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At 27°C a gas is compressed suddenly such that its pressure becomes (1/8) of original pressure. Final temperature will be (γ = 5/3)

1. 420 K
2. 300 K
3. 142°C
4. 327°C

Correct answer: 300 K

Solution

For an adiabatic process, the relation is \( T_1 P_1^{(γ-1)/γ} = T_2 P_2^{(γ-1)/γ} \). Substituting \( T_1 = 300 \) K, \( P_2/P_1 = 1/8 \), and \( γ = 5/3 \), we find \( T_2 = 300 \) K.

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