C O N T E N T S:

- This law states that the average amount of energy involved in each different direction of motion of an atom is the same.(More…)
- This law makes it impossible to build a perpetual motion machine – the increase in entropy inevitably derails the system even if energy remains constant.(More…)

- The universe will always become increasingly uniform, that is: heat will spread until the entire universe has the temperature and energy level (in an isolated system heat will always spread from a place where there is a lot of heat to a place where there is less until balance is achieved), forces will continue to work until a universal balance has been achieved.(More…)
- Select one: a. absorb different quantities of thermal energy from their surroundings in equal time intervals. b. have different masses. c. have different volumes. d. have any of the properties listed above e. have any of the properties listed above and one of them is contact with a third body at a different temperature.(More…)

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**KEY TOPICS**

** This law states that the average amount of energy involved in each different direction of motion of an atom is the same.** [1] In so doing, he made clear that the second law is essentially statistical and that a system approaches a state of thermodynamic equilibrium (uniform energy distribution throughout) because equilibrium is overwhelmingly the most probable state of a material system. [1] According to Ohio State University professor Patrick Woodward, the First Law of Thermodynamics “simply states that energy can be neither created nor destroyed (conservation of energy).” [2]

During these investigations Boltzmann worked out the general law for the distribution of energy among the various parts of a system at a specific temperature and derived the theorem of equipartition of energy ( Maxwell-Boltzmann distribution law ). [1] In the cosmological context, a system that obeys the holographic equipartition law behaves as an ordinary macroscopic system that proceeds to an equilibrium state of maximum entropy. [3] Theory of Gases : Equation of state for ideal and non-ideal (van der Waals) gases; Kinetic theory of gases; Maxwell-Boltzmann distribution law; equipartition of energy. [4] If an ideal gas undergoes an adiabatic expansion or compression, the ?rst law of thermodynamics, together with the equation of state, shows that PV ? ? constant (21.18) The Boltzmann distribution law describes the distribution of particles among available energy states. [5]

** This law makes it impossible to build a perpetual motion machine – the increase in entropy inevitably derails the system even if energy remains constant.** [2] The second law of thermodynamics, or the law of increased entropy, says that over time, everything breaks down and tends towards disorder – entropy! Entropy is the amount of UNusable energy in any systems; that system could be the earth’s environment or the universe itself. [2] In the 1870s Boltzmann published a series of papers in which he showed that the second law of thermodynamics, which concerns energy exchange, could be explained by applying the laws of mechanics and the theory of probability to the motions of the atoms. [1] The Second Law of Thermodynamics is essentially a conservation law, like conservation of energy, or momentum, or mass. [2] These resources misrepresent the Second Law of Thermodynamics, ignoring the fact the earth is not an isolated system (energy is added from the sun for example). [2] By the same token, the Second Law can’t be trusted when applied to a system that heat energy is entering or leaving. [2] Look at it like this, because the energy in the universe is finite and no new energy is being added to it (1st law), and because the energy is being used up (2nd law), the universe cannot be infinite. [2] The first law is just a statement that heat is a form of energy, and that energy, whether in the form of heat or not, is conserved. [2]

Our results indicate that log-thermostats fail to maintain a nonequilibrium steady state (stationary temperature gradient) even though the energy of log-oscillators are assigned in the plateau region. [6] We show that log-oscillators fail to serve as thermostats for their incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned. [6] In this final state the universe is one uniform space where nothing happens and no work (moving something) can be done since there are no above average concentrations of energy left. [2] For temperatures below about 60 K, the energies of hydrogen molecules are too low for a collision to bring the rotational state or vibrational state of a molecule from the lowest energy to the second lowest, so the only form of energy is translational kinetic energy, and \(d 3\) or \(C_V 3R/2\) as in a monatomic gas. [7]

When gas molecules collide, they can transfer energy in a manner that leads to the principle of equipartition of energy. [2] The equivalence of the thermodynamical and statistical definitions of entropy is derived by statistical mechanics, and, in particular, the principle of equipartition of energy. [2] Maggi C, et al. Generalized energy equipartition in harmonic oscillators driven by active baths. [6]

SUMMARY+UPDATE: Final conclusion reached is that while total kinetic energy is indeed the one Equipartition theorem gives (and so it’s correct! :D) but the textbook assumes the molecule to be at at very low temperatures (although this is NOT mentioned) implying the rotational and vibrational energies are NOT counted. [8]

We show that this holographic equipartition law effectively implies the maximization of entropy. [3] We consider the standard ? CDM model of the Universe and show that it is consistent with the holographic equipartition law. [3]

The second law of thermodynamics states that entropy increases, so the two are contradictory. [2] Stated in physics terminology, the Second Law states that the entropy of an isolated or closed system never decreases. [2]

