A Carnot engine, having an efficiency of η = (1)/(10) as heat...

For engine and refrigeration operating between two same temperature, the relationship between efficiency and coefficient of performance $\beta$,

$η = \dfrac{1}{1 + \beta}$

$\dfrac{1}{10} = \dfrac{1}{1 + \beta} ⇒ \beta = 9$

From the principle of the refrigerator, coefficient of performance is given by the ratio of the amount of energy absorbed from the reservoir to work, i.e.,

$\dfrac{{Q}_{2}}{W} = \beta$

$\dfrac{{Q}_{2}}{10} = 9$

${Q}_{2} = 90J$.