A New Perspective for Kinetic Theory and Heat Capacity

Volume 13 (2017) PROGRESS IN PHYSICS Issue 3 (July) A New Perspective for Kinetic Theory and Heat Capacity Kent W. Mayhew 68 Pineglen Cres., Ottawa, Ontario, K2G 0G8, Canada. E-mail: Kent.Mayhew@gmail.com The currently accepted kinetic theory considers that a gas’ kinetic energy is purely translational and then applies equipartition/degrees of freedom. In order for accepted theory to match known empirical finding, numerous exceptions have been proposed. By redefining the gas’ kinetic energy as translational plus rotational, an alternative explanation for kinetic theory is obtained, resulting in a theory that is a better fit with empirical findings. Moreover, exceptions are no longer required to explain known heat capacities. Other plausible implications are discussed. 1 Introduction Various explanations for equipartition’s failure in describing heat capacities have been proposed. Boltzmann suggested The conceptualization of a gaseous system’s kinematics origthat the gases might not be in thermal equilibrium [8]. Planck inated in the writings of the 19th century greats. In 1875, [9] followed by Einstein and Stern [10] argued the possibility Maxwell [1] expressed surprise at the ratio of energies (transof zero-point harmonic oscillator. More recently Dahl [11] lational, rotational and/or vibrational) all being equal. Boltzhas shown that a zero point oscillator to be illusionary. Lord mann’s work on statistical ensembles reinforced the current Kelvin [12–13] realized that equipartition maybe wrongly deacceptance of law of equipartition with a gas’s energy being rived. The debate was somewhat ended by Einstein claiming equally distributed among all of its degrees of freedom [2–3]. that equipartition’s failure demonstrated the need for quantum The net result being that the accepted mean energy for each theory [14–15]. Heat capacities of gases have been studied independent quadratic term being kT/2. throughout the 20th century [16–19] with significantly more The accepted empirically verified value for the energy of complex models being developed [20–21]. a /textitN molecule monatomic gas is kT/2 with its isometIt becomes a goal of this paper to clearly show that an ric molar heat capacity (Cv ) being (3R/2). An implication alternative kinetic theory/model exists. A simple theory that is that a monatomic gas only possesses translational energy correlates better with empirical findings without relying on [4–5]. The reasoning for this exception is that the radius of a exceptions while correlating with quantum theory. monatomic gas is so small that its rotational energy remains negligible, hence its energy contribution is simply ignored. 2 Kinetic theory and heat capacity simplified Mathematically speaking equipartition based kinetic theory states that a molecule with n′′ atoms has 3n′′ degrees of Consider wall molecules 1 through 8, in Fig. 1. The total mean energy along the x-axis of a vibrating wall molecule is freedom (f ) [5–6] i.e.: f = 3n′′ . (1) E x = kT. (3) This leads to the isometric molar heat capacity (Cv ) for large Half of a wall molecule’s mean energy would be kinetic enpolyatomic molecules: ergy, and half would be potential energy. Thus, the mean 3 ′′ kinetic energy along the x-axis, remains Cv = n R. (2) 2 kT . (4) Ex = Interestingly, the theoretical expected heat capacity for N di2 atomic molecules is 7NkT/2. This is the summation of the following three energies a) three translational degrees, i.e. In equilibrium, the mean kinetic energy of a wall molecule, as 3NkT/2. b) three rotational degrees of freedom, however defined by equation (4) equals the mean kinetic energy of the since the moment of inertia about the internuclear axis is van- gas molecule along the same x-axis. Herein, the wall in the ishing small w.r.t. other moments, then it is excluded, i.e. y-z plane acts as a massive pump, pumping its mean kinetic NkT . c) Vibrational energy, i.e. NkT . This implies a molar energy along the x-axis onto the much smaller gas molecules. In equilibrium each gas molecule will have received a heat capacity Cv =7NkT/2 = 29.3 J/(mol*K). However, empirical findings indicate that the isometric molar heat capacity component of kinetic energy along each orthogonal axis. Alfor a diatomic gas is actually 20.8 J/(mol*K), which equates though there are six possible directions, at any given instant, to 5RT/2 [6]. This discrepancy for diatomic gases certainly a gas molecule can only have components of motion along allows one to question the precise validity of accepted kinetic three directions, i.e. it cannot be moving along both the postheory! In 1875 Maxwell noted that since atoms have internal itive and negative x-axis at the same time. Therefore, the parts then this discrepancy maybe worse than we believe [7]. total kinetic energy of the N molecule gas is defined by 166 Kent Mayhew. A New Perspective for Kinetic Theory and Heat Capacity Issue 3 (July) PROGRESS IN PHYSICS Volume 13 (2017) Fig. 1: Ideal monoatomic gas at pressure Pg and temperature T g sourrounded by walls at temperature T w = T g . Gas molecules have no vibrational energy. Fig. 2: Ideal diatomic gas at pressure Pg and temperature T g sourrounded by walls at temperature T w = T g . Gas molecules have vibrational energy. equation (4) i.e. 3NkT/2. Up to this point we remain in agreement with accepted theory. Consider that you hit a tennis ball with a suitable racquet. If the ball impacts the racquet’s face at a 90 degree angle, then the ball will have significant translational energy in comparison to any rotational energy. Conversely, if the ball impacts the racquet at an acute angle, although the same force is imparted onto that ball, the ball’s rotational energy can be significant in comparison to its translational energy. The point being, in real life both the translational and rotational energy, are due to the same impact. Now reconsider kinetic theory. Understandably, momentum transfer between both the wall’s and gas’ molecules result in energy exchanges between the massive wall and small gas molecules. Moreover, the exact nature of the impact will vary, even though the exchanged mean energy is constant. it cannot rotate hence both energies can only result in vibrational energy of the wall molecules along its three orthogonal axis. After numerous wall impacts, our model predicts that an N molecule monatomic gas will have a total kinetic energy (translational plus rotational) defined by EkT (t,r) = 3 NkT. 2 (5) Fig. 2 illustrates a system of diatomic gas molecules in a container. The wall molecules still pass the same mean kinetic energy onto the diatomic gas molecule’s center of mass with each collision. Therefore the diatomic gas’ kinetic energy is defined by equation (5). The diatomic gas molecule’s vibrational energy would be related to the absorption and emission of its surrounding blackbody/thermal radiation. Therefore, the mean x-axis vibrational energy within a diatomic gas Case 1: Imagine that a monatomic gas molecule collides molecule remains defined by equation (3) and the total mean head on with a wall molecule, e.g. the gas molecule energy for a diatomic gas molecule becomes defined by hitting wall molecule no. 3 in Fig. 1. Herein, the gas 3 5 molecule might only exchange translational energy E tot = E kT (t,r) + E v = kT + kT = kT. (6) with the wall, resulting in the gas molecule’s mean ki2 2 netic energy being purely translational, and defined by Therefore the total energy for an N molecule diatomic gas equation (4). becomes Case 2: Imagine that a monatomic gas molecule strikes wall 3 5 Etot = EkT (t,r) + Ev = NkT + NkT = NkT. molecule no. 1 at an acute angle. The gas molecule 2 2 would obtain both rotational and translational energy from the impact such that the total resultant mean en- For an N molecule triatomic gas: ergy of the gas molecule would be the same as it was 7 3 Etot = EkT (t,r) + Ev = NkT + 2NkT = NkT, in Case 1, i.e. defined by equation (4). 