Question

If the vapour pressure at two temperatures of a solid phase in equilibrium with its liquid phase is known, then the latent heat of fusion can be calculated by the:

• A. Nernst Heat Theorem
• B. Maxwell's equation
• C. Van Laar equation
• D. Clapeyron–Clausius equation

Hint:

Use the Clausius–Clapeyron equation when vapour pressure data at different temperatures is given and you need to calculate the latent heat of fusion or vaporization.

Answer 1

The Correct Option is D

The Clapeyron–Clausius equation describes the relationship between pressure and temperature during phase transitions, such as melting (fusion), vaporization, or sublimation.
When a solid and liquid are in equilibrium, and their vapour pressures are measured at two different temperatures, this equation allows us to compute the latent heat of fusion.
The integrated form of the Clausius–Clapeyron equation is:
\[ \ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{\text{fus}}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \]
Where:
$P_1, P_2$ = vapour pressures at temperatures $T_1$ and $T_2$ respectively (in Kelvin)
$\Delta H_{\text{fus}}$ = latent heat of fusion
$R$ = universal gas constant
By rearranging this equation, we can solve for $\Delta H_{\text{fus}}$ if the vapour pressures and corresponding temperatures are known.
Other options like Nernst Heat Theorem, Maxwell’s equations, and Van Laar equations do not directly apply to phase transition calculations involving vapour pressure and latent heat.
Hence, the correct method for such a calculation is the Clapeyron–Clausius equation.