# Heat Engines, Refrigerators and Heat pumps

• A heat engine is a device which converts thermal energy in to other useful forms of energy such as Mechanical energy, Electrical energy
• Efficiency of heat engine \tt \eta=1-\frac{Q_2}{Q_1}=1-\frac{T_2}{T_1}, where Q1 is the absorbed heat and Q2 is the rejected heat.
• The efficiency of an irreversible engine is always less than or equal to that of reversible engine when operated between the same temperature limits.
• A refrigerator is just reverse to heat engine in refrigerator the working substance extracts an amount of heat from cold reservoir.
• Coefficient of performance of a refrigerator \tt \beta=\frac{Q_2}{W}, where Q2 is amount of heat extracts from cold reservoir. W is the external work.

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1. Thermal efficiency of a heat engine is given by \tt \eta = \frac{Work \ done / cycle}{Total \ amount \ of \ heat \ absorbed/cycle}
\tt \eta = 1 - \frac{Q_{2}}{Q_{1}} = 1 - \frac{T_{2}}{T_{1}}

2. A refrigerator or heat pump is a device used for cooling things. It absorb heat from sink at lower temperature and reject a large amount of heat to source at higher temperature.
Coefficient of performance of refrigerator is given by
\beta = \frac{Q_{2}}{W} = \frac{Q_{2}}{Q_{1} - Q_{2}} = \frac{T_{2}}{T_{1} - T_{2}}

3. Relation between efficiency (η) and coefficient of performance (β)
\beta = \frac{1 - \eta}{\eta}