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An ideal gas at 27°C is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (γ = 5/3):

1. 475°C
2. 402°C
3. 275°C
4. 175°C

Correct answer: 475°C

Solution

For an adiabatic process, the relation between temperature and volume is given by \( T_2/T_1 = (V_1/V_2)^{\gamma-1} \). Substituting \( T_1 = 300 \, K \), \( V_1/V_2 = 27/8 \), and \( \gamma = 5/3 \), we get \( T_2 = 300 \times (27/8)^{2/3} \approx 748 \, K \). Converting to Celsius, \( T_2 - 273 = 475 \, ^\circ C \).

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