Isothermal Compression

If we shoved the piston back in, from a volume V₂ to a volume V₁ in Figure (1), we would have to do work on the gas. If we kept the temperature constant, then the pressure would increase along the curve shown in Figure (1) and the work we did would be precisely equal to the area under the curve. In this case work is done on the gas (we could say that during the compression the gas does negative work). When work is done on the gas, the temperature of the gas will rise unless we let heat flow out of the cylinder. Thus if we have an isothermal compression, where there is no increase in the thermal energy of the gas, then we have the pure conversion of useful work into the heat expelled by the piston. This is the opposite of what we want for a power plant.

Figure 1: The work done by an expanding gas is equal to the sum of all pΔ V 's , which is the area under the pressure curve.