Heat capacity of an ideal gas

The remaining question is how we got from G3MP2 (OK) = —117.672791 to G3MP2 Enthalpy = —117.667683. This is not a textbook of classical thermodynamics (see Klotz and Rosenberg, 2000) or statistical themiodynamics (see McQuarrie, 1997 or Maczek, 1998), so we shall use a few equations from these fields opportunistically, without explanation. The definition of heat capacity of an ideal gas... 

Equation (10.148) does not correctly predict CV.m at low temperatures because it assumes all the atoms are vibrating with the same frequency. In the ideal gas, this is a good assumption, and in the previous section we used an equation similar to (10.148) to calculate the vibrational contribution to the heat capacity of an ideal gas. 

We have shown that the two molar heat capacities of an ideal gas are related by... 

The molar heat capacity of an ideal gas at constant pressure is greater than that at constant volume the two quantities are related by Eq. 13. 

Assuming that the heat capacity of an ideal gas is independent of temperature, calculate the entropy change... 

Assuming that the heat capacity of an ideal gas is independent of temperature, calculate the entropy change associated with lowering the temperature of 2.92 mol of ideal gas atoms from 107.35°C to —52.39°C at (a) constant pressure and (b) constant volume. 

By the equipartition principle it now follows that each rotational degree of freedom can absorb energy of kT while each vibrational mode can absorb kT. By the same principle the heat capacity of an ideal gas... 

We divide this equation by T and integrate between the limits T and T for the temperature and V and V for the volume, because the heat capacity of an ideal gas is a function of the temperature alone. Thus, for an adiabatic reversible expansion of an ideal gas... 

The molar heat capacity of a substance is defined as the energy required to raise the temperature of 1 mole of that substance by 1 K. Thus we might conclude that the molar heat capacity of an ideal gas is yR. However, we will have to qualify this conclusion when we consider the implications of the PV work that can occur when a gas is heated. 

When an ideal gas is heated in a rigid container in which no change in volume occurs, there can be no PV work (AV = 0). Under these conditions all the energy that flows into the gas is used to increase the translational energies of the gas molecules. Thus Cv, the molar heat capacity of an ideal gas at constant volume, is fR, the result anticipated in the above discussion ... 

The molar heat capacity of an ideal gas, whose energy is that of translational motion only, should thus have a constant value, independent of temperature as well as of pressure ( 9e), namely / . Since R is 1.987 cal. deg. mole S it follows that... 

The coefficients for some gaseous compound in the above equations are listed in Table 11.3.45 It is found that the heat capacity of a real gas is almost the same as its ideal state if the pressure is not too high. Therefore, it is proper to use the heat capacity of an ideal gas for a practical gas when the pressure is low. The approximate method to calculate the heat capacity can also be used if empirical data is not readily available.6... 

This example demonstrates that reliable PVT correlation and constant-pressure heat capacity of an ideal gas are sufficient to determine a variety of thermodynamic properties, as enthalpy, entropy, Gibbs free energy, etc., and built comprehensive charts. This approach will be extended by means of departure functions. 

Qualitatively sketch the heat capacity of an ideal gas of diatomic molecules as a function of temperature. Indicate the characteristic temperatures (in terms of vibrational frequency, moment of inertia, and so on) where various degrees of freedom begin to contribute. 

Analogously, the equations for the specific internal energy (w), the entropy (s), the Gibbs energy (g), and the Helmholtz energy (a) can be derived. All these equations are summarized in Table 2.1. Furthermore, for the specific heat capacities of an ideal gas it can be shown that... 

The specific heat capacity of an ideal gas is the basic quantity for the enthalpy calculation, as it is independent from molecular interactions. It is also possible to define a real gas heat capacity, but for process calculations it is more convenient to account for the real gas effects with the enthalpy description of the equation of state used (see Section 6.2). In process calculations, the specific heat capacity of ideal gases mainly determines the duty of gas heat exchangers, and it has an influence on the heat transfer coefficient as well. 

The specific heat capacity of an ideal gas is defined as the heat per amount of substance in the ideal gas state necessary to obtain a certain temperature change. It must be distinguished between the specific isobaric heat capacity c p (at constant pressure) and the specific isochoric heat capacity c[f (at constant volume). For ideal gases, both quantities are related [52] via... 

The heat capacity of an ideal gas depends on whether the gas is monatomic, diatomic, or whatever, and is derived through statistical mechanics, which we will not go into. For the simplest case, a monatomic ideal gas. 

Heat capacity of an ideal gas. The energy of an ideal gas does not depend on volume,... 

Starting from the relationship between temperature and kinetic energy for an ideal gas, find the value of the molar heat capacity of an ideal gas when its temperature is changed at constant volume. Find its molar heat capacity when its temperature is changed at constant pressure. 

Consequently the isochoric heat capacity of an ideal gas of point particles is given by... 

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