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A diatomic gas with adiabatic index γ = 1.4 is initially at a pressure of 2 atm. It is compressed adiabatically until its temperature increases from 27°C to 927°C. What is the final pressure of the gas?

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

Correct answer: 256 atm

Solution

Adiabatic: P^(1-gamma)*T^gamma = const, so P2 = P1*(T2/T1)^(gamma/(gamma-1)). With T2/T1 = 1200/300 = 4 and gamma/(gamma-1) = 3.5: P2 = 2*4^3.5 = 2*128 = 256 atm.

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