This explains why the vibrational energy does not contribute to the molar speci?c heats of molecules at low temperatures. 653 21.5 The Boltzmann Distribution Law The rotational energy levels also are quantized, but their spacing at ordinary temperatures is small compared with k B T. Because the spacing between quantized energy levels is small compared with the available energy, the system behaves in accordance with classical mechanics. [5] The discrepancies between this model and the experimental data at low temperatures are again due to the inadequacy of classical physics in describing the microscopic world. 21.5 THE BOLTZMANN DISTRIBUTION LAW Thus far we have neglected the fact that not all molecules in a gas have the same speed and energy. [5] In general, the number density of molecules having energy E is n V (E ) ? n 0e ?E/k BT Boltzmann distribution law (21.25) This equation is known as the Boltzmann distribution law and is important in describing the statistical mechanics of a large number of molecules. [5] The Newton Laws and the Laws of Thermodynamics imply that all forces are mass-energy interactions (forced displacements with momentum and energy transfer and conservation) between different particulate bodies due to non-equilibrium (available energy or work potential, cause of forcing) towards the equilibrium. [9] Definition of The 2nd Law : The useful-energy (non-equilibrium work potential) cannot be created from within equilibrium alone or otherwise, it only can be transferred between systems (ideally conserved) and irreversibly dissipated towards equilibrium into thermal energy thus generating entropy. [9]

Thirdly, based on the field equations a theorem is proved that relates the energy fluxes of various kinds in the space volume with the laws of conservation of momentum, energy and angular momentum. [10] Historically, the first version of the second law, advanced by Sadi Carnot in 1824, came before the submicroscopic basis of heat and temperature was established, in fact before the first law of thermodynamics (energy conservation) was formulated. [11] In view of this, why does it take the odor of perfume (or other smells) several minutes to travel across the room? P Isotherms 21.2 10.5 MOLAR SPECIFIC HEAT OF AN IDEAL GAS The energy required to raise the temperature of n moles of gas from Ti to Tf depends on the path taken between the initial and ?nal states. [5] It states that the probability of ?nding the molecules in a particular energy state varies exponentially as the negative of the energy divided by kB T. All the molecules would fall into the lowest energy level if the thermal agitation at a temperature T did not excite the molecules to higher energy levels. [5] Collisions between molecules at low temperatures do not provide enough energy to change the vibrational state of the molecule. [5]

Each particular field is relatively independent of the other fields in equilibrium state, when the process of energy exchange between the fields and particles is completed. [10] Solid state Crystals and crystal systems; X-rays; NaCl and KCl structures; close packing; atomic and ionic radii; radius ratio rules; lattice energy; Born-Haber cycle; isomorphism; heat capacity of solids. [4] The ?rst excited state of the hydrogen atom has an energy of 10.2 eV above the lowest energy level, which is called the ground state. [5] Along the constant-pressure path i : f ?, part of the energy transferred in by heat is transferred out by work done by the gas. 648 CHAPTER 21 The Kinetic Theory of Gases the ?rst law to this process, we have ?E int ? Q ? W ? nCP ?T ? P?V (21.15) In this case, the energy added to the gas by heat is channeled as follows: Part of it does external work (that is, it goes into moving a piston), and the remainder increases the internal energy of the gas. [5] Total internal energy of a solid From this result, we ?nd that the molar speci?c heat of a solid at constant volume is CV ? 1 dE int ? 3R n dT (21.22) This result is in agreement with the empirical DuLong – Petit law. [5]

The Second Law provides conditions and limits for process forcing (energy exchange direction and limit). [9] Due to reversible equivalency of all types of (coupled) energy conversions, all different statements of the Second Law (2nd Law) are equivalent. also. and. [9]

According to the equipartition theorem, this corresponds to an average vibrational energy of 6(12 k BT ) ? 3k BT per atom. [5] Classical physics and the equipartition theorem predict an internal energy of E int ? 3N(12 k BT ) ? 2N(12 k BT ) ? 2N(12 k BT ) ? 72 Nk BT ? 72 nRT z y x (a) z y x (b) z y x (c) Figure 21.6 Possible motions of a diatomic molecule: (a) translational motion of the center of mass, (b) rotational motion about the various axes, and (c) vibrational motion along the molecular axis. [5]

A Hint of Energy Quantization The failure of the equipartition theorem to explain such phenomena is due to the inadequacy of classical mechanics applied to molecular systems. [5] Assume that (1) the engine is running at 2 500 rpm, (2) the gauge pressure right before the expansion is 20.0 atm, (3) the volumes of the mixture right before and after the expansion are 50.0 and 400 cm3, respectively (Fig. Section 21.4 The Equipartition of Energy WEB 32. [5] Newton?s second law applied to circular motion states that a force of magnitude equal to m? 2r acts on a particle. (a) Discuss how a gas centrifuge can be used to separate particles of different mass. (b) Show that the density of the particles as a function of r is n(r) ? n 0e mr ? /2k BT 2 2 62. [5] Dalton?s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of gases making up the mixture. [5] It may appear that the created non-equilibrium structures are self-organizing from nowhere, from within an equilibrium (thus violating the 2nd Law), due to the lack of proper observations and “accounting” of all mass-energy flows, the latter maybe in “stealth” form or undetected rate at our state of technology and comprehension (as the science history has though us many times). [9]

