Answer:
the maximum possible coefficient performance is 13.7
Explanation:
inside temperature, [tex]T_{C}[/tex] = 61 F = 289.26 K
outside temperature, [tex]T_{H}[/tex] = 99 F = 310.37 K
coefficient of performance, COP (real) = 3.2
according to Carnot's theorem, the coefficient of performance is
[tex]COP_{max}[/tex] = [tex]\frac{T_{C} }{T_{H}-x_{C} }[/tex]
where
[tex]T_{C}[/tex] is cold temperature
[tex]T_{H}[/tex] is hot temperature
thus,
[tex]COP_{max}[/tex] = [tex]\frac{289.26}{310.37-289.26}[/tex]
= 13.7
