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Chapter 3: Q14E (page 677)

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

Short Answer

Expert verified

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

Step by step solution

01

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 \(m = 85\;{\rm{kg}}\)

02

Conceptual Explanation

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

03

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 \(2.84 \times {10^7}\;{\rm{J}}\).

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