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