Question

A Carnot engine is made to operate as a refrigerator. This refrigerator is used to freeze water at $0^o$C to ice at $0^o$C and the heat from the working substance is discharged into a large tank containing water at ${34}^o$C. The latent beat of fusion of ice is $334\times {10}^{3}J/kg$. The minimum amount of work required to freeze 3 kg of water is close to

• A. $83\times {10}^{3}J$
• B. $125\times {10}^{3}J$
• C. $94\times {10}^{3}J$
• D. $147\times {10}^{3}J$

Answer 1

The correct option is B $125\times {10}^{3}J$

For a refrigerator:-

$COP=\frac{T_c}{T_h-T_c}$

Here, $T_c=273K$ and $T_h-T_c=34K$

Hence,

$COP=\frac{273}{34}=8.03$

Now, we know that-

$COP=\frac{Heatextractedfromcoldsource}{Amountofworkdone\left(W\right)}$

Heat extracted=$mL=3\times 334\times {10}^{3}J$

Hence,

$8.03=\frac{3\times 334\times {10}^3}{W}$

$⟹W=\frac{3\times 334\times {10}^3}{8.03}$

$⟹W=125\times {10}^{3}J$

Hence, answer is option-(B).