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Three identical gas samples A, B, and C (each with gamma = 3/2) start with the same volume V. Each sample is then expanded to 2V: sample A undergoes an adiabatic process, sample B an isobaric process, and sample C an isothermal process. If the final pressure is the same (P_f) for all three, what is the ratio of their initial pressures P_A: P_B: P_C?

1. 2*sqrt(2): 2: 1
2. 2*sqrt(2): 1: 2
3. sqrt(2): 1: 2
4. 2: 1: sqrt(2)

Correct answer: 2*sqrt(2): 1: 2

Solution

For A (adiabatic), P_A*(V)^(3/2) = P_f*(2V)^(3/2), giving P_A = 2^(3/2)*P_f = 2*sqrt(2)*P_f. For B (isobaric), pressure is constant so P_B = P_f. For C (isothermal), P_C*V = P_f*2V, giving P_C = 2*P_f. Ratio = 2*sqrt(2): 1: 2.

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