A carnot refrigerator absorbs heat from water at `0^(@)C` and gives it to a room at `27^(@)C.` Find the work done by the refrigerator and the coefficient of performance of the machine when it changes 2 kg of water at `0^(@)C` to ice at `0^(@)C.` Specific latent heat of ice `=333 xx 10^(3) Jkg ^(-1)?`

Explanation

To solve the problem, we need to find the work done by the Carnot refrigerator and the coefficient of performance (COP) when it converts 2 kg of water at 0°C to ice at 0°C. We will follow these steps:

### Step 1: Calculate the heat absorbed (Q2)
The heat absorbed by the refrigerator (Q2) when converting water to ice can be calculated using the formula:
\[ Q_2 = m \cdot L_f \]
where:
- \( m = 2 \, \text{kg} \) (mass of water),
- \( L_f = 333 \times 10^3 \, \text{J/kg} \) (specific latent heat of ice).
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