Question

Two moles of an ideal gas at $300\, K$ were cooled at constant volume so that the pressure is reduced to half the initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature. Find the total heat absorbed by the gas, if $R$ is the gas constant.

• A. $150\, R J$
• B. $300\, R J$
• C. $75\, R J$
• D. $100 \,R J$

Answer 1

Answer: (B)

For $1$ mol of gas, $Q=C_{v} \Delta T+P \Delta T$
At constant volume, $\Delta T=0$
For $2$ moles of gas, $\Delta=2 C_{v} \Delta T$
From $P V=n R T=2 R \times 300$
and $ \frac{P}{2} V=2 RT _{f}$
$\therefore T_{f}=150\, K$
$\therefore Q=2 C_{v}\left(T_{f}-T_{i}\right)=2 C_{v}(150-300)=-300 C_{v} J$
In the next process,
$Q=2 C_{p} \Delta T=2 C_{p} (300-150)=300 C_{p} J$
$\therefore $ Net heat absorbed $ =-300 C_{v}+300 C_{p} $
$=300\left(C_{p}-C_{v}\right)=300 \,R J$