Q48 / 54 · KVPY 2017 (5 Nov SA) · Physics

Two different liquids of same mass are kept in two identical vessels, which are placed in a freezer that extracts heat from them at the same rate causing each liquid to transform into a solid. The schematic figure below shows the temperature T vs time t plot for the two materials. We denote the specific heat in the liquid statusto be $C_{L 1}$ and $C_{L 2}$ for materials 1 and 2 respectively, and latent heats of fusion $U_{1}$ and $U_{2}$ respectively. Figure
Choose the correct option.

  • A
    $C_{\text {L1 }}>C_{L 2}$ and $U_{1} < U_{2}$
  • B
    $C_{\mathrm{L} 1}>\mathrm{C}_{\mathrm{L} 2}$ and $\mathrm{U}_{1}>\mathrm{U}_{2}$
  • Correct answer
    C
    $\mathrm{C}_{\mathrm{L1}} < \mathrm{C}_{\mathrm{L} 2}$ and $\mathrm{U}_{1}>\mathrm{U}_{2}$
  • D
    $C_{\mathrm{L1}} < \mathrm{C}_{\llcorner 2}$ and $U_{1} < U_{2}$

Solution

Let Refrigerater extract $Q$ joul/per second $\text { Q.t } \Rightarrow \mathrm{ms}\left(\mathrm{T}_{\mathrm{f}}-\mathrm{T}\right)$ Higher the specific heat, Higher the slope

Hence, the correct answer is option: 'C'.

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