2 2 Case 3: Imagine a rotating and translating monatomic gas molecule striking the wall. Both the rotational and translational energies will be passed onto the wall molecule. Since the wall molecule is bound to its neighbors, (7) (8) n′′ signifies the polyatomic number. Therefore for N molecules of n′′ -polyatomic gas, the vibrational energy is Kent Mayhew. A New Perspective for Kinetic Theory and Heat Capacity Ev = (n′′ − 1)NkT. (9) 167 Volume 13 (2017) PROGRESS IN PHYSICS Issue 3 (July) acetylene (C2 H2 , n′′ = 4, Cv = 35.7) are linear bent molecules and good fit, while pyramidal ammonia (NH3 , n′′ = 4, Cv = 3 ′′ 27.34) is not. Could the gas molecule’s shape influence how NkT + (n − 1) NkT Etot = EkT (t,r) + Ev = 2 ! (10) it absorbs surrounding thermal radiation, hence its vibrational 1 energy? = n′′ + NkT. 2 Table 2 shows the accepted adiabatic index versus our theoretical adiabatic index for most of the same substances Dividing both sides by temperature and rewriting in terms of shown in Table 1. Our theoretical adiabatic index compares per mole (N=6.02 × 1023 ) then equation (10) becomes: rather well with the accepted empirical based values, espe! ! cially for low n′′ < 4 and high n′′ > 11, as is clearly seen 1 1 Etot = R n′′ + . (11) in Fig. 4. Although not 100% perfect, this new theory/model = nk n′′ + T 2 2 certainly warrants due consideration by others. For most temperature regimes, the heat capacity of gases 3 Kinetic theory and thermal equilibrium remains fairly constant, hence equation (11) can be rewritten Kinetic theory holds because the walls act as massive energy in terms of the isometric molar heat capacity (Cv ), i.e. pumps, i.e. gas molecules take on the wall’s energy with ev! 1 ery gas-wall collision. For sufficiently dilute gases, this re′′ Cv = R n + . (12) mains the dominant method of energy exchange. Mayhew 2 [23–24] has asserted that inter-gas molecular collisions tend The difference between molar isobaric heat capacity (C p ) and to obey conservation of momentum, rather than adhere to kimolar isometric heat capacity (Cv ) for gases is the ideal gas netic theory. Therefore, when inter-gas collisions dominate constant (R) [see equation (15)]. Therefore, a gas’s isobaric over gas-wall collisions, then kinetic theory, the ideal gas law, heat capacity C p becomes Avogadro’s hypothesis, Maxwell’s velocities etc. all can start ! ! to lose their precise validity. 3 1 It is accepted that there are changes to heat capacity in + R = R n′′ + . (13) C p = R n′′ + 2 2 and around dissociation temperatures. Firstly, at such high temperatures, the pressure tends to be high; hence the interThe adiabatic index is the ratio of heat capacities, i.e. dividing gas collisions may dominate. This author believes that this equation (13) by equation (12) gives the adiabatic index actually helps explain why kinetic theory falters in polytropic   stars, wherein high-density gases collide in a condensed mat3 ′′ n +2 Cp . γ= (14) ter fashion hence one must use polytropic solutions. Sec= Cv n′′ + 12 ondly, at high temperatures a system’s thermal energy density is no longer proportional to temperature, i.e. a blast furnace’s Table 1 shows the accepted isometric and isobaric mo- thermal energy density is proportional to T 4 [22]. lar heat capacities for various substances for 0 > n′′ > 27. Blackbody radiation describes the radiation within an enThese values were calculated using data (specific heats) from closure. For an open system and/or none blackbody, the theran engineering table (Rolle [22]) that is shown in Table 2. mal radiation surrounding the gas molecules may be better Note: Engineer’s use specific heats (per mass), physicists and to considered. Herein thermal radiation means radiation that chemists prefer heat capacity (per mole). is readily absorbed and radiated by condensed matter and/or In Fig. 3, both our theoretical molar isometric and isobaric polyatomic gases, resulting in both intramolecular and inter[equations (12) and (13)] heat capacities are plotted against molecular vibrations. the number of atoms (n′′ ) in each molecule. The accepted For a system of dilute polyatomic gas e.g. Fig. 2, therempirically determined values for heat capacities versus n′′ mal equilibrium requires that all of the following three states (from Table 1) are also plotted. The traditional theoretical remain related to the same temperature (T): values for molar heat capacities [eq. (2)] are also plotted. 