Coefficient of Performance of Reversible Heat Pump Cycles

Coefficient of performance of reversible heat pump cycles working between given hot and cold reservoirs

\(\displaystyle \gamma = \frac{Q_H}{W_R} = \frac{Q_H}{Q_H - Q_C} = \frac{T_H}{T_H - T_C}\)

Symbols

\(\gamma\) — coefficient of performance of reversible heat pump cycle
\(Q_H\) — heat rejection to hot reservoir
\(Q_C\) — heat absorption from cold reservoir
\(W_R\) — work input to reversible heat pump cycle
\(T_H\) — thermodynamic temperature of the hot reservoir
\(T_C\) — thermodynamic temperature of the cold reservoir

Schematic

Inputs & Outputs

\(T_C\) — cold reservoir temperature (K)

\(T_H\) — hot reservoir temperature (K)

γ (-)

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Plot

The plot shows γ vs T_H for different T_C values. The red dot marks the current operating point for the input T_C value's curve — drag it or use the T_H slider above to see how γ changes as T_H changes at the current input T_C value.