Carnot Machine

The Carnot Machine brought to class during the line integral lecture. If you look at the explanation about Carnot cycle you see a lot of line integrals, the integral of the vector field F(p,V) = [0,p]T, in the p-V plane. This is the vector field [0,x]T we have used also for computing area. If there is a temperature gradient, then you can draw two curves in the pV-plane. One curve is when the temperature T1 is large. The other curve when the termperature is lower. Now, if you go counter clockwise around, decreasing the volume and pressure if the temperature is large and decreasing the volume if the temperature and pressure is lower, we have a closed curve in the p-V plane. The work we get is the area.