1. The walls are in thermal equilibrium with the enclosed The theory/model proposed herein remains a better fit to blackbody/thermal radiation. empirical findings for all polyatomic molecules. Importantly, 2. The gas’ translational plus rotational energy is in meit does not rely upon the exceptions that plague the traditionchanical equilibrium with the molecular vibrations of ally accepted degrees of freedom based kinetic theory. the walls. Interestingly, there is a discrepancy, between our model ′′ 3. The gas’ vibrational energies are in thermal equiliband empirical known values for 4 < n < 9. Moreover, rium with the enclosed blackbody/thermal radiation. the slope of our theoretical values visually remains close to ′′ the slope of empirically determined values for n > 8. FurImagine that a system of dilute polyatomic gas is taken thermore, hydrogen peroxide (H2 O2 , Cv = 37.8, n′′ = 4) and to remote outer space, and that the walls are magically reTherefore, the total energy for a polyatomic gas molecule is: 168 Kent Mayhew. A New Perspective for Kinetic Theory and Heat Capacity Issue 3 (July) PROGRESS IN PHYSICS Volume 13 (2017) Table 1: Accepted isometric and isobaric heat capacities versus theoretical i.e. empirical findings versus Eqn. (12), Eqn. (13), as well as Eqn. (2). Note: Accepted heat capacities were calculated from the engineer’s specific heats in Table 2 (Rolle [22]), exception being H2 O2 which was taken from Giguere [19]. n′′ Accepted Cv [J/mol*K] Eqn. (12) Cv [J/mol*K] Accepted Cp [J/mol*K] Eqn. (13) Cp [J/mol*K] Substance Eqn. (2) Cv [J/mol*K] Helium He 1 12.48 12.47 20.80 20.78 Neon Ne 1 12.47 12.47 20.79 20.78 Argon Ar 1 12.46 12.47 20.81 20.78 Xenon Xe 1 12.47 12.47 20.58 20.78 Hydrogen H2 2 20.52 20.78 28.83 29.09 Nitrogen N2 2 20.82 20.78 29.14 29.09 Oxygen O2 2 21.02 20.78 29.34 29.09 Nitric oxide NO 2 21.55 20.78 29.86 29.09 Water vapor H2 O 3 25.26 29.09 33.58 37.40 37.40 Carbon dioxide CO2 3 28.83 29.09 37.14 37.40 37.40 Sulfur dioxide SO2 3 31.46 29.09 39.78 37.40 37.40 Hydrogen peroxide H2 O2 4 37.4 37.73 46.05 45.71 49.86 Ammonia NH3 4 27.37 37.40 35.70 45.71 49.86 Methane CH4 5 27.4 45.71 35.72 54.0 62.33 Ethylene C2 H4 6 35.24 54.02 43.54 62.33 74.79 Ethane C2 H6 8 44.35 70.64 52.65 78.95 99.72 Propylene C3 H6 9 53.82 78.95 63.92 87.26 112.19 Propane C3 H8 11 65.18 95.57 73.51 103.88 137.12 Benzene C6 H6 12 73.50 103.88 81.63 112.19 149.58 Isobutene C4 H8 12 77.09 103.88 85.68 112.19 149.58 n-Butane C4 H10 14 89.10 120.50 97.42 128.81 174.51 Isobutane C4 H10 14 88.52 120.50 96.84 128.81 174.51 n-Pentane C5 H12 17 111.91 145.43 120.20 153.74 211.91 Isopentane C5 H12 17 111.69 145.43 119.99 153.74 211.91 n-Hexane C6 H14 20 134.78 170.36 143.06 178.67 249.30 n-Heptane C7 H16 23 157.62 195.29 165.94 203.60 286.70 Octane C8 H18 26 180.60 220.22 188.83 228.53 324.09 moved and the gas disperses. Spreading at the speed of light the blackbody/thermal radiation density decreases faster than the density of slower moving gas molecules. As the radiation density decreases, the rate at which polyatomic gaseous molecules absorbs blackbody/thermal radiation decreases in time. Hence their vibrational energy decreases although their mean velocity remains constant. Now place a thermometer in the expanding wall-less gas, what will it read? Traditional kinetic theory claims that the temperature will be the same because the gas molecule’s velocity remains constant i.e. temperature is