The drawing (not to scale) shows the way in which the

Chapter , Problem 61

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The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point a (pressure 5 Pa, volume 5 Va) and expands isothermally at temperature TH until point b (pressure 5 Pb, volume 5 Vb) is reached. During this expansion, the input heat of magnitude uQHu enters the gas from the hot reservoir of the engine. Then, from point b to point c (pressure 5 Pc, volume 5 Vc), the gas expands adiabatically. Next, the gas is compressed isothermally at temperature TC from point c to point d (pressure 5 Pd, volume 5 Vd). During this compression, heat of magnitude uQCu is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point d to point a, where the gas is back in its initial state. The overall process a to b to c to d to a is called a Carnot cycle. Prove for this cycle that uQCu/uQHu 5 TC/TH.