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

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SUMMARY

The discussion focuses on solving the reversible expansion of an ideal gas under constant pressure conditions. The user is tasked with calculating the heat transfer (q), work done (work), and change in internal energy (ΔU) for a process where pressure remains constant while volume and temperature vary. The user initially considers using the heat capacity at constant pressure (Cp) but is confused by the textbook's recommendation to use the heat capacity at constant volume (Cv). The resolution lies in understanding that Cv can be applied due to the negligible change in volume during the process.

PREREQUISITES
  • Understanding of ideal gas laws and properties
  • Familiarity with thermodynamic concepts such as heat capacity (Cp and Cv)
  • Knowledge of calculus for evaluating integrals
  • Basic principles of reversible processes in thermodynamics
NEXT STEPS
  • Study the derivation and application of the ideal gas law
  • Learn about the differences between Cp and Cv in thermodynamic processes
  • Explore the concept of reversible versus irreversible processes in thermodynamics
  • Practice solving integrals related to heat transfer in thermodynamic systems
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, particularly those tackling problems related to ideal gases and reversible processes. It is also useful for educators looking to clarify concepts of heat capacity in different conditions.

SpringWater
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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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