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A thermodynamic process 1 to 2 to 3 involving one mole of helium is described as follows: states 1 and 3 lie on the same isochore (constant volume V), the total heat supplied during the entire process 1 to 2 to 3 is zero, and state 2 lies off this isochore. Choose the CORRECT statement(s).

1. The volume at state 2 depends on the pressure at state 2.
2. The volume at state 2 is independent of the pressure at state 2.
3. The volume at state 2 is 4V.
4. Heat supplied will be positive if the cycle 1 to 2 to 3 to 1 is completed.

Correct answer: The volume at state 2 is independent of the pressure at state 2.

Solution

Since 1 and 3 are on the same isochore (V constant), the process 3 to 1 is isochoric (no work). The overall process 1 to 2 to 3 has Q = 0. By first law: delta_U (1 to 3) = -W (1 to 2 to 3). The work done in 1 to 2 to 3 depends on path through state 2. For helium (monatomic): Cv = 3R/2, Cp = 5R/2. The analysis of all possible paths through state 2 shows that the volume V2 at state 2 is determined solely by the constraint Q=0 and doesn't depend on P2; specifically V2 = 4V regardless of P2.

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