Question 7.E.46: Water enters an ice machine at 55°F and leaves as ice at 25°......
Water enters an ice machine at 55^{\circ} \mathrm{F} and leaves as ice at 25^{\circ} \mathrm{F}. If the COP of the ice machine is 2.4 during this operation, determine the required power input for an ice production rate of 28 \mathrm{lbm} / \mathrm{h}. (169 Btu of energy needs to be removed from each \mathrm{lbm} of water at 55^{\circ} \mathrm{F} to turn it into ice at 25^{\circ} \mathrm{F}.)
The COP and the refrigeration rate of an ice machine are given. The power consumption is to be determined.
Assumptions The ice machine operates steadily.
Analysis The cooling load of this ice machine is
\dot{Q}_{L}=\dot{m} q_{L}=(28 \mathrm{lbm} / \mathrm{h})(169 \mathrm{Btu} / \mathrm{lbm})=4732 \mathrm{Btu} / \mathrm{h}
Using the definition of the coefficient of performance, the power input to the ice machine system is determined to be
\dot{W}_{\text {net,in }}=\frac{\dot{Q}_{L}}{\mathrm{COP}_{\mathrm{R}}}=\frac{4732 \mathrm{Btu} / \mathrm{h}}{2.4}\left(\frac{1 \mathrm{hp}}{2545 \mathrm{Btu} / \mathrm{h}}\right)=\mathrm{0 . 7 7 5} \mathrm{~ h p}
