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# Why Do Gases Have Two Specific Heat Capacity?

why do gases have two specific heat capacity?

If a gas is heated in a sealed container having constant volume it cannot expand, and so no external work is done by the gas during the heating process. All of the thermal energy supplied is used to increase the KE of the molecules or atoms of the gas, and this causes the temperature to rise. In the case of a gas heated at constant pressure, the gas will expand during the heating process; this is necessary in order to keep the pressure constant despite the rise in temperature. During the expansion, the gas will do work against whatever it is that is maintaining the pressure constant (for example a piston in a cylinder). This external work (We) must be accounted for by the thermal energy provided (Wh), and only the difference (Wh - We) will be available for raising the KE of the gas particles. The temperature will therefore rise less than if the same amount of Wh were absorbed at constant volume. Specific heat is a measure of the energy required to raise the temperature of 1kg of the material by 1 degree C; this will be greater in the case of heating at constant pressure than it is when heating at constant volume. In the case of solids and liquids, thermal expansion is much less, so the the amount of external work done when a solid or liquid expands on heating is negligibly small. Consequently the difference between the two specific heats is hardly noticeable, and can be ignored.

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Why is the change of heat non zero in a isothermal process?

In freshman physics, they did us a disservice by incorrectly teaching us that heat capacity is defined by \$Q=CDelta T\$ (or \$Q=mCDelta T\$, where C is the heat capacity per unit mass) (or \$Q=nCDelta T\$, where C is the heat capacity per mole). This definition works fine as long as no work is done. However, when work is done, this equation gives the wrong answer. Moreover, in thermodynamics, we learn that Q represents a quantity that depends on path, while C is a physical property of the material that is independent of path. So, in thermodynamics, they corrected their error by redefining heat capacity properly. \$\$nC_v=left(fracpartial Upartial T

ight)_V\$\$ For a process at constant volume, this remains consistent with the definition from freshman physics, and, moreover is a physical property of state (independent of path). But for processes in which work is done, it gives the correct answer for all cases.There is also another heat capacity property that is used in thermodynamics called the heat capacity at constant pressure \$C_p\$. This is defined as \$\$nC_p=left(fracpartial Hpartial T

ight)_P\$\$where H is the enthalpy. In this case, the relationship is consistent with the freshman definition specifically for situations in which work is done in a constant pressure process. However, here too, the relationship is much more general than this. The real question is, "why did not they teach this to us properly in the first case?" One can only speculate on the answer, but it has been the source of confusion to thermodynamics students for centuries.

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Volumetric heat capacity of gases

Large complex gas molecules may have high heat capacities per mole of gas molecules, but their heat capacities per mole of total gas atoms are very similar to those of liquids and solids, again differing by less than a factor of two per mole of atoms. gas molecules of various complexities. In monatomic gases (like argon) at room temperature and constant volume, volumetric heat capacities are all very close to 0.5 kJ/K/m3, which is the same as the theoretical value of â€‹3â„2RT per kelvin per mole of gas molecules (where R is the gas constant and T is temperature). As noted, the much lower values for gas heat capacity in terms of volume as compared with solids (although more comparable per mole, see below) results mostly from the fact that gases under standard conditions consist of mostly empty space (about 99.9% of volume), which is not filled by the atomic volumes of the atoms in the gas. Since the molar volume of gases is very roughly 1000 times that of solids and liquids, this results in a factor of about 1000 loss in volumetric heat capacity for gases, as compared with liquids and solids. There is some difference in the heat capacity of monatomic vs. polyatomic gasses, and also gas heat capacity is temperature-dependent in many ranges for polyatomic gases; these factors act to modestly (up to the discussed factor of 2) increase heat capacity per atom in polyatomic gases, as compared with monatomic gases. Volumetric heat capacities in polyatomic gases vary widely, however, since they are dependent largely on the number of atoms per molecule in the gas, which in turn determines the total number of atoms per volume in the gas. The volumetric heat capacity is defined as having SI units of J/(mÂ³Â·K). It can also be described in Imperial units of BTU/(ftÂ³Â·Â°F).

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