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KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • 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) \[{{L}_{1}}>{{L}_{2}};\text{ }{{C}_{1}}<{{C}_{2}}\]

    B) \[{{L}_{1}}<{{L}_{2}};\text{ }{{C}_{1}}<{{C}_{2}}\]

    C) \[{{L}_{1}}>{{L}_{2}};\text{ }{{C}_{1}}>{{C}_{2}}\]

    D) \[{{L}_{1}}<{{L}_{2}};\text{ }{{C}_{1}}>{{C}_{2}}\]

    Correct Answer: A

    Solution :

    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         \[slope=\frac{P}{mS}\]
    \[=\left[ as\frac{\Delta T}{\Delta t}=slope \right]\,\,;\] Hence \[{{C}_{1}}<{{C}_{2}}\]


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