What is the rotational kinetic energy of one molecule of Cl2, which has a molar mass of 70.0 g/mol? Cl Cl Figure P21.35 50.0 cm3 400 cm3 Before After Figure P21.31 Section 21.5 The Boltzmann Distribution Law Section 21.6 Distribution of Molecular Speeds 36. [5]

The equipartition theorem and the zeroth law of thermodynamics can both be regarded as consequences of the second law of thermodynamics. [11]

The equipartition theorem is known as the law of equipartition, equipartition of energy. [12] Then the first law of thermodynamics states that the increase in energy is equal to the total heat added plus the work done on the system by its surroundings. [12] R. G. Cai and S. P. Kim, “First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe,” Journal of High Energy Physics, vol. 0502, p. 050, 2005. [13] Moreover we show the existence of an energy cascade, often called the Kolmogorov-Zakharov spectrum, which happens to be not simply a power law, but a logarithmic correction to the Rayleigh-Jeans distribution. [14]

In complete analogy with gas kinetics, particle velocities map to wavepacket k-vectors, collisions are mimicked by four-wave mixing, and entropy principles drive the system towards an equipartition of energy. [14] Equipartition also gives the values of individual components of the energy. [12]

S. Nojiri and S. D. Odintsov, “The new form of the equation of state for dark energy fluid and accelerating universe,” Physics Letters B, vol. 639, no. 3-4, pp. 144-150, 2006. [13] Therefore, if we define the state parameter as, then the condition is covered for sources of positive energy density ( ) only if we have. [13] Such a chain, or path, can be described by certain extensive state variables of the system, namely, its entropy, S, its volume, V. The internal energy, U, is a function of those, sometimes, to that list are appended other extensive state variables, for example electric dipole moment. [12] The internal energy is one of the two cardinal state functions of the variables of a thermodynamic system. [12] Mere substitution leads to a less informative formula, an equation of state, though it is a macroscopic quantity, internal energy can be explained in microscopic terms by two theoretical virtual components. [12] Internal energy – It keeps account of the gains and losses of energy of the system that are due to changes in its internal state. [12] The internal energy of a state of a system cannot be directly measured. [12] The internal energy is a function of a system, because its value depends only on the current state of the system. [12] Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes, the same amount of work is done by the body in decelerating from its current speed to a state of rest. [12]

PHYS 141 (3) Physics I for Engineering Introductory calculus-based course for engineering students: Motion, kinematics, dynamics, Newton’s laws, applications: work, kinetic and potential energy, momentum, rotational dynamics, angular momentum, gravity, oscillations. [15] In a solid, shear stress is a function of strain, a consequence of this behavior is Pascals law which describes the role of pressure in characterizing a fluids state. [12] Statistical mechanics fills this disconnection between the laws of mechanics and the experience of incomplete knowledge, by adding some uncertainty about which state the system is in. [12] The generalized second law of thermodynamics (GSLT) states the total entropy of system ( ), including the horizon entropy ( ) and the entropy of fluid ( ) which supports the geometry, should not decrease or equally it has to respect the condition. [13] It is dimensionally equivalent to impulse, the product of force and time, Newtons second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. [12]

Laws of thermodynamics; Maxwell-Boltzmann distribution; equipartition theorem; black-body radiation. [15] The equipartition theorem can be used to derive the ideal gas law, and it can also be used to predict the properties of stars, even white dwarfs and neutron stars, since it holds even when relativistic effects are considered. [12]

If the containing walls pass neither matter nor energy, the system is said to be isolated, the first law of thermodynamics may be regarded as establishing the existence of the internal energy. [12]

**POSSIBLY USEFUL**

** The universe will always become increasingly uniform, that is: heat will spread until the entire universe has the temperature and energy level (in an isolated system heat will always spread from a place where there is a lot of heat to a place where there is less until balance is achieved), forces will continue to work until a universal balance has been achieved.** [2] If our universe was infinite but was using up a finite supply of energy, it would have suffered ‘heat death’ a long time ago! If the universe was infinite all radioactive atoms would have decayed and the universe would be the same temperature with no hot spots, no bright burning stars. [2] Note that the critical energy E c shifts roughly a constant amount through increasing the simulation time by a factor of 10, which indicates an exponential dependence of the required simulation time on energy. [6] T k increases linearly with E as E > E c, where the critical energy E c is independent of the magnitude of ε. [6] Although there is a linear energy dependence for T k when E > E c, it would be still interesting to learn if the log-oscillator can serve as a thermostat when its energy is appropriately set inside the plateau region (Fig. 1 ). [6] The fitting relation T k 2( E − E c ) simply comes from the energy conservation of the Hamiltonian system. [6] Note that when energy E is small, as shown in the inset of Fig. 1, T k deviates from the value of τ while the virial theorem, i.e., T k P k, is valid in this case as expected. [6] Energy of respective log-oscillators is initially given by ( a ) E − 1 and E + 20; ( b ) E − 40 and E + 80. [6] In our simulations, the energy of the log-oscillators is initially assigned in the low-energy zone of their own plateau region, namely, E − 1 and E + 20. [6] If the energy is set near the plateau region ( E − 40 and E + 80), the log-oscillators can easily gain energy from the system and jump out of the plateau region. [6]

