## Question

###### An ideal refrigerator or ideal heat pump is equivalent to a Carnot engine running in reverse. That is, energy $mid Q_{d}$ is taken in from a cold reservoir and energy $left|Q_{h}ight|$ is rejected to a hot reservoir. (a) Show that the work that must be supplied to run the refrigerator or heat pump is$$W=frac{T_{h}-T_{c}}{T_{c}}left|Q_{c}ight|$$(b) Show that the coefficient of performance of the ideal refrigerator is$$mathrm{COP}=frac{T_{c}}{T_{h}-T_{c}}$$

An ideal refrigerator or ideal heat pump is equivalent to a Carnot engine running in reverse. That is, energy $mid Q_{d}$ is taken in from a cold reservoir and energy $left|Q_{h} ight|$ is rejected to a hot reservoir. (a) Show that the work that must be supplied to run the refrigerator or heat pump is $$ W=frac{T_{h}-T_{c}}{T_{c}}left|Q_{c} ight| $$ (b) Show that the coefficient of performance of the ideal refrigerator is $$ mathrm{COP}=frac{T_{c}}{T_{h}-T_{c}} $$

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