Leidenfrost effect at thermodynamic equilibrium

[digogalvao]

Homework Statement

A spherical drop of a pure substance floats on top of the vapor of the same substance so the system vapor+drop is isolated. The drop has a surface tension σ. Show that at the thermodynamic equilibrium P_L≠P_V and calculate the difference.

Homework Equations

Three laws of thermodynamics

The Attempt at a Solution

I solved this one already but I would like to check my result. Following the three laws of thermodynamics and maximizing the entropy at the equilibrium yadda yadda yadda I got P_L-P_V=3σ/a, where a is the radius of the drop. The dimension of the result seems correct.

 

[kuruman]

Is there a question here? If the question is "Am I right?", you have to supply the "yadda, yadda, yadda" so that someone can check your work and point out possible mistakes.

 

[digogalvao]

Is there a question here? If the question is "Am I right?", you have to supply the "yadda, yadda, yadda" so that someone can check your work and point out possible mistakes.

Ok...
For σ=0, Thermodynamic equilibrium says: P_L=P_V, but if we add a work therm for the liquid -σdS=-3σdV/a we get P_L-P_V=3σ/a.