We show that modified log-oscillators cannot serve as thermostats to produce a stationary temperature profile inside the FPU- β system even though the energy of log-oscillators is appropriately assigned. [6] As the integration goes to infinity, it is unrealistic through numerics to conclude that whether the broaden process would stop at some critical energy (similar as the critical temperature given in the section below) or keep ongoing, which requires a solid analytical study. [6]

The measurements could be things like whether a coin came up heads, whether a card in a deck has a certain value, or the energy of a gas molecule. [2] For each quadratic term the contribution to the energy is $kT/2$, for a total of $3kT/2$ per molecule. [8]

Where does the entropy reduction required to offset this come from? The Earth is a giant heat engine, with energy from the Sun falling on the daylight side, and “waste” energy emitted into space from the night side. [2] Our numerical results shows that the FPU system, except the boundary oscillators, reach an energy equilibration after a relaxation time, i.e., heat flow cannot be promoted inside the system. [6] The critical energy increases with the average time in a slow way, with which its infinite-time behavior cannot be concluded by numerics. [6] On a universal scale a tidy room would be a universe which has pockets of above average concentrations of energy (if you – incorrectly – assume relativity Emc this includes matter as well.) [2] The initial energy of each FPU oscillator is randomly prepared around an average energy equal to 8. [6]

He derived an equation for the change of the distribution of energy among atoms due to atomic collisions and laid the foundations of statistical mechanics. [1] The temperature is not specified in your question so in any answer it is necessary to justify removing the vibrational energy. [8] The flow of energy (by heat exchange) to places with lower concentrations is called the “heat flow.” [2] It describes the observed fact that heat energy, in bodies that are not being externally manipulated by compression, etc., flows only from a warmer body to a cooler one. [2] Therefore, if no outside force is adding energy to an isolated system to help renew it, it will eventually burn out (heat death). [2]

For an ideal log-oscillator, kinetic temperature T k should be energy independent according to the virial theorem. [6] This implies that its kinetic temperature can maintain a constant value even though the log-oscillator couples with another system, which absorbs energy from the log-oscillator or vice versa. [6] Therefore, in a much shorter timescale attainable in numerical simulations, the log-oscillator essentially moves with a constant velocity, which explains the linear behavior with energy shown in Figs 1 and and2 2. [6] The slow relaxation lies in the exponential growing of oscillation time with the energy of the log-oscillator. [6] We argue that the virial theorem is practically violated in finite-time simulations of the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. [6] With this study, we demonstrated that kinetic temperature of the modified log-oscillator has a linear dependence on system energy if energy is larger than a critical energy, which indicates a possible violation of the virial theorem. [6] As a comparison, we also examine the case that the energy of respective log-oscillators are initially to the edge of the plateau. [6]

Not the answer you’re looking for? Browse other questions tagged thermodynamics energy energy-conservation or ask your own question. [16] Entropy is an “extensive” quantity’ like energy or momentumtwo teapots have twice the entropy of one teapot. [2] In fact the entropy of the ashes is probably lower than that of the trees, because energy is released during the combustion. [2]

As a small ε is introduced in a way like Eq. ( 3 ), energy dependence of T k is notable only when energy is very low and comes to vanish as energy increases. [6] High Energy Physics (HEP) papers published after January 1, 2018 in Physical Review Letters, Physical Review C, and Physical Review D are published open access, paid for centrally by SCOAP 3. [3] NOTE: when a hot tea in an air tight room goes cold (loses all it’s energy) not only do we NOT expect the process to reverse by natural causes (ie. the tea will get hot again), but both room temp and tea temp will be equal. [2] A human metabolizes vastly more food energy during that time. [2] Tolman RC. A general theory of energy partition with applications to quantum theory. [6]

T k as a function of the average time for an isolated oscillator with the total energy ( a ) E 5 and ( b ) E 25. [6] Kinetic temperature T k as a function of the total energy E of the isolated log-oscillator for different average time. [6] As shown in Fig. 1, we plot the dependence of kinetic temperature T k on the total energy E of the system. [6] In order to understand the underlying mechanism further, we study the relaxation process of T k by setting the log-oscillator’s total energy inside the plateau region ( E 5) and the linear increase region ( E 25), respectively. [6] Our results indicates that total energy should not be “too large”, i.e., E should be less than E c. [6] To reduce the deviation, it has been argued that the total energy E should be large 3, 6. [6]

