# Helmholtz energy problem

## Homework Statement

Explain why the formula (dF/dV)=-P , where T and N are constant variables , makes intuitive sense, by discussing graphs of F vs. V with different slopes.

## The Attempt at a Solution

dF=SdT-PdV+mu*dN

dT and DN are zero since T and N are fixed.

As volume increases, P will be negative. as dV increase and P remains negative, then I suspect F will decrease therefore the slope dF/dV will be a negative value.

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Mapes
Homework Helper
Gold Member
This is a good start. So what would it mean if a graph of F vs. V had a very large or very small negative slope for a particular material?

This is a good start. So what would it mean if a graph of F vs. V had a very large or very small negative slope for a particular material?
If dF/dV had a very small slope, would the slope be closed to the shape of that of a vertical line and the change in dV would be very small?

Mapes
Homework Helper
Gold Member
If dF/dV had a very small slope, would the slope be closed to the shape of that of a vertical line and the change in dV would be very small?
A small slope means that the line is nearly horizontal.

A small slope means that the line is nearly horizontal.
oh yeah, since the slope of a horizontal line is zero. that means dV is approaching inifinty.