Question

A Carnot freezer takes heat from water at $0^{o}C$ inside it and rejects it to the room at a temperature of ${27}^{o}C$ The latent heat of ice is $336\times {10}^{3}Jk{g}^{-1}$. If $5kg$ of water at $0^{o}C$ is converted into ice at $0^{o}C$ by the freezer, then the energy consumed by the freezer is close to:

• A. $1.51\times {10}^{5}J$
• B. $1.68\times {10}^{6}J$
• C. $1.71\times {10}^{7}J$
• D. $1.67\times {10}^{5}J$

Answer 1

Answer: (D)

$1.67\times {10}^{5}J$

$\Delta \theta =mL$
$=5\times 336\times {10}^3=Q_{sink}$
$\frac{Q_{sink}}{Q_{source}}=\frac{T_{sink}}{T_{source}}$
$\therefore Q_{source}=\frac{T_{source}}{T_{sink}}\times Q_{sink}$
$\therefore E=Q_{source}-Q_{sink}$
$=Q_{sink}(\frac{T_{source}}{T_{sink}}-1)$
$=5\times 336\times {10}^3(\frac{300}{273}-1)$
$=1.67\times {10}^{5}J$