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An ideal gas undergoes a process described by PV^(5/3) = constant. The gas is taken from state A(P1, V1) to state B(P2, V2). If the work done by the gas equals (x/2)(P1*V1 - P2*V2), find the value of x.

1. 1
2. 2
3. 3
4. 5

Correct answer: 3

Solution

For a polytropic process PVⁿ = constant, the work done is W = (P1*V1 - P2*V2)/(n - 1). With n = 5/3, W = (P1*V1 - P2*V2)/(5/3 - 1) = (P1*V1 - P2*V2)/(2/3) = (3/2)(P1*V1 - P2*V2). Comparing with x/2 * (P1*V1 - P2*V2), we get x/2 = 3/2, so x = 3.

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