only associated with the system’s kinemat- ics [2–3]. However, without walls the blackbody/thermal radiation decouples from thermal equilibrium i.e. the mean velocity of the gas molecules are associated with one temperature, but the radiation density is no longer associated with that temperature. This bodes the question: What is the real temperature? Of course this means accepting that the thermometer not only exchanges kinetic energy with the gas molecules, but it also exchanges blackbody/thermal radiation with its surroundings. The above is another reason that this author hypothesizes that kinetic theory can falter in systems without walls. The Kent Mayhew. A New Perspective for Kinetic Theory and Heat Capacity 169 Volume 13 (2017) PROGRESS IN PHYSICS Issue 3 (July) Table 2: Engineer’s accepted adiabatic index compared to theoretical: Eqn. (14). Note: Data in first six columns after Rolle [22]. Rolle’s reference: J.F. Masi, Trans. ASME, 76:1067 (October, 1954): National Source of Standards (U.S.) Circ. 500, Feb. 1952; Selected Values of Properties of Hydrocarbons and Related Compounds, American Petroleum Institute Research Project 44, Thermodynamic Research Center, Texas, A&M University, College Station, Texas. n′′ Molar mass [g/mol] Engineer’s R [J/kg*K)] Engineer’s Cp [kJ/mol*K)] Engineer’s Cv [kJ/mol*K)] Accepted adiabatic index(γ) Theoretical index (γ) Eqn. (14) Substance Helium He 1 4.00 2079 5.196 3.117 1.67 1.67 Neon Ne 1 20.18 412 1.030 0.618 1.67 1.67 Argon Ar 1 39.94 208 0.521 0.312 1.67 1.67 Xenon Xe 1 131.30 63 0.1568 0.095 1.67 1.67 Hydrogen H2 2 2.02 4124 14.302 10.178 1.41 1.4 Nitrogen N2 2 28.02 297 1.040 0.743 1.4 1.4 Oxygen O2 2 32.00 260 0.917 0.657 1.4 1.4 Nitric oxide NO 2 30.01 277 0.995 0.718 1.39 1.4 Water vapor H2 O 3 18.02 462 1.864 1.402 1.33 1.29 Carbon dioxide CO2 3 44.01 189 0.844 0.655 1.29 1.29 Sulfur dioxide SO2 3 64.07 130 0.621 0.491 1.26 1.29 Ammonia NH3 4 17.03 488 2.096 1.607 1.30 1.22 Methane CH4 5 16.04 519 2.227 1.708 1.30 1.18 Ethylene C2 H4 6 28.05 297 1.552 1.256 1.24 1.15 Ethane C2 H6 8 30.07 277 1.751 1.475 1.19 1.12 Propylene C3 H6 9 42.08 198 1.519 1.279 1.19 1.11 Propane C3 H8 11 44.10 189 1.667 1.478 1.13 1.09 Benzene C6 H6 12 78.11 106 1.045 0.939 1.11 1.08 Isobutene C4 H8 12 56.11 148 1.527 1.374 1.11 1.08 n-Butane C4 H10 14 58.12 143 1.676 1.533 1.09 1.07 Isobutane C4 H10 14 58.12 143 1.666 1.523 1.09 1.07 n-Pentane C5 H12 17 72.15 115 1.666 1.551 1.07 1.06 Isopentane C5 H12 17 72.15 115 1.663 1.548 1.07 1.06 n-Hexane C6 H14 20 86.18 96 1.660 1.564 1.06 1.05 n-Heptane C7 H16 23 100.20 83 1.656 1.573 1.05 1.04 Octane C8 H18 26 114.23 73 1.653 1.581 1.05 1.04 other reason kinetic theory may falter without walls is that wall-gas interactions no longer exist, hence kinetic theory’s complete virtues may be limited to systems with walls [24–25] i.e. experimental systems. body radiation has a temperature associated with it, should no longer be ignored. In other words, even a vacuum can have a temperature, although it has no matter and comparatively speaking only contains a minute amount of energy. Pressure is traditionally envisioned as being solely due to change in translational energy i.e. “every molecule that im4 Discussion of other implications pinges and rebounds exerts an impulse equal to the difference This author [24–25] has hypothesized that blackbody/thermal in its momenta before and after impact” [pg. 32, 20]. Inradiation within a system has a temperature associated with terestingly, the analysis given herein does alter such explanait. So although the total energy associated with radiation of- tions just because the rotational energy plus the translational ten is infinitesimally small in comparison to the total energy energy of the gas molecules now combine to exert pressure. associated with the kinematics of matter, the idea that black- Moreover, consider the tennis ball impacting a wall. Ask 170 Kent Mayhew. A New Perspective for Kinetic Theory and Heat Capacity