Question

Air conditioners are rated by their coefficient of performance at 61 ∘ F inside temperature and 99 ∘ F outside temperature. An efficient but realistic air conditioner has a coefficient of performance of 3.2. What is the maximum possible coefficient performance?

Answer 1

Answer:

the maximum possible coefficient performance is 13.7

Explanation:

inside temperature, $T_{C}$ = 61 F = 289.26 K

outside temperature, $T_{H}$ = 99 F = 310.37 K

coefficient of performance, COP (real) = 3.2

according to Carnot's theorem, the coefficient of performance is

$COP_{max}$ = $\frac{T_{C} }{T_{H}-x_{C} }$

where

$T_{C}$ is cold temperature

$T_{H}$ is hot temperature

thus,

$COP_{max}$  = $\frac{289.26}{310.37-289.26}$

             = 13.7