Question

A molten metal of mass $150g$ is kept at its melting point ${800}^{o}C$. When it is allowed to freeze at the same temperature, it gives out $75,000J$ of heat energy
(a) What is the specific latent heat of the metal?
(b) If the specific heat capacity of metal is $200J{kg}^{-1}{K}^{-1}$, how much additional heat energy will the metal give out in cooling to $-{50}^{o}C$?

Answer 1

Let L be the latent specific heat of the metal.

When the metal is allowed to be solidified its mp i.e. ${800}^{\circ }C$, it will give out latent heat only.

$\begin{array}{c}mL=75000\\ 0.150\times L=75000\\ L=500000Jk{g}^{-1}\end{array}$

Now,

Heat given out by the metal in cooling down to $-{50}^{\circ }C$. Fall in temperature will be ${800}^{\circ }C-\left(-{50}^{\circ }C\right)={850}^{\circ }C$

Heat given out= $m\times s\times t=\left(0.150\times 200\times 850\right)=25500J$