Question

The graph below shows the rise in temperature of a solid of specific heat capacity 0.5 cal $g^{-1}$${}^{\circ }{C}^{-1}$ and the heat supplied to it. Find its mass and specific latent heat of fusion. Also find the specific heat capacity of the body in its liquid state.

Answer 1

In the given graph, the slope $\frac{\Delta T}{\Delta Q}=\frac{1}{mC}...........\left(i\right)$, where m is mass and C is specific heat capacity =$0.5cal$ $g^{-1}°C^{-1}$

From the graph,

AB is the slope of solid, BC is when solid is melting and CD is the slope of liquid

So, slope of AB, $\frac{90}{1000}=\frac{1}{mC}$

$⟹m=100090\times 0.5=22.2g$

Hence, the mass of solid is 22.2g.

The formula heat supplied is, $Q=mL$

Hence, Specific Latent heat of fusion is, $L=\frac{Q}{m}=\frac{1700-1000}{22.2}=31.25cal$ $g^{-1}$

Now consider the liquid state, it is from CD,

The specific heat capacity of the body in its liquid state is,

$\frac{50}{2600-1700}=\frac{1}{mC}$

$⟹C=\frac{900}{50\times 22.2}=0.8cal$ $g^{-1}°C^{-1}$