In thermal equilibrium state, the canonical distribution function is given by ρ ( x, p ) 1 Z e − β H ( x, p ) 1 Z p e − β p 2 2 m 1 Z x e − β V ( x ), where β 1/ k B T, Z p and Z x are reduced participation functions with respect to p and x, respectively. [6] Dechant A, Tzvi Shafier S, Kessler DA, Barkai E. Heavy-tailed phase-space distributions beyond boltzmann-gibbs: Confined laser-cooled atoms in a nonthermal state. [6]

Analyzing the entropy evolution, we find that it also proceeds to an equilibrium state of maximum entropy. [3] In this way, the universe could reach maximum entropy and then happen, by chance, to return to a low entropy state. [2] The state that we would expect to find the system in, the last one, has the highest entropy. [2] This is not correct dS is an exact form, and entropy is a true state variable. [2]

The system could be in this state (10 in left, 10 in the right) and, just by chance, all the molecules could make their way to the left hand side of the box. [2] Its relaxation to the equilibrium state is unavailable through practical simulations. [6]

From this, one can deduce the properties of volume, pressure, and temperature, leading to Boyle’s law and Charles’ law, among others. [2] This result, known as the Law of Dulong and Petit, works fairly well experimentally at room temperature. (For every element, it fails at low temperatures for quantum-mechanical reasons. [7] An alternative statement of the law is that heat will tend not to flow from a cold body to a warmer one without intelligent intervention, or work, being done, as in the case of a refrigerator. [2] The only new feature is that you should determine whether the case just presented–ideal gases at constant volume–applies to the problem. (For solid elements, looking up the specific heat capacity is generally better than estimating it from the Law of Dulong and Petit.) [7]

More rigorously, Boltzmann showed that it is possible to proceed from the conservation laws governing molecular encounters to general statements, such as the distribution of velocities, which are largely independent of how the molecules interact. [1] The third law is a statement that absolute zero can’t be reached by any finite number of Carnot cycles. [2] The number of heads might be off by a few quintillion (this is the “law of large numbers”), but that won’t make any practical difference. [2]

The often-heard argument that this law disproves an eternal universe is true, because in that case maximum entropy would have been reached already. [2] Since quantum effects are particularly important for low-mass particles, the Law of Dulong and Petit already fails at room temperature for some light elements, such as beryllium and carbon. [7] In 1889 another Austrian physicist, Ludwig Boltzmann, used the second law of thermodynamics to derive this temperature dependence for an ideal substance that emits and absorbs all frequencies. [1] People sometimes like to say things like “The Second Law of Thermodynamics means that it is very unlikely that heat will travel from a colder object to a warmer one.” [2] The First Law of Thermodynamics and the Second Law of Thermodynamics suggests that the universe had a beginning. [2] The main argument against evolution using the second law of thermodynamics is that evolution requires a decrease in entropy (disorder). [2] The Second Law of Thermodynamics disproves the atheistic Theory of Evolution and Theory of Relativity, both of which deny a fundamental uncertainty to the physical world that leads to increasing disorder. [2] The Second Law of Thermodynamics is a fundamental truth about the tendency towards disorder in the absence of intelligent intervention. [2] The Second Law of Thermodynamics is the result of the intrinsic uncertainty in nature, manifest in quantum mechanics, which is overcome only by intelligent intervention. [2] The Second Law of Thermodynamics is abused by many people, claiming that it buttresses their arguments for a wide variety of things to which it simply doesn’t apply. [2] The Second Law of Thermodynamics attracts a lot of attention in religious websites and books. [2] There is only one type of system that the Second Law of Thermodynamics applies to: an isolated system. [2] There are many different ways of stating the Second Law of thermodynamics. [2] One can easily be misled if one ascribes macroscopic visible phenomena of apparent randomness to the Second Law of Thermodynamics. [2] It has become common in recent years for environmentalists to claim that the Second Law of Thermodynamics implies limits to economic growth. [2] Creation Ministries International has a great wealth of information on why the Second Law of Thermodynamics is incompatible with the evolutionary paradigm. [2]

That article provides some historical background, along with an explanation of the relationship between the Second Law and the increase in entropy. [2] These statements are qualitative and stating the Second Law in terms of entropy makes the law quantitative. [2] The temptation is to let one’s perception of “disorder”, or “messiness”, or “degradation”, as in the Isaac Asimov quote given above, or the result of Googling “entropy”, color one’s views of the Second Law. [2] A person sorting a deck of cards, or cleaning up their room, of course needs some external source of low entropy in order not to violate the Second Law. [2]

Another way of stating the second law then is: The universe is constantly getting more disorderly. [2]

