Heat pump
Take 15 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
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It has two pools of masses
and
.
is desired to convert into heated pool and
into an ice rink with a heat pump operating reversibly.
The specific heat capacity of water
is given.
Question
Initially,
.
decreases by
.
Determine the final temperature
and the work
to provide.
(Hint : consider a low temperature variation on an elementary cycle).
On an elementary cycle :
Yet :
So :
The provided work is :
Question
In a
stage, the second water basin passes its frozen state.
The specific latent heat of water is
.
Determine the new final values of
and
.
Then :
Work is :
Question
In a third step, the temperature of the ice is lowered by
.
Determine the new final values
and
.
Reasoning identical to that of the question
.
