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Helmholtz energy problem

  • Thread starter pentazoid
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  • #1
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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.
 

Answers and Replies

  • #2
Mapes
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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?
 
  • #3
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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?
 
  • #4
Mapes
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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.
 
  • #5
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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.
 

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