Question

During each cycle of operation a refrigerator absorbs 55 cal from the freezer compartment and expels 85 cal to the room. If one cycle occurs every 10 s, how many minutes will it take to freeze 500 g of water, initially at 0°C? (Lv = 80 cal/g)

Answer 1

Heat to be removed to freeze `500\ g` of water at `0^@,Q=mL_v`

`Q=500xx80=40000\ Cal`

This must be removed from the water for it to freeze.

Assuming that 1. water is kept in the freezer and 2. all the heat absorbed during each cycle is removed from water only.
Let the calculated heat is removed in `N` cycles.
Each cycle removes `55\ Cal` from freezer.
Calculating total heat removed and equating with heat to be removed we get

`55xxN=40000`
`=>N=40000/55`

Each cycle `=10\ s`.
Hence time taken in minutes `=40000/55xx10/60=121.bar21\ mts`