Question

A copper block of mass $2\text{kg}$ is heated to a temperature of ${500}^{\circ }\text{C}$ and then placed in a large block of ice at $0^{\circ }\text{C}$. What is the maximum amount of ice that can melt? The specific heat of copper is $400{\text{J kg}}^{-1}$ ${}^{\circ }{\text{C}}^{-1}$and latent heat of fusion of water is $3.5\times {10}^5{\text{J kg}}^{-1}$.

• A. $\frac{4}{3}\text{kg}$
• B. $\frac{6}{5}\text{kg}$
• C. $\frac{8}{7}\text{kg}$
• D. $\frac{10}{9}\text{kg}$

Answer 1

The correct option is C $\frac{8}{7}\text{kg}$

Specific heat of copper$S_{cu}=400{\text{J kg}}^{-1}$ ${}^{\circ }{\text{C}}^{-1}$
Latent heat of fusion $L_f=3.5\times {10}^5{\text{J kg}}^{-1}$
Mass of copper block $M_{cu}=2\text{kg}$
Let $M\text{kg}$ of ice melts.
$\therefore$ Heat released by $cu$ block $=$Heat gained by ice to melt.
$M_{cu}{S}_{cu}\Delta \theta =M{L}_f$
$\Rightarrow 2\times 400\times 500=M\times 3.5\times {10}^5$
$\Rightarrow M=\frac{2\times 400\times 500}{3.5\times {10}^5}=\frac{8}{7}\text{kg}$