One mole of an ideal monatomic gas expands reversibly from the same initial state $(P_{1}, V_{1}, T_{1})$ to the volume $2 V_{1}$ , once isothermally and once adiabatically. Select the correct statement(s).

Answer: A, B, C

In the isothermal path

T

is constant, so

Δ U = 0

and the gas absorbs heat equal to the work it does. In the adiabatic path

q = 0

, so the gas does work at the expense of

U

and cools, giving

Δ U < 0

and less work than in the isothermal case. Hence

Δ U

differs between the paths, and statements 1, 2 and 3 are correct.