Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 59

Figure 19.10 shows two paths that may be taken by a gas from an initial point \(i\) to a final point \(f\). Path 1 consists of an isothermal expansion (work is 50 J in magnitude), an adiabatic expansion (work is 40 J in magnitude), an isothermal compression (work is 30 J in magnitude), and then an adiabatic compression (work is 25 J in magnitude). What is the change in the internal energy of the gas if the gas goes from point \(i\) to point \(f\) along path 2?