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# Refrigeration Formulas

## Compression work, coefficient of performance and more

### Compression Work

Compressor 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 = hl - he                                             (4)

where

NRE = Net Refrigeration Effect (Btu/lb)

hl = enthalpy of vapor leaving evaporator (Btu/lb)

he = 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 (ft3/min)

c = capacity (Btu/min)

v = volume of gas entering compressor (ft3/lb)

NRE = Net Refrigeration Effect (Btu/lb)

### Heat of Compression

h = hlc - hec                                                   (7)

where

h = heat of compression (Btu/lb)

hlc = enthalpy of vapor leaving compressor (Btu/lb)

hec = enthalpy of vapor entering compressor (Btu/lb)

### Volumetric Efficiency

μ = 100 wa / wt                                         (8)

where

μ = volumetric efficiency

wa = actual weight of refrigerant

wt = theoretical weight of refrigerant

### Compression Ratio

CR = ph / ps                                                (9)

where

CR = compression rate

ph = head pressure absolute (psia)

ps = suction pressure, absolute (psia)

## Related Topics

• Air Conditioning - Air Conditioning systems - heating, cooling and dehumidification of indoor air for thermal comfort

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