Question

If specific heat capacity of a substance in solid and liquid state is proportional to temperature of the substance, then if heat is supplied to the solid initially at $-{20}^{\circ }C$ (having melting point $0^{\circ }C$) at constant rate. Then the temperature dependence of solid with time will be best represented by:

• A. diagram
• B. diagram
• C. diagram
• D. diagram

Answer 1

The correct option is C diagram

Formula used: $dQ=msdT$
Given: $s\propto T,\frac{dQ}{dt}=$constant
$dQ=msdT$
$\frac{dQ}{dt}=ms\frac{dT}{dt}\dots \left(i\right)$
From question, $s\propto T$
$s=K_{1}T(K_1$ being proportionality constant)$\dots \left(ii\right)$
It is given that
$\frac{dQ}{dt}=\text{constant}=K_2$ (say)
From equation $\left(i\right)$
$ms\frac{dT}{dt}=K_2$
From equation $\left(ii\right)$
$m\left(K_{1}T\right)\frac{dT}{dt}=K_2$
$TdT\propto dt$
$T^2\propto t$
$\therefore T\propto \sqrt{t}$
Hence, the graph will be parabolic bending towards $t$.
And horizontal line in graph represents change in state of body at same temperature.

FINAL ANSWER: (c).