Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 61

A gas is to be expanded from initial state \( i \) to final state \( f \) along either path 1 or path 2 on a \( p-V \) diagram. Path 1 consists of three steps: an isothermal expansion (work is 40 J in magnitude), an adiabatic expansion (work is 20 J in magnitude), and another isothermal expansion (work is 30 J in magnitude). Path 2 consists of two steps: a pressure reduction at constant volume and an expansion at constant pressure. What is the change in the internal energy of the gas along path 2?