Adding heat to a gas during a cycle influences the net work done by the gas on its surroundings. In this case, the work done by the gas is calculated by considering the individual work values: Wbc is -3315.4J and Wca is -2108.98J. The total work done can be determined by summing these values, resulting in a net work of -5424.38J. The net heat added to the gas is 1200J, which indicates that the gas does work on its surroundings despite the heat input. Therefore, the relationship between heat added and work done is crucial in understanding the thermodynamic cycle.