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Adiabatic process

  • Thread starter Gyroscope
  • Start date
  • #1
Gyroscope

Homework Statement


3.14
(0.5) How is the fractional change in temperature related to [tex]\frac{dT}{T}[/tex] the fractional change in pressure [tex]\frac{dP}{P}[/tex] ?
(IPhO 2006)

Homework Equations



[tex]PV^{\gamma}=\rm constant[/tex]

The Attempt at a Solution



nC_vdT=-PdV (1), dV/dP=-nRT/(P^2)

If I substitute dV in the equation (1) it does not give the right result.

Can someone help me, please? :tongue2:

Thanks my dear friends.
 

Answers and Replies

  • #2
marcusl
Science Advisor
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It appears you are talking about an ideal gas? Then in
[tex]P=nRT/V[/tex]
we see right away that P changes the same way as T. This is shown mathematically as

[tex]\frac{dP}{dT}=\frac{nR}{V},[/tex]

[tex]\frac{dP}{P}=\frac{nRdT}{PV}=\frac{dT}{T}.[/tex]
 
  • #3
Gyroscope
Thanks marcusl for your help. But you are wrong. :( I already solved it. Thanks anyway my dear friend.
 
  • #4
marcusl
Science Advisor
Gold Member
2,714
377
Sorry! Glad you solved it.
 

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