Help with Adiabatic Derivation

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    Adiabatic Derivation
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SUMMARY

The discussion focuses on the derivation of the adiabatic process equation in thermodynamics, specifically transforming the equation from the form T^(f/2)V = constant to PV^((f+2)/f) = constant. The user utilizes the relationship dU = dW and the ideal gas law PV = NkT to manipulate the equations. The final expression achieved is lnP + ((f+2)/f)lnV = constant, confirming the correct form of the adiabatic condition.

PREREQUISITES
  • Understanding of thermodynamic principles, particularly adiabatic processes.
  • Familiarity with the ideal gas law (PV = NkT).
  • Knowledge of calculus, specifically logarithmic differentiation.
  • Concept of internal energy (dU) and work done (dW) in thermodynamics.
NEXT STEPS
  • Study the derivation of the adiabatic process equations in detail.
  • Learn about the implications of the ideal gas law in various thermodynamic processes.
  • Explore the application of logarithmic differentiation in physics problems.
  • Investigate the relationship between internal energy, work, and heat in thermodynamic systems.
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Students and professionals in physics and engineering, particularly those focusing on thermodynamics and energy systems.

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Using [tex]dU = dW[/tex],

[tex]\frac{f}{2}NkdT = -PdV[/tex]

I eventually came to

[tex]T^\frac{f}{2}V = \mbox{constant}[/tex]

I tried to then get it to the form in the book - [tex]PV^\frac{f+2}{f}=\mbox{constant}[/tex] using the formula [tex]PV = NkT[/tex]:

[tex]\left(\frac{PV}{Nk}\right)^\frac{f}{2}V=\mbox{constant}[/tex]

[tex]P^\frac{f}{2}V^\frac{f+2}{2}=\mbox{constant}[/tex]

How do I get it in the right form? Thanks
 
Last edited:
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[tex]P^{\frac{f}{2}} V^{\frac{f+2}{2}}=const[/tex]
so i have:
[tex]\frac{f}{2}lnP+\frac{f+2}{2}lnV=constant[/tex]
then:
[tex]lnP+\frac{f+2}{f}lnV=constant[/tex]
 
Thanks quydau35 :)
 

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