ParthKohli
  • ParthKohli
A gas undergoes a process such that the ratio of P and V is constant and equal to one. What's the molar heat capacity?
Mathematics
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ParthKohli
  • ParthKohli
A gas undergoes a process such that the ratio of P and V is constant and equal to one. What's the molar heat capacity?
Mathematics
chestercat
  • chestercat
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ParthKohli
  • ParthKohli
\[|dw:1444507155788:dw|\]
ParthKohli
  • ParthKohli
\[C_{m} = \frac{\partial q }{\partial T}\]Is this relation right?
hwyl
  • hwyl
MATH PROCESSING ERROR

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ParthKohli
  • ParthKohli
That drawing isn't important. Just a PV graph with slope one.
ParthKohli
  • ParthKohli
\[q = \Delta U - w\]\[= \frac{3}2RT + pV = \frac{3}{2}RT + RT =\frac{5}{2}RT\]
ParthKohli
  • ParthKohli
I don't think it's 5R/2 though.
ParthKohli
  • ParthKohli
Looks like I nowhere used the fact that \(p=V\).
thomas5267
  • thomas5267
I suspect \(w=\int p(t)V(t)\,dt=\int p(t)^2\,dt\).
ParthKohli
  • ParthKohli
Oh, what a stupid mistake.
ParthKohli
  • ParthKohli
\[\frac{pV}{2}=\frac{p^2}{2}= \frac{V^2}{2}\]
ParthKohli
  • ParthKohli
well duh
ParthKohli
  • ParthKohli
then we're done here.
thomas5267
  • thomas5267
Why?
hwyl
  • hwyl
WHY IS MATH NOT PROCESSING
hwyl
  • hwyl
\(TEST\)
hwyl
  • hwyl
WTF
ParthKohli
  • ParthKohli
just refresh
hwyl
  • hwyl
K NOW IT IS BACK
thomas5267
  • thomas5267
So the answer is 3/2R?
ParthKohli
  • ParthKohli
No. 2R.
thomas5267
  • thomas5267
How does p^2=RT?

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