Question

A solid material is supplied with heat at constant rate. The temperature of the material is changing with the heat input as shown in the figure. Study the graph carefully and answer the following questions.

$\left(i\right)$ What do the horizontal regions $AB$ and $CD$ represent?

$\left(ii\right)$ If $CD=2AB$, what do you infer?

$\left(iii\right)$ What does the slope $DE$ represent?

$\left(iv\right)$ The slope of $OA>$the slope of $BC$. What does this indicate?

Answer 1

$\left(i\right)$ The horizontal portion $AB$ represents the change of state from solid to liquid at constant temperature. This gives the latent heat of fusion. Similarly, $CD$ represents the change of state from liquid to vapour state at constant temperature. This gives the latent heat of vapourisation.

$\left(ii\right)$ When $CD=2AB$, the latent heat of vapourisation is twice the latent heat of fusion of that substance.

$\left(iii\right)dQ=mcdT$

or $\frac{dT}{dQ}=\frac{1}{mc}=\frac{1}{heatcapacityofvapour}=$Slope of $DE$

$\therefore$, the slope of $DE$ represents the reciprocal of heat capacity of the vapour state of the substance.

$\left(iv\right)$Slope of $OA>$Slope of $BC,$

$\Rightarrow {\left(\frac{dT}{dQ}\right)}_{OA}>{\left(\frac{dt}{dQ}\right)}_{BC}$

$\Rightarrow \frac{1}{m{S}_{solid}}>\frac{1}{m{S}_{liquid}}$

$\Rightarrow S_{liquid}>S_{solid}$

Thus,the spectific heat of the liquid state is more than that of the solid state.