Issue 3 (July) PROGRESS IN PHYSICS Volume 13 (2017) Fig. 3: Theoretical molar heat capacity based on our theoretical equations (12) and (13) versus empirical values, plus the traditional theoretical isometric molar heat capacity plot [based upon degrees of freedom, equation (2)]. Fig. 4: Theoretical adiabatic index [eq. (14)] versus number of atoms (solid line). Adiabatic index data points based upon engineering table for gases. yourself: Are not both the rotational and translational energy of that ball exchanged with the wall. So why would a gas molecule behave any differently? Just because wall molecules are bound i.e. cannot rotate, does not mean that they don’t exchange rotational energy/momentum with an impacting gas! The gas’ mean translational velocity (mv2 /2) can no longer be simply equated in terms of Boltzmann’s constant (kT/2). This has consequences to fundaments such as Maxwell’s velocity distributions for gases. In our analysis, the magnitude of translational energy compared to rotational energy is not defined beyond that they add up to and equal, the summation of the walls molecule’s kinetic energies! Since the gas’ total kinetic energy remains the same, then most of what is known in quantum theorem still applies with the change being how a gas’ kinetic energy is expressed. Consider the hypothesis that rotational energy of a gas is frozen out at low temperatures [26]. This is like claiming that gas molecules never impact a wall at acute angles, when in a cold environment. This author thinks in terms of thermal energy being energy that results in both intermolecular and intramolecular vibrations within condensed matter. Just consider the blackbody radiation curve for 3 K, whose peak is located at wavelength of 1 mm. Compare this to 300 K, where the radiation curves’ peak occurs in the infrared spec- Kent Mayhew. A New Perspective for Kinetic Theory and Heat Capacity 171 Volume 13 (2017) PROGRESS IN PHYSICS trum, wavelength equals 10 micrometers. Accepting that the majority of thermal energy is in the infrared then this author also believes that somewhere between 3 K and 300 K, a system’s thermal energy density will no longer proportional to temperature i.e. probably aroound 100 K. Perhaps it is the gas’ vibrational energy that is frozen out? Understandably, at low temperatures the blackbody/thermal radiation within the system may be such that it does not provide enough thermal energy (infrared) for measurable gas vibration. However, this should equally apply to the system’s walls, unless the walls have more thermal energy relative to the gas i.e. apparatus considerations? This is conjecture, as remains the current notion that rotational energies are frozen out. For gases the accepted difference between molar isobaric heat capacity and molar isometric heat capacity is the ideal gas constant (R). Accordingly [2–3]: C p − Cv = R. (15) The difference in heat capacities is obviously independent of the type of gas. This implies that the difference depends upon the system’s surroundings and not the experimental system, nor its contents. This fits this author’s assertion that “the ideal gas constant is the molar ability of a gas to do work per degree Kelvin” [27]. This is based upon the realization that work is required by expanding systems to upwardly displace our atmosphere’s weight, i.e. an expanding system does such work, which becomes irreversibly lost into the surrounding Earth’s atmosphere. The lost work being [24, 28–29] Wlost = Patm dV. (16) This does not mean that the atmosphere is always upwardly displaced, rather that the energy lost by an expanding system is defined by equation (17). This lost energy can be associated with a potential energy increase of the atmosphere, or a regional pressure increase. Note: A regional pressure increase will result in either a volume increase, or viscous dissipation i.e. heat created = lost work. This requires the acceptance that the atmosphere has mass and resides in a gravitational field. It is no different than realizing that an expanding system at the bottom of an ocean, i.e. a nucleating bubble, must displace the weight of the ocean plus atmosphere. Accordingly, any expanding system here on Earth’s surface must expend energy/work to displace our atmosphere’s weight and such lost work, is immediately or eventually lost into the surrounding atmosphere. Accepting this then allows one to question our understanding of entropy [24, 29]. 