Refrigeration and Air Conditioning
The bypass factor (B. P. F.) in case of sensible heating of air is (Where td₁ = Dry bulb temperature of air entering the heating coil, td₂ = Dry bulb temperature of air leaving the heating coil, and td₃ = Dry bulb temperature of heating coil)

(td₃ - td₁)/(td₃ - td₂)
(td₃ - td₁)/(td₂ - td₃)
(td₂ - td₃)/(td₃ - td₁)
(td₃ - td₂)/(td₃ - td₁)

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Refrigeration and Air Conditioning
In a vapour compression refrigeration system, a throttle valve is used in place of an expander because

It improves the C.O.P., as the condenser is small
The positive work in isentropic expansion of liquid is very small
It leads to significant cost reduction
It considerably reduces mass of the system

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