Question

Heatis being supplied to a homogeneous material at a uniform rate and its temperature is plotted against time.


Which of the following options hold true for the specific heat capacity of the material?

• A. Specific heat capacity is greater in solid state than in liquid state.
• B. Specific heat capacity is greater in liquid state than in solid state.
• C. Specific heat capacity is equal in both liquid state and in solid state and is equal to zero.
• D. Specific heat capacity is equal in both liquid state and in solid state and is equal to infinity.

Answer 1

The correct option is A Specific heat capacity is greater in solid state than in liquid state.

Heat supplied to change the temperature is given by,
$Q=ms\Delta T$,
Here, $m$ is mass, $s$ is specific heat capacity and $\Delta T$ is change in temperature.
So, rate of heat transfer,
$R=\frac{Q}{\Delta t}=\frac{ms\Delta T}{\Delta t}=$ constant
Therefore, $\frac{\Delta T}{\Delta t}=\frac{R}{ms}$
For a given material,
$s\propto \frac{1}{\frac{\Delta T}{\Delta t}}$
$\Rightarrow s\propto \frac{1}{\text{slope of T versus t graph}}$

From the graph, we can see that the slope of $T$ versus $t$ graph for material in liquid state is greater than that for solid state. Therefore, specific heat capacity of material in liquid state is lower than that of material in solid state.