# UY1: Heat Engines – Thermal Efficiency

First law for an engine cycle says:

Wout = Qh – Qc

,where
Wout is work output by engine
Qh is heat input from hot reservoir
Qc is heat output to cold reservoir

Thermal efficiency is defined to be the ratio of work output to the heat input from the hot reservoir per cycle,

\begin{aligned} e \, &= \frac{W_{\text{out}}}{Q_{h}} \\ &= \frac{Q_{h} \, – Q_{c}}{Q_{h}} \\ &= 1 \, – \frac{Q_{c}}{Q_{h}} \end{aligned}

This thermal efficiency is simply 1 minus the fraction of heat rejected into the cold reservoir.

### Heat Pump: Coefficients of performance

First law for a heat pump is:

$$W_{\text{in}} = Q_{h} – Q_{c}$$

Here, Qh is defined as heat output to hot reservoir and Qc is heat input from cold reservoir, because we are dealing with a heat pump.

In the heating mode, where we are interested in the ratio of heat output into the hot reservoir to the work input per cycle, we define coefficient of performance (for heating):

$$K_{h} = \frac{Q_{h}}{W_{\text{in}}} = \frac{Q_{h}}{Q_{h} – Q_{c}}$$

In the cooling mode, where we are interested in the ratio of heat extracted from the cold reservoir to the work input per cycle, we define coefficient of performance (for cooling):

$$K_{c} = \frac{Q_{c}}{W_{\text{in}}} = \frac{Q_{c}}{Q_{h} – Q_{c}}$$

Next: Definition of second law of thermodynamics

Previous: Heat pumps

Back To Thermodynamics

##### Mini Physics

As the Administrator of Mini Physics, I possess a BSc. (Hons) in Physics. I am committed to ensuring the accuracy and quality of the content on this site. If you encounter any inaccuracies or have suggestions for enhancements, I encourage you to contact us. Your support and feedback are invaluable to us. If you appreciate the resources available on this site, kindly consider recommending Mini Physics to your friends. Together, we can foster a community passionate about Physics and continuous learning.

This site uses Akismet to reduce spam. Learn how your comment data is processed.