Solve Reversible Expansion of Ideal Gas: q, Work, ΔU

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In a reversible expansion of an ideal gas with constant pressure, the user is confused about whether to use Cp or Cv for calculating work and heat. The user initially assumes Cp should be used due to constant pressure but finds the textbook suggests using Cv instead. The discussion highlights the distinction between heat capacities at constant pressure and constant volume, with the user questioning the rationale behind the textbook's guidance. Clarification is sought on whether the change in volume is negligible enough to justify using Cv. Understanding the correct application of these concepts is crucial for accurately solving the problem.
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Homework Statement


The problem provides two paths. P1,V1,T1------->P1,V2,T3 (this is the only one i do not understand) for AN IDEAL GAS reversible expansion

Pressure---constant
Volume---not constant
Temperature---not constant

Calculate the q(rev)=? work(rev)=? and ΔU=?

Homework Equations





The Attempt at a Solution



Because the pressure is constant I assumed that Cp(heat cap@ constant pressure) should be used instead of Cv (heat cap@constant volume)

so...

Work(rev)=∫Cp(T)dT however the book says use ∫Cv(T)dT why is this?

It does not make sense to me because the pressure is constant and the volume changes so why use Cv over Cp Cp=5/2*R Cv=3/2R or is the book stating that the change in volume is so small that we can still use Cv(T).

Any help would be greatly appreciated

Thank you
 
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