Question

A piece of ice (heat capacity $=2100 \,J \,kg ^{-1}{ }^{\circ} C ^{-1}$ and latent heat $=3.36 \times 10^{5} \,J \,kg ^{-1}$ ) of mass $m$ grams is at $-5^{\circ} C$ at atmospheric pressure. It is given $420 \,J$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 \,g$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

Answer: (C)

$\left[m \times 2100 \times 5+1 \times 3.36 \times 10^{5}\right] \times 10^{-3}$
$=420$ where $m$ is in grams.
or $ m \times 2100 \times 5 \times 10^{-3}+336=420$
or $m \times 2100 \times 5 \times 10^{-3}=84$ or
$m=\frac{84}{2100 \times 5 \times 10^{-3}}=8 \,g$