Question

An air conditioner operates exactly as a refrigerator; it removes heat from a cold place (a bedroom, for example) and conveys it to a warmer place (usually the outside). Quantities of practical importance in understanding the efficiency of air conditioners are the rate of heat removal and the electric power input to the unit (i.e., the electric energy consumed per unit time). Find an expression for the coefficient of performance KKK of an air conditioner that has a rate of heat removal HHH and a power consumption PPP .

Answer 1

The expression for coefficient of heat performance is; K = H/P

We are given the expressions;

Coefficient of performance = K

Rate of heat removal = H

Power consumption = P

Formula for coefficient of performance is usually;

K = Q/W

However, the rate of heat removal H can be further expressed as;

H = Q/T

Where;

Q is heat removed

T is time

Similarly, for power consumption, it can also be expressed as;

P = W/T

Where;

W is workdone

T is time taken

Thus, Q = HT and W = PT

Finally;

K = HT/PT

K = H/P

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