Question

A certain refrigerator has a COP of 5.00. When the refrigerator is running, its power input is 500 W. A sample of water of mass 500 g and temperature 20.0 ºC is placed in the freezer compartment. How long does it take to freeze the water to ice at 0ºC?ANS = 83.3 s

I can't seem to get 83.3s

Answer 1

First, let's compile all the information we have about the problem.

Alright, so the COP for our refrigerator is 5.00. Using the definition of COP, we can write,

where, = The change in heat that will reduce the temperature of the sample to 0 degrees and also facilitate a phase transition.
            = Work done by the refrigerator.

Now, to calculate the change in heat, we use the specific heat formula for water,

= heat capacity of water.
   = latent heat for water

The term latent heat is something accompanies almost all first order phase transitions. Without going into first and second order transitions, latent heat is simply the amount of energy required by a substance to change its phase at a constant temperature. So, when water reaches 0 degrees, it doesn't just turn into ice. It requires some extra energy to actually change phase. and are fairly standard for water, and

Substituting all the values in the above equation we get,

Using this value and the COP given to us,

Now, using the definition of power, we can find out the time it takes to impart the energy required for the process, when the input power is 500 Watts.