Q. 42

Expert-verifiedFound in: Page 596

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A freezer with a coefficient of performance that of a Carnot refrigerator keeps the inside temperature at in a room. of water at are placed in the freezer. How long does it take for the water to freeze if the freezer’s compressor does work at the rate of while the water is freezing?

Time taken by water to freeze is seconds.

Carnot refrigerator specifications :

Temperature of heat sink

Temperature of heat source

Amount of water

The work done by compressor .

Conversion of temperature into kelvin

We know that the temperature conversion if given by

Therefore,

Conversion of refrigerator temperature

Calculation of the coefficient of performance of the new refrigerator

Temperature of heat sink

Temperature of heat source

Let the coefficient of performance of refrigerator is defined as the reciprocal of the ideal efficiency of the Carnot engine

Substituting the value of temperature if source and temperature of sink in the above equation, the coefficient is calculated as

It is given that the freezer takes coefficient of performance to the old me, therefore the coefficient of performance for new refrigerator is calculated as

The coefficient of performance is defined as the ratio of the quantity of heat removed per cycle to the energy spent per cycle to remove this heat.

Here is the heat removed per cycle and W is the energy spent per cycle to remove this heat.

The heat removed per cycle is defined as the mass of the water times the latent heat of freezing.

Now, from equation (I), the energy spent per cycle to remove this heat is given by

Substituting the values of and in the above equation, the energy spent per cycle to remove this heat is calculated as

Calculation of the time to freeze water

Let be the work done by the compressor

We know that work done by compressor to transfer the amount of energy the time is found as

Conclusion: The time taken by water to freeze is 3150 seconds

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