How to Solve for the Fractional Change in Temperature in an Adiabatic Process?

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Homework Help Overview

The discussion revolves around the relationship between fractional changes in temperature and pressure in the context of an adiabatic process involving an ideal gas, as posed in a physics problem from the IPhO 2006.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate the fractional change in temperature to the fractional change in pressure using the ideal gas law and adiabatic conditions. Some participants question the correctness of the original poster's approach and suggest that the changes in pressure and temperature are mathematically linked.

Discussion Status

The discussion includes attempts to clarify the relationship between temperature and pressure changes, with some participants providing insights into the mathematical relationships. However, there is no explicit consensus, as one participant claims to have resolved the issue independently.

Contextual Notes

The original poster expresses difficulty in deriving the correct result from their substitution in the equations, indicating potential gaps in information or understanding of the relationships involved.

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? :-p

Thanks my dear friends.
 
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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]
 
Thanks marcusl for your help. But you are wrong. :( I already solved it. Thanks anyway my dear friend.
 
Sorry! Glad you solved it.
 

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