Carnot Limits On Performance

Heat Engines extract heat from a hot source, convert some of the heat energy into mechanical energy and rejects the remaining heat to a cool sink. A classic example is a steam engine.

$$Maximum \, Theoretical \, Efficiency \,\,\,\,\,\,\,\,\,\,\eta \, = 1 - {T_c \over T_h} $$ $$\eta \, = 1 - {T_c \over T_h} $$

Refrigerators use mechanical energy input to extract heat from a cold environment and reject it to a warmer environment. A classic example of this is a domestic fridge (or freezer.

$$Maximum \, Theoretical \, Coeficient \, of \, Performance \,\,\,\,\,\,\,\,\,\,COP{_r} \, = \, {T_c \over T_h - T_c} $$ $$COP{_r} \, = \, {T_c \over T_h - T_c} $$

Heat Pumps use mechanical energy to extract heat from a cool environment and deliver a larger amount of heat to a warm environment. A classic example of this is a domestic fridge only opposite way around (the fridge is warm at the back).

$$Maximum \, Theoretical \, Coeficient \, of \, Performance \,\,\,\,\,\,\,\,\,\,COP_{hp} \, = \, {T_h \over T_h - T_c} $$ $$COP_{hp} \, = \, {T_h \over T_h - T_c} $$