Example: The Otto cycle

Here is a particular example of a heat engine - the Otto cycle, which approximates the working cycle of a car engine. The work done is the area enclosed by the curve in the $P-V$ plane. The expansion and compression stokes are adiabatic, so heat enters and leaves only during the constant volume phases. (This ignores the exhaust stroke, which can be modelled as a horizontal line from point 1 left and then right again.)

This link, courtesy of Xing Min Wang, has clear and helpful animations of the idealised Otto, Diesel and Carnot cycles.

Animated Engines has animations of a large variety of realistic engines, though without the accompanying cycles.

The efficiency of a reversible Otto cycle for an ideal gas is

$$\eta=1-\left({V_2\over V_1}\right)^{\gamma-1}$$

Try to prove it yourself. More details are given here. You should also convince yourself that the efficiency is less than that of a Carnot engine acting between the reservoirs at the hottest and coldest ponts of the cycle.