Answer
$|W| = 5.0 \space J $
Work Step by Step
Finally at the lowest, T= 50K
$|W| = \frac{|Q_L|}{K_C}$
Where
$K_C = \frac{T_L}{T_H - T_L} $
and $W = 1.0 J$
Substitute all the unknowns into the equation
$|W| = (1.00 J)( \frac{T_H - T_L}{T_L})$
$|W| = (1.00 J) (\frac{300 K- 50 K}{50K} )$
We obtain
$|W| = 5.0 \space J $