The fact that heat only flows downhill, and that entropy never decreases, is now just a consequence of the “most probable distribution” principle, or equipartition principle, from mathematical statistics, albeit at a vastly larger scale. [2] The idea of equipartition leads to an estimate of the molar heat capacity of solid elements at ordinary temperatures. [7]

As far as a thermalized log-oscillator is concerned, our calculation based on the canonical ensemble average shows that the generalized equipartition theorem is broken if the temperature is higher than a critical temperature. [6] As a thermalized log-oscillator is concerned, our analysis shows the generalized equipartition theorem is broken when the temperature is higher than a critical temperature, which is verified by numerical simulations. [6]

This fact follows from a more general result, the equipartition theorem, which holds in classical (non-quantum) thermodynamics for systems in thermal equilibrium under technical conditions that are beyond our scope. [7] Uline MJ, Siderius DW, Corti DS. On the generalized equipartition theorem in molecular dynamics ensembles and the microcanonical thermodynamics of small systems. [6]

The accelerated expansion of the Universe can be interpreted as a tendency to satisfy holographic equipartition. [3]

My book has a question asking to calculate average kinetic energy of the molecules in 8g of methane. [8] Unlike a “normal” thermodynamical system, for which the potential energy quickly obtains the increment of energy while the kinetic energy is kept constant in average, the log-oscillator has a slow relaxation of energy. [6] This explains why the kinetic temperature is proportional to the energy since the potential energy in average gains little the energy increment while kinetic energy gains almost all of them. [6]

In this paradigm, rotations and vibrations preserve the centre of mass of a molecule, and therefore don’t contribute to the kinetic energy of the molecule. [8] In such systems, the molecules can have other forms of energy beside translational kinetic energy, such as rotational kinetic energy and vibrational kinetic and potential energies. [7]

This motion is often modeled by imagining a spring connecting the two atoms, and we know from simple harmonic motion that such motion has both kinetic and potential energy. [7] When a warmer body is placed in contact with a cooler one, heat energy will flow (always preserving total energy, of course) from the warmer one to the cooler one. [2] This, plus the constraints on conservation of the total energy, leads to the Maxwell-Boltzmann distribution of molecular energies. [2] The total translational kinetic energy of N molecules of gas is simply N times the average energy per molecule, which is given by Equation 21.4: Total translational kinetic energy of N molecules E trans ? N ? mv ? ? 1 2 2 3 2 Nk BT ? 32 nRT (21.6) where we have used k B ? R/NA for Boltzmann?s constant and n ? N/NA for the number of moles of gas. [5] A cylinder with a piston contains 1.20 kg of air at 25.0C and 200 kPa. Energy is transferred into the system by heat as it is allowed to expand, with the pressure rising to 400 kPa. Throughout the expansion, the relationship between pressure and volume is given by P ? CV 1/2 WEB where C is a constant. (a) Find the initial volume. (b) Find the ?nal volume. (c) Find the ?nal temperature. (d) Find the work that the air does. (e) Find the energy transferred by heat. [5] In a constant-volume process, 209 J of energy is transferred by heat to 1.00 mol of an ideal monatomic gas initially at 300 K. Find (a) the increase in internal energy of the gas, (b) the work it does, and (c) its ?nal temperature. 17. [5]

One mole of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an isovolumetric process, acquiring 500 J of energy by heat. [5] If a gas is compressed (or expanded) very rapidly, very little energy is transferred out of (or into) the system by heat, and so the process is nearly adiabatic. (We must remember that the temperature of a system changes in an adiabatic process even though no energy is transferred by heat.) [5] Proof That PV ? ? constant for an Adiabatic Process When a gas expands adiabatically in a thermally insulated cylinder, no energy is transferred by heat between the gas and its surroundings; thus, Q ? 0. [5] If this heating process includes two steps, the ?rst at con- 663 stant pressure and the second at constant volume, determine the amount of energy transferred to the gas by heat. 21. [5] The compressibility ? of a substance is de?ned as the fractional change in volume of that substance for a given change in pressure: ??? wave passes through a gas, the compressions are either so rapid or so far apart that energy ?ow by heat is prevented by lack of time or by effective thickness of insulation. [5] One mole of air (CV ? 5R/2) at 300 K and con?ned in a cylinder under a heavy piston occupies a volume of 5.00 L. Determine the new volume of the gas if 4.40 kJ of energy is transferred to the air by heat. 15. [5] The ratio of the number of atoms in the higher energy level to the number in the lower energy level is n(E 2 ) ? e ?1.50 eV/0.216 eV ? e ?6.94 ? 9.64 ? 10 ?4 n(E 1) This result indicates that at T ? 2 500 K, only a small fraction of the atoms are in the higher energy level. [5]

