Answer
(a) $T_C = 200K = -73.1 ^oC $
(b) $N_c = 3.34 \times 10^4 \space cycles$
Work Step by Step
(a) $Q_C = W - Q_H $
$Q_C = 300J - 400J $
$Q_C = -100J$
So
$T_C = -T_H(\frac{Q_C}{Q_H})$
$T_C = −(800.15 K)(\frac{−100 J}{400 J})$
$T_C = 200K = -73.1 ^oC $
(b)$ Q = -mL_f $
$ Q = -(10.0 kg) (334 \times 10^3 J/kg) $
$ Q = -3.34 \times 10^6 J$
The number of cycles required is
$N_c =\frac{-3.34 \times 10^6 J}{-100J/cycle} $
$N_c = 3.34 \times 10^4 \space cycles$
