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A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27°C to 927°C. The pressure of the gas in final state is:

1. 28 atm
2. 68.7 atm
3. 256 atm
4. 8 atm

Correct answer: 68.7 atm

Solution

For an adiabatic process, we use the relation \( P_1 T_1^{\frac{\gamma}{\gamma-1}} = P_2 T_2^{\frac{\gamma}{\gamma-1}} \). Substituting \( \gamma = 1.4 \), \( T_1 = 300 \, K \), \( T_2 = 1200 \, K \), and \( P_1 = 2 \, atm \), we solve for \( P_2 \) to get approximately 68.7 atm.

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