A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent…
A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat $=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$ ) of mass $\mathrm{m}$ gram is at $-5^{\circ} \mathrm{C}$ at atmospheric pressure. It is given $420 \mathrm{~J}$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 \mathrm{~g}$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is
Solution
Language of question is slightly wrong. As heat capacity and specific heat are two different physical quantities. Unit $\mathrm{J}-\mathrm{kg}^{-1} \cdot{ }^{\circ} \mathrm{C}^{-1}$. The heat capacity given in the question is really the specific heat. Now applying the heat exchange equation.
$
\begin{array}{r}
420=\left(m \times 10^{-3}\right)(2100)(5)+\left(1 \times 10^{-3}\right) \\
\left(3.36 \times 10^5\right)
\end{array}
$
Solving this equation we get,
$
m=8 \mathrm{~g}
$
$\therefore$ The correct answer is 8