• # question_answer 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) ${{L}_{1}}<{{L}_{2}}\,\,;\,\,{{C}_{1}}>{{C}_{2}}$

 If heat is supplied at constant rate P, then $Q=P\Delta \,t$ 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. $\Delta \,Q=mC\,\Delta T$ and $\Delta \,Q=P\Delta \,t$ So, $\frac{\Delta \,T}{\Delta \,t}=\frac{P}{mC}$ or slope$=\frac{P}{mS}=\left[ \text{as}\frac{\Delta \,T}{\Delta \,t}=\text{slope} \right]$