How does the Helmholtz energy formula intuitively make sense?

[pentazoid]

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.

Homework Equations

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.

 

[Mapes]

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?

 

[pentazoid]

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]

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.

 

[pentazoid]

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.