Heat and Thermodynamics 1 Question 18
18. A piece of ice (heat capacity $=2100 Jkg^{-1}{ }^{\circ} C^{-1}$ and latent heat $=3.36 \times 10^{5} J kg^{-1}$ ) of mass $m$ gram 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
(2010)
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Solution:
- Language of question is slightly wrong. As heat capacity and specific heat are two different physical quantities. Unit of heat capacity is $J-kg^{-1}$ not $J-kg^{-1}-{ }^{\circ} C^{-1}$. The heat capacity given in the question is really the specific heat. Now applying the heat exchange equation.
$$ 420=\left(m \times 10^{-3}\right)(2100)(5)+\left(1 \times 10^{-3}\right)\left(3.36 \times 10^{5}\right) $$
Solving this equation, we get
$$ m=8 g $$
$\therefore \quad$ The correct answer is 8 .
