**Heat Engine Efficiency Formula**

Under Thermodynamics, Heat engine is a system that converts heat energy and chemical energy into mechanical energy. This occurs by bringing a working substance from higher temperature state to a lower temperature state. Â

The heat engine efficiency is the measure of energy which can be converted to work as a fraction of the total energy. The mathematical representation of an equation for calculating the efficiency is expressed by

The heat engine efficiency is a measure of the energy that can be converted to work as a fraction of the total energy. The concept can be expressed mathematically in an equation for calculating efficiency. Accordingly the heat engine efficiency formula is given by

**Î· = (T****h ****âˆ’ T****l**** / T****h**** ) **

Where,

Î· = Heat Engine Efficiency

Th = Higher temperature

Tl = Lower temperature state

The numerical value of efficiency is a fraction having a value between 0 and 1. Sometimes it is more convenient to express efficiency as a percentage rather than a fraction. This is done by applying the comparable formula.

**%Î· = 100 (T****h****âˆ’T****l**** / T****h****)**

Here, the efficiency is a value between 0% and 100%. Both the equations are equivalent and represent the same information. The ratio of the available energy to the total energy describes the maximum efficiency of a heat engine.

**Example 1**

Water near the surface of a tropical ocean has a temperature of 298.5 K, whereas the temperature of the water 700m underground is 290 K. Determine the efficiency of such an engine.

**Solution:**

Given parameters are,

Th = 298.5 K

TI = 290 K

The maximum efficiency is the efficiency that an engine would possess operating between these two temperatures.

Substitute the value in the given formula, we get

Î· = (Th âˆ’ Tl / Th)

Â Â Â = (298.5 âˆ’ 290 / 298.5)

Therefore, maximum efficiency, Î· = 0.028 (2.8%)

**Example 2**

The minimum power to drive a heat pump which maintains a house at 30oC is 5KW. If the temperature outside is 5oC, calculate the amount of heat the house loses per minute.

**Solution:**

The given parameters are

Th= 303.15 K

TI= 278.15 K

The heat efficiency formula is given by,

Î· = (Th âˆ’ Tl / Th)

Â Â = (303.15 âˆ’ 278.15 / 303.15)

Therefore, Î· = 0.082 (8.2%)