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 = Pa, volume = Va) and expands isothermally at temperature TH until point b (pressure = Pb, volume = Vb) is reached. During this expansion, the input heat of magnitude |QH| enters the gas from the hot reservoir of the engine. Then, from point b to point c (pressure = Pc, volume = Vc), the gas expands adiabatically. Next, the gas is compressed isothermally at temperature TC from point c to point d (pressure = Pd, volume = Vd). During this compression, heat of magnitude |QC| 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 |QC|/ |QH| =TC/TH.

Transcribed Image Text:

Isotherm temperature TH dIsotherm C temperature To Volume