A Carnot freezer takes heat from water at \(0\,^oC\) inside it and rejects it to the room at a temperature of \(27\,^oC\). The latent heat of ice is \(336 \times 10^3\, J\,kg^{-1}\).  lf \(5\, kg\) of water at \(0\,^oC\) is converted into ice at  \(0\,^oC\) by the freezer, then the energy consumed by the freezer is close to

\(\frac{{{Q_{sink}}}}{{{Q_{source}}}} - \frac{{{T_{sink}}}}{{{T_{source}}}}\)

\(\therefore {Q_{source}} = \frac{{{T_{source}}}}{{{T_{sink}}}} \times {Q_{sink}}\)

Energy consumed by freezer

\(\therefore {W_{output}} = {Q_{source}} - {Q_{sink}}\)

\( = {Q_{sink}}\left( {\frac{{{T_{source}}}}{{{T_{sink}}}} - 1} \right)\)

\(Given:\,{T_{source}} = {27^ \circ }C + 273 = 300K,\)

\({T_{sink}} = {0^ \circ }C + 273 = 273\,K\)

\({W_{output}} = 5 \times 336 \times {10^3}\left( {\frac{{300}}{{273}} - 1} \right) = 1.67 \times {10^5}J\)