temperature, as it always must. [10] How do we find the pressure? We need to find the change in internal energy when we change the volume at fixed entropy. [10] Density of states You should remember how to use a density of states together with the above distributions to find properties of a system of noninteracting fermions or bosons \ As special cases of this, you should be able to find $$N$$ (or given $$N$$ find $$\mu$$ ) or the internal energy. [10] If we assume that only states with one particular energy $$E$$ have a non-zero probability of being occupied, then $$UE$$, i.e. the thermodynamic internal energy is the same as the energy of any allowed microstate. [10]

We can find the internal energy and the average quantum number (or number of “phonons”). [10] Small groups Solve for the high-temperature and low-temperature limits of the internal energy and/or the average number of quanta $$\langle n\rangle$$. [10] Thermal averages You should remember that the internal energy is given by a weighted average: \ And similarly for other variables, such as $$N$$ in the grand canonical ensemble. [10]

Most of convectional heating of air, doesn’t involve air masses rising- the average velocity of air molecules increase, and the kinetic energy rises. and also goes the other way when surface cools. [14] The thermal average kinetic energy is independent of height. [10] As the object comes to rest, its kinetic energy appears as heat (in both the object itself and in the table top) as the kinetic energy becomes randomized as thermal energy. [18] The sum total of all of this microscopic-scale randomized kinetic energy within a body is given a special name, thermal energy. [18] Kinetic energy is associated with the motion of an object ; a body with a mass m and moving at a velocity v possesses the kinetic energy mv 2 /2. [18] Show that the order of magnitude of the kinetic energy of the electrons in the ground state is \ where $$m$$ is the mass of an electron and $$M_H$$ is the mas of a proton. [10] Find the kinetic energy of the particle when in the ground state. [10]

We need to check which of these equal pressure states have the same chemical potential. [10] If those two points also have that pressure as their slope, then they have both equal slope and equal chemical potential, and are our two coexisting states. [10]

We’ll do a fair amount of computing of the internal chemical potential this week, but keep in mind that the total chemical potential is what becomes equal in systems that are in equilibrium. [10] The total chemical potential at the top of the atmosphere, is equal to the chemical potential at the bottom. [10] The distinction between internal and external chemical potential allows us to reason about systems like the atmosphere. [10] The internal chemical potential thus only contains effects of concentration, etc. [10] Where the external chemical potential is high (at high altitude), the internal chemical potential must be lower, and there is lower density. [10] We do want to keep in mind that the $$\mu$$ above is the internal chemical potential. [10] Carbon monoxide poisoning The main idea here is that because the oxygen and carbon monoxide are in equilibrium with air, we can determine the activities (or equivalent chemical potential) of the molecules from the air. [10] Any mass of air on the ground can only rise if it is lifted by a force, which can be due to buoyancy difference caused by thermal heating of the air by sunlight or the displacement upwards by a colder more dense air mass coming in from the side (the advection of a cold arctic air mass) that forms the katabatic lifting potential of a cold weather front. [14] Note In general, there is one chemical potential for each kind of particle, thus the word “chemical” in chemical potential. [10] Provided the number of electrons is fixed (as is usual), the chemical potential must shift such that the two areas are equal. [10] While the chemical potential of the reservoir and the simulation cell are equal, mu_ex is not, and as a result, the densities of the two are generally quite different. [16] The chemical potential expands our set of thermodynamic variables, and allows all sorts of nice excitement. [10] This tells us that the density increases as we increase the chemical potential. [10]

The gravitational potential of the atmosphere doesn’t change, ON AVERAGE” ( sorry, no italics). [14] Every time one molecule moves up, another molecule moves down, so gravitational potential can’t change. [14]

Electrical work is done when a body having a certain charge moves through a potential difference. [18]

Heat engines do indeed work (and the real world is closer to adiabatic transitions than isentropic as in the ideal Carnot cycle), but your explanation was simply wrong. [14] This would help them understand the ideal and not-so-ideal laws of thermodynamics that control the atmospheric temperature in the convective troposphere up to radiative dominant altitudes, and help them understand where “lapse rate? comes from. [14]

As manned ships sent to Venus would be able to compensate for differences in temperature to a certain extent, anywhere from about 50 to 54 km or so above the surface would be the easiest altitude in which to base an exploration or colony, where the temperature would be in the crucial “liquid water” range of 273 K (0 C) to 323 K (50 C) and the air pressure the same as habitable regions of Earth.” [14] All these molecules of CO2 are nt acting like a blanket reducing the heat loss, and there is a drop of temperature of 24degC in just 2 meteres (24degC at your feet, 0 degC at your head). [14] Or currently our tropics have average temperature of about 26 C. And at Mars distance, our tropics might be near 0 C in terms of average temperature. [14]

V^2), the average velocity of the particles for each gas in the mixture will be significantly different. [14] Adiabatic autocompression Hypothesis 3 gas law parameters with the IGL and the S-B equation. [14] Vapor pressure equation (David) Consider a phase transformation between either solid or liquid and gas. [10]

Fluctuations in the Fermi gas We are looking here at a single orbital, and asking what is the variance of the occupancy number. \ Now this single orbital has only two possible states: occupied and unoccupied! So we can write this down pretty quickly, using the probability of those two states, which are $$f$$ and $$1-f$$. [10] This number is undeniably large, considering that a gas is mostly empty space. is huge, even in small volumes. [17]

Small groups Solve for the density of states of an electron gas (or of any other spin- $$\frac12$$ gas, which will have the same expression. [10] Density of states for particular systems You need not remember any expression for the density of states e.g. for a gas. [10]

If we think about $$N$$ atoms, we can define an eigenstate according to how many atoms are in state 0, how many are in state 1, etc. This is a combination kind of problem, which we have encountered before. [10]

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