Question

The saturation pressure \(P_{\text{sat}}\) of a pure liquid is represented by an equation of the form: \[ \ln P_{\text{sat}} = A - \frac{B}{T}, \] where \(A\) and \(B\) are constants, and \(T\) is the absolute temperature. For this substance, which of the following expression for the specific entropy difference between the saturated vapour and the saturated liquid phase \((s_{fg})\) is correct?

• A. \( s_{fg} = v_{fg} \frac{B P_{\text{sat}}^2}{T^2} \)
• B. \( s_{fg} = v_{fg} \frac{B P_{\text{sat}}}{T^2} \)
• C. \( s_{fg} = v_{fg} \frac{B P_{\text{sat}}}{T^3} \)
• D. \( s_{fg} = v_{fg} \frac{B P_{\text{sat}}^3}{T^2} \)

Hint:

For the saturation pressure equation, the entropy difference between the saturated vapour and the liquid phase can be derived using thermodynamic relations.

Answer 1

The Correct Option is B

We are given the equation for saturation pressure: \[ \ln P_{\text{sat}} = A - \frac{B}{T}. \] To find the specific entropy difference \(s_{fg}\), we use the relationship between entropy and the change in pressure with respect to temperature. From thermodynamics, we can derive the expression for the specific entropy difference: \[ s_{fg} = v_{fg} \frac{B P_{\text{sat}}}{T^2}. \] This matches option (B). Final Answer: \text{(B) \( s_{fg} = v_{fg} \frac{B P_{\text{sat}}}{T^2} \)}