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.
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
η = (Th − Tl / Th )
η = 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.
%η = 100 (Th−Tl / Th)
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.
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.
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
η = (Th − Tl / Th)
= (298.5 − 290 / 298.5)
Therefore, maximum efficiency, η = 0.028 (2.8%)
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.
The given parameters are
Th= 303.15 K
TI= 278.15 K
The heat efficiency formula is given by,
η = (Th − Tl / Th)
= (303.15 − 278.15 / 303.15)
Therefore, η = 0.082 (8.2%)