A gas is taken from state A to state B along two different paths, shown in the pressure-volume diagram. Along path ACB it absorbs $80\ \text{J}$ of heat and does $30\ \text{J}$ of work. Along path ADB it does $10\ \text{J}$ of work. Later the gas is brought back from B to A along the curved path, and $20\ \text{J}$ of work is done on the gas on the way. Which statement is correct?

Fig. 1: Pressure-volume diagram with states A (lower pressure, smaller volume) and B (higher pressure, larger volume). Path ACB goes up and then right, path ADB goes right and then up, and a curved path runs from B back to A.