Question

Question:An ice-making machine operates in a Carnot cycle. It takes heat from water at 0.0°C and rejects heat to a room at 24.0°C. Suppose that 85.0 kg of water at 0.0°C are converted to ice at 0.0°C. (a) How much heat is discharged into the room? (b) How much energy must be supplied to the device?

Short answer

The heat discharged into room is \(2.84 \times {10^7}\;{\rm{J}}\).

Step-by-step solution

Identification of given data

The temperature ice and water is\({T_{iw}} = 0\;^\circ {\rm{C}}\)

The temperature of room is\({T_r} = 24\;^\circ {\rm{C}}\)

The mass of water is \(m = 85\;{\rm{kg}}\)

Conceptual Explanation

The het discharged to room is equal to the latent heat of the water to convert the ice into water.

Determination of heat discharged into room

The heat discharged into room is given as:

\({Q_r} = mL\)

Here,\(L\)is the latent heat of the ice and its value is\(3.34 \times {10^5}\;{\rm{J}}/{\rm{kg}}\)

Substitute all the values in the above equation.

\(\begin{array}{l}{Q_r} = \left( {85\;{\rm{kg}}} \right)\left( {3.34 \times {{10}^5}\;{\rm{J}}/{\rm{kg}}} \right)\\{Q_r} = 2.84 \times {10^7}\;{\rm{J}}\end{array}\)

Therefore, the heat discharged into room is \(2.84 \times {10^7}\;{\rm{J}}\).