GATE 2022 ME (ME2) – Question 34
Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume $c_v$ is equal to 750 J kg$^{-1}$ K$^{-1}$. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be ______ bar (in integer).
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Correct answer: 2
Explanation
**Step 1: energy balance.** The tank is rigid (no boundary work) and perfectly insulated (no heat), so the only energy input is the stirrer work. The internal energy rises by that amount:
$$W=mc_v\,(T_2-T_1).$$
**Step 2: temperature rise.**
$$T_2-T_1=\frac{225\,000}{1\times750}=300\text{ K}\;\Rightarrow\;T_2=600\text{ K}.$$
**Step 3: pressure.** For a fixed mass in a fixed volume, $p\propto T$:
$$p_2=p_1\frac{T_2}{T_1}=1\times\frac{600}{300}=\mathbf{2\ bar}.$$