Question 622: Thermodynamics & KTG

Question

If minimum possible work is done by a refrigerator in converting 100 grams of water at 0oC to ice,
how much heat (in calories) is released to the surroundings at temperature 27oC (Latent heat of
ice = 80 Cal/gram) to the nearest integer ?

Accepted Answer

Q
1
= mL = 8000cal
Q
2
= W + Q
1
Coefficient of performance (C.O.P)
$$ = {{{Q_1}} \over W} = {{{Q_1}} \over {{Q_2} - {Q_1}}} = {{{T_1}} \over {{T_2} - {T_1}}}$$
$${{{Q_1}} \over W} = {{273} \over {300 - 273}}$$
$${{{Q_1}} \over W} = {{273} \over {27}}$$
$$W = {{27} \over {273}}{Q_1}$$
$$W = {{27} \over {273}}mL$$
$$W = {{27} \over {273}} 	imes 80 	imes 100$$
$${Q_2} = {{27} \over {273}} 	imes 80 	imes 100 + 80 	imes 100$$
$$ = 8791.2$$ cal

Thermodynamics & KTG

If minimum possible work is done by a refrigerator in converting 100 grams of water at 0oC to ice, how much heat (in calories) is released to the surroundings at temperature 27oC (Latent heat of ice = 80 Cal/gram) to the nearest integer ?

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