Ideal Gas law Partial derivative

  • Thread starter Punkyc7
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  • #1
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This is a question from my calculus book that i thought was interesting, its not homework but im curious to how you go about showing it.


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T (∂P/∂T)(∂V/∂T)=NR


We know PV=NRT

so if we take a partial how does the T end up on the other side?
 

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  • #2
SammyS
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[tex]\frac{\partial P}{\partial T} = \frac{\partial }{\partial T} \left(\frac{NRT}{V}\right)= \frac{NR}{V}[/tex]

[tex]\frac{\partial V}{\partial T} = \frac{\partial }{\partial T} \left(\frac{NRT}{P}\right)= \frac{NR}{P}[/tex]

So, what is [tex]T\ \left(\frac{\partial P}{\partial T}\right)\left(\frac{\partial V}{\partial T}\right)\ ? [/tex]
 
  • #3
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it should be NR. But the way it is written shouldnt it be T N^2R^2/(PV)
 
  • #4
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it should be NR. But the way it is written shouldnt it be T N^2R^2/(PV)

But if PV = NRT, what does NRT/PV equal?
 
  • #5
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T(∂P/∂T)(∂V/∂T)=NR

T(NR/V)(NR/P)=[T(NR)^2]/PV but PV equals NRT

[T(NR)^2]/NRT ==> NR

you just needed the substitution for PV
 

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