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A gas at 27°C temperature and 30 atmospheric pressure is allowed to expand to atmospheric pressure. If the volume becomes 10 times its initial volume, then the final temperature becomes

1. 100°C
2. 173°C
3. 273°C
4. -173°C

Correct answer: -173°C

Solution

Using the combined gas law, \( P_1 V_1 / T_1 = P_2 V_2 / T_2 \). Substituting \( P_1 = 30P, V_1 = V, T_1 = 300 \text{ K}, P_2 = P, V_2 = 10V \), we solve for \( T_2 \) and find \( T_2 = 100 \text{ K} \), which is \( -173°C \).

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