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For one mole of an ideal gas undergoing a reversible adiabatic process, which of the following relations is correct? (gamma = Cp/Cv, T = temperature, V = volume, P = pressure)

1. (A) TV^(gamma-1) = constant
2. (B) PV^gamma = constant
3. (C) T^gamma * P^(1-gamma) = constant
4. (D) All of the above are correct

Correct answer: (D) All of the above are correct

Solution

For a reversible adiabatic process: PV^gamma = constant (Poisson's law). Using PV = RT: (RT/V)*V^gamma = constant => TV^(gamma-1) = constant. Also: P*(RT/P)^gamma = constant => T^gamma / P^(gamma-1) = constant => T^gamma * P^(1-gamma) = constant. All three forms are equivalent expressions of the same adiabatic constraint.

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