• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! 5.19

Expert-verified Found in: Page 163 ### An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279 # In the previous section I derived the formula $\left(\partial F/\partial V{\right)}_{T}=-P$. Explain why this formula makes intuitive sense, by discussing graphs of F vs. V with different slopes.

The equilibrium condition occurs when the slope of a curve of F verses V is equal.

See the step by step solution

## Given

$P=-{\left(\frac{\partial F}{\partial V}\right)}_{T,N}$

## Explanation

From thermodynamics Helmholtz free energy is given by
$P=-{\left(\frac{\partial F}{\partial V}\right)}_{T,N}$Here, P is the pressure, F is Helmholtz free energy, V s the volume, T is the temperature and N is the number of molecules.

Write the expression for Helmholtz free energy: F=U-T SWhere, U is the internal energy and S is the entropy of the system.The equilibrium state occurs when the energy of the system is the minimum and when the overall entropy is maximum.For a given number of molecules and given temperature, the increase in the volume yields an increase in the entropy and decrease in the Helmholtz free energy.Draw a graph to show the variation of F with V.Conclusion:So, the equilibrium condition occurs when the slope of a curve of F verses V is equal ### Want to see more solutions like these? 