# Refrigeration Formulas

## Compression work, coefficient of performance and more

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### Compression Work

Compression work can expressed as

*W = h q (1)*

*where *

*W = compression work (Btu min)*

*h = heat of compression (Btu/lb)*

*q = refrigerant circulated (lb/min)*

### Compression Horsepower

Compression horsepower can be expressed as

*P = W / 42.4 (2)*

*where *

*P = compression power (hp)*

*W = compression work (Btu min)*

Alternatively

*P = c / (42.4 COP) (2b)*

*where *

*P = compression power (hp)*

*c = capacity (Btu/min)*

*COP = coefficient of performance*

### Compression horsepower per Ton

*p = 4.715 / COP (2c)*

*where *

*p = compressor horsepower per Ton (hp/Ton)*

*COP = coefficient of performance*

### COP - Coefficient of Performance

*COP = NRE / h (3)*

*where *

*COP = Coefficient of Performance*

*NRE = Net Refrigeration Effect (Btu/lb)*

*h = heat of compression (Btu/lb)*

### Net Refrigeration Effect

Net refrigeration effect can be expressed as

*NRE = h*_{l}* - h*_{e}* (4)*

*where *

*NRE = Net Refrigeration Effect (Btu/lb)*

*h _{l} = enthalpy of vapor leaving evaporator (Btu/lb)*

*h _{e} = enthalpy of vapor entering evaporator (Btu/lb)*

### Capacity

*c = q NRE (5)*

*where *

*c = capacity (Btu/min)*

*q = refrigerant circulated (lb/min)*

*NRE = Net Refrigeration Effect (Btu/lb)*

### Compressor Displacement

*d = c v / NRE (6)*

*where *

*d = compressor displacement (ft ^{3}/min)*

*c = capacity (Btu/min)*

*v = volume of gas entering compressor (ft ^{3}/lb)*

*NRE = Net Refrigeration Effect (Btu/lb)*

### Heat of Compression

*h = h_{lc} - h_{ec } (7)*

*where *

*h = heat of compression (Btu/lb)*

*h _{lc} = enthalpy of vapor leaving compressor (Btu/lb)*

*h _{ec} = enthalpy of vapor entering compressor (Btu/lb)*

### Volumetric Efficiency

*μ = 100 w _{a} / w_{t} (8)*

*where *

*μ* = volumetric efficiency

*w _{a} = actual weight of refrigerant*

*w _{t} = theoretical weight of refrigerant*

### Compression Ratio

*CR = p _{h} / p_{s} (9)*

*where *

*CR = compression rate*

* p _{h} = head pressure absolute (psia) *

*p _{s} = suction pressure, absolute (psia) *

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