Heat Engine Cycle | Sahithyan's Notes

Efficiency

\eta_\text{thermal} = \frac{W_\text{net}}{Q_\text{in}} = 1 - \frac{Q_\text{out}}{Q_\text{in}}

Carnot Cycle

Ideal reversible cycle for a heat engine. Has maximum thermal efficiency for given temperature limits.

Has 4 processes. All processes are reversible.

through the boiler: isothermal heat addition
through the turbine: adiabatic expansion
through the condenser: isothermal heat rejection
through the pump: adiabatic compression

Carnot Efficiency

\eta_\text{Carnot} = 1 - \frac{T_L}{T_H}

Here:

$T_L$ : temperature of the cold reservoir (K)
$T_H$ : temperature of the hot reservoir (K)

No real engine can exceed Carnot efficiency operating between the same temperature limits.

Coefficient of Performance

For reverse heat engines (refrigerators and heat pumps), performance is expressed as Coefficient of Performance (COP) rather than efficiency, since COP can exceed 1.

Refrigerator

\text{COP}_R = \frac{Q_L}{W_\text{net,in}} = \frac{Q_L}{Q_H - Q_L}

Carnot COP for refrigerator:

\text{COP}_{R,\text{Carnot}} = \frac{T_L}{T_H - T_L}

Heat Pump

\text{COP}_{HP} = \frac{Q_H}{W_\text{net,in}} = \frac{Q_H}{Q_H - Q_L}

Relation between the 2 COP values:

\text{COP}_{HP} = \text{COP}_R + 1