GATE 2022 BT – Question 35
The melting-line slope at −2°C is $-5.0665\times10^6\ \mathrm{Pa/K}$ and liquid-minus-solid molar volume is $-4.5\times10^{-6}\ \mathrm{m^3/mol}$. The latent heat of fusion (J/mol, nearest integer) is ___________.
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Correct answer: 6182
Explanation
The **Clapeyron equation** relates the slope of the melting line to the latent heat:
$$\frac{dP}{dT}=\frac{\Delta H_{fus}}{T\,\Delta V}\;\Rightarrow\;\Delta H_{fus}=T\,\Delta V\,\frac{dP}{dT}.$$
**Numbers.** $T=-2\,^\circ\text{C}=271.15$ K, $\Delta V=V_{liquid}-V_{solid}=-4.5\times10^{-6}$ m³/mol, $dP/dT=-5.0665\times10^6$ Pa/K:
$$\Delta H=271.15\times(-4.5\times10^{-6})\times(-5.0665\times10^6)=271.15\times22.80=6182\text{ J/mol}.$$
The latent heat of fusion is **6182 J/mol**. (Both signs are negative as for ice, whose volume decreases on melting, so the product is positive.)