Answer to Question #100864 in Molecular Physics | Thermodynamics for Pham Anh Khoa

Question

Calculate the change in entropy of gases in the following cases: a) A 3.0 mol sample of an ideal gas expands reversibly and isothermally at 350 K until its volume doubled. b) The temperature of 1.0 mol of an ideal monatomic gas is raised reversibly from 200 K to 300 K, with its volume kept constant.

Answer 1

The change of entropy of an ideal gas

$$\Delta S(T,V)=n C_V \ln\frac{T_f}{T_i}+nR\ln\frac{V_f}{V_i}$$

(a) $T_f=T_i$, $V_f=2V_i$

$$\Delta S(T,V)=nR\ln\frac{V_f}{V_i}=3.0\times 8.3\ln 2=17.3\:\rm J/K$$

(b) $T_i=200\:{\rm K}, \; T_f=300\:{\rm K},$ $V_f=V_i$

$$\Delta S(T,V)=n C_V \ln\frac{T_f}{T_i}=1.0\times 12.5\times\ln\frac{300}{200}=5.0\:\rm J/K$$