Entropy of ideal gas

S Entropy, e.u./mole S Molar entropy of ideal gas e.u./mole... 

The U level relative to the Fermi level for the metal (and hence to the U level related to it by Eqs. (1) and (2)) can be determined from w — the metal-to-solution electronic work function. It should be noted that the work functions comprise variations in internal energy. For going from these to free energies, a correction has to be made for the entropy of delocalized electrons (in a gas or liquid), determined by the formula for the entropy of ideal gas... 

The entropy of ideal gas is given in eg. (d.22). For an isentropic process, AS s = o. Applying this condition to eg. fd.22) we obtain a relationship between pressure and temperature along the isentropic path ... 

The equations given for enthalpy and entropy of ideal-gas mixture were given here without proof. They can be proven using the tools of statistical mechanics, but this is beyond the scope of this book. Nonetheless, we can arrive at these equations by qualitative arguments. Since molecules in the ideal-gas state do not interact, the internal energy of the mixture is the same as the total internal energy of the pure components at same pressure and temperature this means = o. And since the volume of the mixture is the sum of the pure component volumes, we conclude the same for enthalpy, or AHm > = o. 

On the other hand. Equation (5.41) shows that the effect of pressure on the entropy of ideal gas is not zero, and therefore pressure also affects the ideal gas Gibbs and Helmholtz energies. 

Values for the free energy and enthalpy of formation, entropy, and ideal gas heat capacity of carbon monoxide as a function of temperature are listed in Table 2 (1). Thermodynamic properties have been reported from 70—300 K at pressures from 0.1—30 MPa (1—300 atm) (8,9) and from 0.1—120 MPa (1—1200 atm) (10). 

To understand the flow in turbomachines, an understanding of the basic relationships of pressure, temperature, and type of flow must be acquired. Ideal flow in turbomachines exists when there is no transfer of heat between the gas and its surroundings, and the entropy of the gas remains unchanged. This type of flow is characterized as a rever.sible adiabatic flow. To describe this flow, the total and static conditions of pressure, temperature, and the concept of an ideal gas must be understood. 

Figure 1.4 The entropy of ideal He gas as a function of pressure and temperature is restricted to the surface shown in the figure. Thus, specifying p and T fixes 5m.

Figure 2.13 Mixing of ideal gas A with ideal gas B at constant temperature and constant total pressure. The entropy change AS is given by equation (2.78).

The entropy changes ASa and ASB can be calculated from equation (2.69), which applies to the isothermal reversible expansion of ideal gas, since AS is independent of the path and the same result is obtained for the expansion during the spontaneous mixing process as during the controlled reversible expansion. Equation (2.69) gives... 

Adiabatic processes are examples of (d). If a mole of ideal gas is allowed to expand adiabatically into an evacuated bulb to twice its initial volume, the entropy of the gas increases by 5.76 J K-1 mol-1. No entropy change occurs in the surroundings, since there is no exchange of heat. Hence, 5.76 J K-1 mol-1 is the net increase in entropy in the universe. 

Comparison and agreement with the calorimetric value verifies the assumption that So = 0. For example, we showed earlier that the entropy of ideal N2 gas at the normal boiling point as calculated by the Third Law procedure had a value of 152.8 0.4 J-K mol. The statistical calculation gives a value of 152.37 J K -mol-1, which is in agreement within experimental error. For PH3, the Third Law and statistical values at p 101.33 kPa and T— 185.41 K are 194.1 0.4 J K, mol 1 and 194.10 J-K 1-mol 1 respectively, an agreement that is fortuitously close. Similar comparisons have been made for a large number of compounds and agreement between the calorimetric (Third Law) and statistical value is obtained, all of which is verification of the Third Law. For example, Table 4.1 shows these comparisons for a number of substances. 

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. 

Calculate the entropy change associated with the isothermal expansion of 5.25 mol of ideal gas atoms from 24.252 L to 34.058 L. 

The translational partition function is a function of both temperature and volume. However, none of the other partition functions have a volume dependence. It is thus convenient to eliminate the volume dependence of 5trans by agreeing to report values that use exclusively some volume that has been agreed upon by convention. The choices of the numerical value of V and its associated units define a standard state (or, more accurately, they contribute to an overall definition that may be considerably more detailed, as described further below). The most typical standard state used in theoretical calculations of entropies of translation is the volume occupied by one mole of ideal gas at 298 K and 1 atm pressure, namely, y° = 24.5 L. 

Determine the entropy change of a sample of ideal gas when its pressure is changed isothermally, Section 7.3. 

Consider the distribution of ideal gas molecules among three bulbs (A, B, and C) of equal volume. For each of the following states, determine the number of ways (W) that the state can be achieved, and use Boltzmann s formula to calculate the entropy of the state ... 

The thermodynamic properties of a substance in the state of ideal gas are calculated as the sums of contributions from translation and rotation of a molecule as a whole, vibrations and internal rotation in the molecule, and electronic excitation. For example, for entropy and heat capacity the following equations hold ... 

Fig. 4.7 Scheme of statistical thermodynamic calculations of ideal-gas entropy for the compounds without internal rotation... 

It is informative, however, to consider the dependence of this function on the temperature. Since we know it is characteristic of the pure gas, we consider only 1 mole of a pure gas. Moreover, we limit the discussion to an ideal gas. There are two possible methods, one concerning the energy and entropy and the other the enthalpy and entropy, but we use only the energy and entropy here. The differential of the energy of 1 mole of ideal gas is dE = v dT. On... 

Two 3-liter bulbs are connected through a stopcock. One contains 0.5 mole of an ideal gas at 27°C, and the other is evacuated. Find the increase in entropy of the gas which occurs on opening the stopcock. 

Entropy gained by the system of ideal gas during isothermal expansion stage is also... 

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