Prelecture 31: Slide 6

Here we see the PV diagram for the Stirling engine from the last slide. Steps 2 and 4 are isothermal (that is, constant temperature) transitions made at the temperatures of the hot and cold reservoirs. Steps 1 and 3 are isochoric (that is, constant volume) transitions.

Let's look at each step in the cycle in turn.

In step 1 the volume of the cylinder is held fixed. The gas, which starts at temperature of the cold reservoir, is put in contact with the hot reservoir. Heat flows from the reservoir into the gas, increasing its pressure, until the temperature of the gas is the same as the reservoir.

In step 2 the gas is still in contact with the hot reservoir so that its temperature is fixed. The volume of the cylinder is increased as the piston rises which means the pressure drops.

In step 3 the volume of the cylinder is held fixed. The gas, which starts at temperature of the hot reservoir, is put in contact with the cold reservoir. Heat flows from the gas into the reservoir, decreasing the pressure, until the temperature of the gas is the same as the reservoir.

In step 4 the gas is still in contact with the cold thermal reservoir so that its temperature is fixed. The volume of the cylinder is decreased as the piston falls which means the pressure increases.

On the next slide, we will calculate the efficiency of this engine when the working substance is an ideal gas.