Heat Engine | Sahithyan's Notes

A device that takes heat from a high-temperature source, converts part of that heat into useful work, and rejects the remaining heat to a low-temperature sink.

Carnot Heat Engine

Aka. reversible heat engine. All processes are reversible.

All carnot engines working with the same two thermal reservoirs have the same efficiency.

\frac{Q_H}{Q_L} = \frac{T_H}{T_L}

Here:

$T_H$ - temperature of hot reservoir in Kelvin
$T_L$ - temperature of cold reservoir in Kelvin
$Q_H$ - heat taken from hot reservoir
$Q_L$ - heat rejected to cold reservoir

Internal Combustion Heat Engine

Combustion inside cylinder (SI, CI engines).

External combustion

Heat supplied externally (Brayton closed cycle).

Carnot Principle

The efficiency of a reversible heat engine operating between two thermal reservoirs is always greater than the the efficiency of an irreversible heat engine operating between the same reservoirs.

Reverse Heat Engine

Heat Pumps and refrigerators. Transfers heat from a cooler body to a hotter body, with the aid of work input. Reversed heat machines. Air conditioners work similarly to refrigerators.

Technically not heat engines. Opposite operation of heat engines.

Machine	Objective
Heat Pump	Heat up an environment by pumping heat into the concerned environment.
Refrigerator	Cool an environment by pumping heat out from the concerned environment.

Coefficient of Performance

Alternative to thermal efficiency. Used in analysis of heat pumps and refrigerators. Always greater than or equal to 1.

\begin{equation} \nonumber \begin{split} \text{COP}_\text{heat pump} & = \frac{Q_{\text{H}}}{W_\text{in}} = \frac{1}{1 - \frac{Q_L}{Q_H}} \\ \text{COP}_\text{ref} & = \frac{Q_{\text{L}}}{W_\text{in}} = \frac{1}{\frac{Q_H}{Q_L} - 1} \end{split} \end{equation}

Relationship between the 2:

\text{COP}_\text{heat pump} - \text{COP}_\text{ref} = 1