(Thermo) Show that in a Reversible Adiabatic process

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SUMMARY

In a reversible adiabatic process involving one mole of an ideal gas, the relationship P1V1γ = P2V2γ holds true, where γ represents the ratio of specific heats (CP/CV). This equation demonstrates that the product of pressure and volume raised to the power of γ remains constant throughout the process. The discussion emphasizes the importance of understanding this fundamental principle in thermodynamics, akin to the constancy of PV in isothermal processes.

PREREQUISITES
  • Understanding of ideal gas laws
  • Familiarity with thermodynamic concepts, specifically adiabatic processes
  • Knowledge of specific heat capacities (CP and CV)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the adiabatic condition for ideal gases
  • Learn about the implications of the first law of thermodynamics in adiabatic processes
  • Explore the differences between adiabatic and isothermal processes
  • Investigate real gas behavior and deviations from ideal gas laws
USEFUL FOR

Students of thermodynamics, physics enthusiasts, and professionals in engineering fields who require a solid understanding of adiabatic processes and their mathematical representations.

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Homework Statement


Show that in a reversible adiabatic process, for 1 mole of ideal gas

P1V1γ=P2V2γ

Where,

γ=CP/CV

Homework Equations


Listed above.

The Attempt at a Solution


Frankly, I don't really understand what I'm being asked to do.
 
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It simply meant to ask that PVγ is constant for a reversible adiabatic process. Actually, the question is asking to prove that the adiabatic processes follows this trend, just like PV=constant for isothermal processes.

Try the question. A good one indeed.
 

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