Question

9.6. In comparing the performance of a real cycle with that of a Carnot cycle, one has in principle a choice of temperatures to use for the Carnot calculation. Consider a vapor-compression refrigeration cycle in which the average fluid temperatures in the condenser and evaporator are TH and TC respectively. Corresponding to TH and TC

​the heat transfer occurs with respect to surroundings at temperature TσH and TσC
​Which provides the more conservative estimate of ωCarnot : a calculation based on THand TC or one based on TσH and TσC?

Answer 1

The Carnot cycle is a theoretical cycle that provides the upper limit of the thermal efficiency that can be obtained for a given temperature difference between the hot and cold reservoirs. According to the Carnot principle, the efficiency of a reversible power cycle is proportional to the temperature difference between the hot and cold reservoirs, and it reaches its maximum value for a Carnot cycle.

The Carnot efficiency is expressed as,η = 1 - Tc / Th

where η is the Carnot efficiency, Tc is the absolute temperature of the cold reservoir, and Th is the absolute temperature of the hot reservoir.

Now, for a vapor-compression refrigeration cycle in which the average fluid temperatures in the condenser and evaporator are TH and TC respectively, the efficiency of the Carnot cycle is calculated based on the maximum and minimum temperatures of the cycle.

The efficiency of a Carnot cycle that corresponds to TH and TC isη = 1 - TC / TH

where η is the Carnot efficiency, TC is the absolute temperature of the cold reservoir (evaporator), and TH is the absolute temperature of the hot reservoir (condenser).On the other hand, the heat transfer occurs with respect to the surroundings at temperature TσH and TσC. Therefore, a calculation based on TσH and TσC provides a more conservative estimate of ωCarnot. Thus, it can be concluded that a calculation based on TσH and TσC provides a more conservative estimate of ωCarnot.