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 $Q=mL$, so, $mL=P\Delta t$
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 $OA$ the substance is in solid state and its temperature is changing.
$\Delta Q=mC\Delta T\text{ and }\Delta Q=P\Delta t$
So, $\frac{\Delta T}{\Delta t}=\frac{P}{mC}$ or slope
$=\frac{P}{mS}=[$ as $\frac{\Delta T}{\Delta t}=$ slope $]$
Hence $C_1<C_2$