Question

Clapeyron equation deals with:

• A. Rate of change of vapour pressure with temperature
• B. Effect of an inert gas on vapour pressure
• C. Calculation of $\Delta F$ for spontaneous phase change
• D. Temperature dependence of heat phase transition

Hint:

When the Clapeyron equation is modified for an ideal gas phase assuming $V_{\text{vapor}} \gg V_{\text{liquid}}$, it becomes the Clausius-Clapeyron equation: $\frac{d \ln P^{\text{sat}}}{dT} = \frac{\Delta H_{\text{vap}}}{R T^2}$.

Answer 1

The Correct Option is A

Concept: The Clapeyron equation is a fundamental thermodynamic relation that governs the boundary line between two phases on a pressure-temperature ($P$-$T$) phase diagram. It describes the slope of the coexistence curve, which represents the rate of change of equilibrium vapor pressure with respect to temperature. The mathematical formulation of the Clapeyron equation is: \[ \frac{dP^{\text{sat}}}{dT} = \frac{\Delta H_{\text{tr}}}{T \cdot \Delta V_{\text{tr}}} \] where:

• $P^{\text{sat}}$ is the saturation vapor pressure.

• $T$ is the absolute temperature.

• $\Delta H_{\text{tr}}$ is the latent heat (enthalpy change) associated with the phase transition.

• $\Delta V_{\text{tr}}$ is the change in specific volume between the two coexisting phases.

Step 1: Analyze the derivative term in the Clapeyron expression.
The term $\frac{dP^{\text{sat}}}{dT}$ represents the derivative of vapor pressure with respect to temperature. Therefore, the equation quantifies exactly how the equilibrium vapor pressure scales as the system temperature changes. This matches Option A.