A certain engine contains n moles of an ideal gas whose molecules each have ν degrees of freedom. It begins its cycle at pressure, volume, and temperature p0, V0, T0. In stage 1 it expands isobarically to volume 2V0. In stage 2 its pressure drops isochorically to p0/2. In stage 3 it is compressed isobarically back to its original volume, V0. In stage 4 it is heated isochorically back to its starting point.
(a) Sketch this cycle on a p–V diagram.
(b) Express T0 in terms of (p0, V0, and n).
(c) Make a table expressing the work done, the heat added, and the change in internal energy for the engine in each of the four stages, expressing them in terms of nRT0.
(d) What is the efficiency of this engine?
(e) The maximum efficiency of an engine operating between the temperature extremes Th and Tc is given by e = (Th − Tc)/Th. What would be the maximum efficiency of an engine operating between the temperature extremes of the engine considered above?
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