Question

Two moles of an ideal gas $(C_{p,m}=\frac{5}{2}R)$ is heated from 300 K to 600 K. Calculate $△S_{gas},$ if process is carried out at constant volume:

• A. $5Rln2$
• B. $\frac{3}{5}Rln2$
• C. $3Rln2$
• D. $-3Rln2$

Answer 1

The correct option is C $3Rln2$

We know for ideal gas, the formula to calculate change in entropy,
$△S_{gas}=n{C}_{v,m}ln\frac{T_2}{T_1}+Rln\frac{V_2}{V_1}$
At constant volume, means $V_2=V_1$
$△S_{gas}=n{C}_{v,m}ln\frac{T_2}{T_1}+Rln1$
$△S_{gas}=n{C}_{v,m}ln\frac{T_2}{T_1}$ $\because ln1=0$
$=2\times (\frac{5}{2}-1)Rln2\because (C_{v,m}=C_{p,m}-R)$
$\Rightarrow △S_{gas}=3Rln2$