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One mole of an ideal diatomic gas undergoes a cycle: process 1->2 is isochoric (volume constant), process 2->3 is a straight line on the P-V diagram, and process 3->1 is isobaric (pressure constant). If state 1 is (P0, V0), state 2 is (2P0, V0), and state 3 is (P0, 2V0), find the ratio of average molecular speeds at states 1, 2, and 3.

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

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

Solution

With T1 = P0V0/R, T2 = 2P0V0/R, T3 = P0*2V0/R = 2P0V0/R, we get T1:T2:T3 = 1:2:2, so the average speed ratio is sqrt(1):sqrt(2):sqrt(2) = 1:sqrt(2):sqrt(2).

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