Work done by an ideal gas during expansion

Consider an ideal gas at a pressure P enclosed in a cylinder of cross sectional area A.

The gas is then compressed by pushing the piston in a distance dx, the volume of the gas decreasing by dV. (We assume that the change in volume is small so that the pressure remains almost constant with a value P).

Work done on the gas during this compression = dW

Force on piston = PA
So the work done during compression = dW = PAdx = PdV

The first law of thermodynamics can then be written as:


In the PV diagram net work is done by the gas if it expands at the higher temperature and net work is done on the gas if is compressed at the higher temperature.