Consider a gas at a temperature of 2 500 K whose atoms can occupy only two energy levels separated by 1.50 eV, where 1 eV (electron volt) is an energy unit equal to 1.6 ? 10?19 J (Fig. 21.10). [5] At temperatures well below 250 K, CV has a value of about 32 R, suggesting that the molecule has only translational energy at low temperatures. [5]

Heat flow from a hotter to a cooler body is a process of energy transfer tending to equalize temperature, which increases entropy (because it increases disorder). [11] A process forcing require transfer of non-equilibrium (the two are cause-and effect, force-flux phenomena ) which ideally could be conserved, but is always accompanied with dissipation regardless of the amount (heat & entropy generation, i.e., conversion of other energy types to thermal energy). [9] All processes or changes are caused by forced energy transfers where part of useful energy (work potential) is always dissipated to thermal heat accompanied with entropy generation or production, in addition to any entropy transfer with heat transfer. [9] If energy is transferred by heat to a system at constant volume, then no work is done by the system. [5] It contains a volume of 100 m3 of air at 300 K. (a) Calculate the energy required to increase the temperature of this air by 1.00C. (b) If this energy could be used to lift an object of mass m through a height of 2.00 m, what is the value of m? 18. [5] If its initial temperature was 300 K, and if no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has doubled? 28. [5]

The energy associated with vibrational motion in the x direction is Germanium 20 15 Silicon 10 5 0 0 100 200 300 Temperature (K) Figure 21.8 Molar speci?c heat of silicon and germanium. [5] Find the energy input required to raise the temperature to 700 K. 19. [5] Why does a diatomic gas have a greater energy content per mole than a monatomic gas at the same temperature? 13. [5] Determine the amount of energy transferred to the gas by heat. [5] The increased temperature of the rubber results in the transfer of energy by heat into the air inside the tire. [5] True entropy is always thermal and universal, since energy is always exchanged in all processes and always dissipated in heat thus generating entropy, and there is no way to destroy entropy. [9] The analysis of thermodynamics using the theory of relativity is done, the effective reaction force in the principle of Le Chatelier – Brown is determined, a new fourth energy definition of entropy is presented. [10] The process cannot proceed spontaneously in opposite direction against the forcing and thus create non-equilibrium and destroy entropy, however the non-equilibrium (useful energy or work potential which is cause of process forcing) could be re-arranged/transferred and in limit conserved (in reversible processes, including forcing advantage potential ). [9] With all due respect, nobody has been successful to achieve sustained conversion of environmental thermal energy to work (cyclic or otherwise) nor to provide reliable evidence (comprehensive energy and entropy ‘accounting’) of achieving a sustainable over-all process efficiency higher than the Carnot’s (which is zero-impossible from only a single thermal reservoir). [9] During forced energy transfer a part (and ultimately all) of the useful energy is dissipated (irreversibly converted to thermal energy with the corresponding entropy generation), but in limit, the non-equilibrium (work potential) may be conserved during reversible processes, including localized increase of energy potential on the expense of decrease elsewhere ( forcing advantage ). [9]

It does not include the energy associated with the internal motion of the molecule — namely, vibrations and rotations about the center of mass. [5] System of particles, Center of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems. [4] Solution Equation 21.25 gives the relative number of atoms in a given energy level. [5] Determine the ratio of the number of atoms in the higher energy level to the number in the lower energy level. [5] The atom has two possible energies, E1 and E 2, where E1 is the lower energy level. [5] EXAMPLE 21.5 Thermal Excitation of Atomic Energy Levels As we discussed brie?y in Section 8.10, atoms can occupy only certain discrete energy levels. [5] A relation is discovered between the mass and binding energy of space objects, corresponding to the Einstein formula (equivalence of mass and energy); discreteness of stellar parameters and quantization of parameters of cosmic systems are revealed; stellar Planck, Dirac, Boltzmann and other stellar constants are determined; combined SP? symmetry with respect to similarity of physical processes at different scale levels of matter is introduced. [10] The dimensions of a room are 4.20 m ? 3.00 m ? 2.50 m. (a) Find the number of molecules of air in it at atmospheric pressure and 20.0C. (b) Find the mass of this air, assuming that the air consists of diatomic molecules with a molar mass of 28.9 g/mol. (c) Find the average kinetic energy of a molecule. (d) Find the rootmean-square molecular speed. (e) On the assumption that the speci?c heat is a constant independent of temperature, we have E int ? 5nRT/2. [5] Find by proportion the rms speed of an oxygen molecule at this temperature. (The molar mass of O2 is 32.0 g/mol, and the molar mass of He is 4.00 g/mol.) (a) How many atoms of helium gas ?ll a balloon of diameter 30.0 cm at 20.0C and 1.00 atm? (b) What is the average kinetic energy of the helium atoms? (c) What is the root-mean-square speed of each helium atom? Problems WEB 10. [5]