5 Conclusions Kinetic theory has been reconstructed with the understanding that a gas’ kinetic energy has both translational and rotational components that are obtained from the wall molecule’s kinetic energy. Therefore, the gas’ translational plus rotational energies along each of the x, y and z-axis, are added 172 Issue 3 (July) and equated to the wall molecules’ kinetic energy along the identical three axes. No knowledge pertaining to the magnitudes of the gas’ rotational energy versus translational energy is claimed. This is then added to the gas’ internal energy e.g. vibrational energy, in order to determine the gas’ total energy. The empirically known heat capacity and adiabatic index for all gases are clearly a better fit to this new theory/model, when compared to accepted theory. The fit for monatomic through triatomic gases is exceptional, without any reliance upon traditionally accepted exceptions! Moreover, our model treats all polyatomic molecules in the same manner as condensed matter. Seemingly, Lord Kelvin’s assertion that equipartition was wrongly derived, may have been right after all. Accepting that the traditional degrees of freedom in equipartition theory may be mathematical conjecture rather than constructive reasoning will cause some displeasure. Certainly, one could argue that what is said herein is really just an adjustment to our understanding. Even so, it will alter how pressure is perceived that being due to the gas molecules’ momenta from both rotation and translation, which is imparted onto a surface. Ditto for the consideration of a gas’ energy in quantum theory. The consequence of a polyatomic gas’ thermal vibrations being related to its surrounding thermal radiation may alter our conceptualization of temperature, i.e. a vacuum now has a temperature. The notion that rotation in cold gases is frozen out was also questioned. Perhaps it is a case that the thermal energy density does not remain proportional to temperature, as T approaches 0, which also is the case for very high temperature gases. The difference between isobaric and isometric heat capacity is gas independent. This fits well with this author’s assertion that lost work represents the energy lost by an expanding system into the surrounding atmosphere. Interestingly, for a mole of gas molecules this lost work can be related to the ideal gas constant. To some, the combining of a gas’ rotational and translational energy may seem like a minor alteration, however the significance to the various realms of science maybe shattering. Not only may this help put to rest more than a century of speculations, it also may alter the way that thermodynamics is envisioned. If accepted it actually opens the door for a simpler new thermodynamics vested in constructive logic, rather than mathematical conjecture. A thanks goes out to Chifu E. Ndikilar for his helpful preliminary comments, as well as both Dmitri Rabounski and Andreas Ries for their insights in finalizing the paper. 6 Example calculations 1. Table 1 for n′′ = 3; our theoretical values: [equation (12)]: I.e. Cv = 72 R = 72 8.31 J/(mol*K) = 29.09 J/(mol*K). Kent Mayhew. A New Perspective for Kinetic Theory and Heat Capacity Issue 3 (July) PROGRESS IN PHYSICS [eq. (13)]: I.e. C p = 29 R = 92 8.31 J/(mol*K) = 37.40 J/(mol*K). For n′′ =3, traditional accepted theoretical value is equation (2): I.e. Cv = 92 R = 92 8.31 J/(mol*K) = 37.40 J/(mol*K). 2. Table 2, for n′′ = 3. 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