Why Use Cv in a Polytropic Process?

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SUMMARY

The discussion focuses on the use of specific heat constants in a polytropic process involving nitrogen gas. The problem states that a piston-cylinder device contains 1.2 kg of nitrogen at 120 kPa and 300 K, undergoing compression where PV^1.3 remains constant, ultimately reducing the volume by half. Participants clarify that while neither pressure nor volume is constant, the constant-volume specific heat (Cv) is applicable for calculating changes in internal energy during the process. This is due to the relationship between internal energy and temperature change for ideal gases.

PREREQUISITES
  • Understanding of polytropic processes in thermodynamics
  • Knowledge of specific heat constants (Cv and Cp)
  • Familiarity with the ideal gas law and internal energy equations
  • Basic principles of entropy change in thermodynamic processes
NEXT STEPS
  • Study the derivation and application of the polytropic process equation PV^n = constant
  • Learn about the differences between Cv and Cp and their applications in various thermodynamic processes
  • Explore the concept of internal energy changes for ideal gases and how to calculate them
  • Investigate entropy change calculations in non-constant pressure and volume scenarios
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, particularly those studying or working with gas processes, internal energy calculations, and entropy changes in engineering applications.

Stonescar
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Homework Statement


A piston-cylinder device contains 1.2kg Nitrogen gas at 120 kPa and 300K. The gas is now compresses slowly in a polytropic process during which PV^1.3 = constant.
The process ends when the volume is reduced by one-half.
Determine the entropy change of Nitrogen during this process.

My question here is about what specific heat constant to use.

Homework Equations


I thought i had to use Cv when the volume is constant.
And Cp when the pressure was constant.

The Attempt at a Solution


As I can see, in this process. Neither the pressure or the volume is constant?
But in the solution provided, tey are using the Cv .
Why is that? The volume did get reduced by one-half:confused:

Im new to Thermodynamics, and not very good at it..
But this is confusing me. Can someone explain this to me? How to know when to use what constant :)
 
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Could the process have been divided into constant-volume and constant-pressure parts to simplify? This is a common strategy. But it's hard to say without seeing the solution.

Another possibility is that the constant-volume specific heat is being used in the equation for internal energy for an ideal gas,

[tex]E=mc_VT+E_0[/tex]

which is always true (and can be used to find the change in internal energy of an ideal gas for any process if one knows the change in temperature).
 

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