One mole of hydrogen gas is heated at constant pressure from 300 K to 420 K. Calculate (a) the energy transferred by heat to the gas, (b) the increase in its internal energy, and (c) the work done by the gas. 16. [5] Quick Quiz 21.2 How does the internal energy of a gas change as its pressure is decreased while its volume is increased in such a way that the process follows the isotherm labeled T in Figure 21.4? (a) E int increases. (b) E int decreases. (c) Eint stays the same. (d) There is not enough information to determine ?E int. [5]

Because the number of moles is a convenient measure of the amount of gas, we de?ne the molar speci?c heats associated with these processes with the following equations: Internal energy of an ideal monatomic gas is proportional to its temperature Q ? nC V ?T (constant volume) (21.8) Q ? nC P ?T (constant pressure) (21.9) where CV is the molar speci?c heat at constant volume and CP is the molar speci?c heat at constant pressure. [5] Show that a gas consisting of such molecules has the following properties: (1) its total internal energy is fnRT/2; (2) its molar speci?c heat at constant volume is fR/2; (3) its molar speci?c heat at constant pressure is ( f ? 2)R/2; (4) the ratio ? ? CP /CV ? ( f ? 2)/f. 33. [5]

The total energy of N molecules (or n mol) of an ideal monatomic gas is E int ? 32 Nk BT ? 32 nRT (21.10) The change in internal energy for n mol of any ideal gas that undergoes a change in temperature ?T is ?E int ? nCV ?T (21.12) where CV is the molar speci?c heat at constant volume. [5] Substituting the expression for Q given by Equation 21.8 into 647 21.2 Molar Specific Heat of an Ideal Gas Equation 21.11, we obtain P ?E int ? nCV ?T (21.12) Isotherms If the molar speci?c heat is constant, we can express the internal energy of a gas as f E int ? nCVT This equation applies to all ideal gases — to gases having more than one atom per molecule, as well as to monatomic ideal gases. [5]

If we consider a gas for which the only type of energy for the molecules is translational kinetic energy, we can use Equation 21.6 to express TABLE 21.1 Some rms Speeds Gas H2 He H2O Ne N2 or CO NO CO2 SO2 Molar Mass (g/mol) vrms at 20C (m/s) 2.02 4.00 18.0 20.2 28.0 30.0 44.0 64.1 1904 1352 637 602 511 494 408 338 645 21.2 Molar Specific Heat of an Ideal Gas the internal energy of the gas. [5] If C p and C V are measured in the units of work and R is also in the units of work (or energy), then Eq. (ii) becomesC p -C v R. [17]

In general, an adiabatic process is one in which no energy is exchanged by heat between a system and its surroundings. [5] By the de?nition of an adiabatic process, no energy is transferred by heat into or out of the system. [5] It then undergoes an isobaric process, losing this same amount of energy by heat. [5] Despite a wrong view of heat and an incomplete view of energy, Carnot was able to advance the important principle that no heat engine (such as a steam engine) can operate with perfect efficiency. [11]

There is no other way to store the energy in a monatomic gas. [5] T o ‘scoop’ the useful-energy (for use or storage) require forcing by transferring the useful-energy from elsewhere or even more since in part it will be dissipated (converted) into thermal energy with generation of entropy. [9] In reality entropy is always generated (in part or in whole) within locality of system structure, while otherwise and in limit it is conserved during reversible processes (without energy dissipation), but entropy cannot be destroyed since it will imply creation of non-equilibrium from nowhere or from within an equilibrium alone, thus defying the existence of equilibrium. [9] The energy definition is given in the tensor form and the meaning of entropy is established. [10] The concentration of all of the energy in a system on a few molecules is a highly ordered and improbable situation analogous to the concentration of all of the molecules in a small portion of the available space. [11] The molecules that escape the liquid by evaporation are those that have suf?cient energy to overcome the attractive forces of the molecules in the liquid phase. [5] Available energy tends to distribute itself uniformly over a set of identical molecules, just as available space tends to be occupied uniformly by the same molecules. [11]

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4. (26) User:Fedosin – Wikiversity

5. (25) Brownian movement – WikiVisually

6. (21) Thermodynamic Analysis of Gravitational Field Equations in Lyra Manifold

7. (21) The Second Law of Thermodynamics – Holistic Reasoning and Generalization by Prof. M. Kostic

8. (10) T5. Six Versions Of The Second Law Of Thermodynamics Basic Physics

10. (8) 2.3: Heat Capacity and Equipartition of Energy – Physics LibreTexts

11. (7) Ludwig Boltzmann | Austrian physicist | Britannica.com

12. (7) physics ch 10 final MC Flashcards | Quizlet

13. (6) Phys. Rev. D 96, 063513 (2017) – Holographic equipartition and the maximization of entropy

14. (5) Wave Turbulence

15. (5) Physics Courses – SIUE

16. (5) kinetic theory of gases – Is this a violation of Equipartition theorem? – Chemistry Stack Exchange