# Thermodynamics

# 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.

If you have more questions, feel free to ask them on the forum.

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).

### Hint

### Solution

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 .

### Hint

### Solution

Then :

Work is :

## Question

In a third step, the temperature of the ice is lowered by .

Determine the new final values and .

### Hint

### Solution

Reasoning identical to that of the question .