Question

A 2.0 mol sample of an ideal monatomic gas undergoes a reversible process at constant volume, increasing its temperature from 400 K to 600K. What is the entropy change of the gas?

Answer 1

Answer on Question #57121, Physics / Molecular Physics | Thermodynamics

A 2.0 mol sample of an ideal monatomic gas undergoes a reversible process at constant volume, increasing its temperature from 400 K to 600 K. What is the entropy change of the gas?

Solution:

For heating or cooling of any system (gas, liquid or solid) at constant volume from an initial temperature $T_0$ to a final temperature $T$, the entropy change is

$$\Delta S = n C_V \ln \left(\frac{T}{T_0}\right)$$

where the constant-volume heat capacity $C_V$ is constant and there is no phase change.

Here $n$ is the number of moles of gas.

In the case of a monatomic gas

$$C_V = \frac{3}{2} R$$

where $R$ is the ideal gas constant

Thus,

$$\Delta S = \frac{3}{2} n R \ln \left(\frac{T}{T_0}\right) = \frac{3}{2} \cdot 2.0 \cdot 8.31 \cdot \ln \left(\frac{600}{400}\right) = 10.1 \frac{\mathrm{J}}{\mathrm{K}}$$

Answer: $\Delta S = 10.1\frac{\mathrm{J}}{\mathrm{K}}$

http://www.AssignmentExpert.com/