91Ó°ÊÓ

Coefficient of performance,\(K = 2.40\)

Mass of water, \(m = 180\;{\rm{kg}}\)

Initial temperature of water,\({T_0} = 25^\circ {\rm{C}}\)

Final temperature of ice,\({T_1} = - 5^\circ {\rm{C}}\)

The expression to calculate the amount of heat when water is converted from \(25^\circ {\rm{C}}\) to \(0^\circ {\rm{C}}\) is given as follows.

\({Q_1} = m{c_w}\Delta T\) …… (i)

Here,\({c_w}\)is the specific heat of water, and\(\Delta T\)is the change in temperature.

The expression to calculate the amount of heat when water is converted from \(0^\circ {\rm{C}}\) of water to \(0^\circ {\rm{C}}\) of ice is given as follows.

\({Q_2} = m{L_f}\) …… (ii)

Here,\({L_f}\)is the fusion of water.

The expression to calculate the amount of heat when water is converted from \(0^\circ {\rm{C}}\) of ice to \( - 5^\circ {\rm{C}}\) of ice is given as follows.

\({Q_3} = m{c_{ice}}\Delta T\) …… (iii)

Here,\({c_{ice}}\)is the specific heat of ice.

The expression to calculate the total heatremoved from the water at \(25^\circ {\rm{C}}\) to convert it to ice at \( - 5^\circ {\rm{C}}\) is given as follows.

\({Q_C} = {Q_1} + {Q_2} + {Q_3}\) …… (iv)

The specific heat of the ice,\({c_{ice}} = 2100\;{{\rm{J}} \mathord{\left/ {\vphantom {{\rm{J}} {{\rm{kg}} \cdot {\rm{K}}}}} \right.\{{\rm{kg}} \cdot {\rm{K}}}}\)

The fusion of water,\({L_f} = 334 \times {10^3}\;{{\rm{J}} \mathord{\left/ {\vphantom {{\rm{J}} {{\rm{kg}}}}} \right.\{{\rm{kg}}}}\)

Calculate the amount of heat when water is converted from \(25^\circ {\rm{C}}\) to \(0^\circ {\rm{C}}\).