Carnot Cycles with Irreversible Heat Transfer

heat engine

heat pump

|

T

h

-

T

H



10

|

T

c

-

T

C



12

This Demonstration shows a Carnot cycle operating either as a heat engine or a heat pump, with finite temperature differences between the hot and cold reservoirs and the high and low temperatures of the Carnot cycle, respectively. The entropy changes for the reservoirs (

Δ

S

h

and

Δ

S

c

) and the overall entropy change

Δ

S

total

are calculated. When the temperature differences between the reservoirs and the engine/pump are nonzero, the total entropy change is positive. The entropy change of the engine/pump, which is at steady state, is zero. All energies and entropy changes are per unit time, since these are continuous processes, but the time scale is arbitrary. The cycle efficiency

η

is calculated for the heat engine, and the coefficient of performance (

COP

) is calculated for the heat pump. As the temperature difference between the reservoirs and the engine/pump increases, the efficiency and the coefficient of performance decrease. For the heat engine,

Q

H

is held constant as the temperature differences change. For the heat pump,

Q

C

is held constant as the temperature differences change.