Question

Two solid bodies of equal mass $m$ initially at $T=0^{\circ} C$ are heated at a uniform and same rate under identical conditions. The temperature of the first object with latent heat $L_{1}$ and specific heat capacity in solid state $C_{1}$ changes according to graph 1 on the diagram. The temperature of the second object with latent heat $L_{2}$ and specific heat capacity in solid state $C_{2}$, changes according to graph 2 on the diagram. Based on what is shown on the graph, the latent heats $L_{1}$ and $L_{2}$ and the specific heat capacities $C_{1}$ and $C_{2}$ in solid state obey which of the following relationships?

• A. $L_{1} > L_{2} ; C_{1} < C_{2}$
• B. $L_{1} < L_{2} ; C_{1} < C_{2}$
• C. $L_{1} > L_{2} ; C_{1} > C_{2}$
• D. $L_{1} < L_{2} ; C_{1} > C_{2}$

Answer 1

Answer: (A)

If heat is supplied at constant rate $P$, then $Q=P \Delta \tau$
and as during change of state $Q=m L$, so, $m L=P \Delta t$
i.e., $L=\left[\frac{P}{m}\right] \Delta t=\frac{P}{m}$ (length of line AB)
Hence $L_{1} > L_{2}$
i.e., the ratio of latent heat of fusion of the two substances are in the ratio $3: 4$.
In the portion $O A$ the substance is in solid state and its temperature is changing.
$\Delta Q=m C \Delta T \text { and } \Delta Q=P \Delta t$
So, $\frac{\Delta T}{\Delta t}=\frac{P}{m C}$ or slope
$=\frac{P}{m S}=\left[\right.$ as $\frac{\Delta T}{\Delta t}=$ slope $]$
Hence $C_{1} < C_{2}$