Answer
a) $6.325$
b) $ 31.62J/s$
c) $231.62J/s$
Work Step by Step
We have
$ T_H = 20^oC =293K$
$T_C = -20^oC = 253K$
$P_C = Q_C / t = 200J/s$
a) We know that
$ K= \frac{T_C}{T_H-T_C}$
$K= \frac{253K}{40K}$
$K= 6.325$
b) We also know
$ K= \frac {Q_C}{W}$
Dividing numerator and denominator on RHS by $t$ we get
$K = \frac{P_C}{P_W} $
where $P_W$ is rate at which work is done on refrigerator
$6.325 = (200J/s)/(P_W)$
$P_W = 31.62J/s$
c) Also we have
$Q_H= Q_C +W$
Dividing throughout by$t$ we get
$P_H = P_C +P_W$
where $P_H$ is rate at which heat is exhausted to hot side
$P_H = 200J/s + 31.62J/s$
$P_H = 231.62J/s$
