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A diatomic gas initially at 18°C is compressed adiabatically to one eighth of its original volume. The temperature after compression will be

1. 18°C
2. 668.4K
3. 395.4°C
4. 144°C

Correct answer: 395.4°C

Solution

For an adiabatic process, the relation between temperature and volume is given by \( T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1} \). For a diatomic gas, \( \gamma = 1.4 \). Substituting the values and solving, the final temperature is approximately 395.4°C.

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