Answer
$|Q_L| = 20.4 J$
Work Step by Step
To find the heat removed from the room, use the following equation
$|Q_L| = |W|K_C$
Where
$K_C = \frac{T_L}{T_H - T_L} $
and $W = 1.0 J$ since it stated "with every joule" in the question. So,
$|Q_L| = (1.00J) (\frac{T_L}{T_H - T_L})$
Where $96^o F = 308.7K$ and $70^o F = 294.3K$
$|Q_L| = (1.00J) (\frac{294.3K}{308.7K - 294.3K}) $
$|Q_L| = 20.4 J$
