How can I solve this thermodynamics problem involving an adiabatic process?

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The discussion focuses on solving a thermodynamics problem involving an adiabatic process for an ideal gas. The work done during this process is expressed as W=(1/(\gamma - 1))(PfVf - PiVi), where Pf and Pi represent the final and initial pressures, respectively. The user initially attempted to substitute P with the expression constant/V^\gamma into the integral W=-∫Pdv but encountered difficulties with the gamma exponent. A solution is provided by suggesting the replacement of V^{\gamma} with constant/P to simplify the integration process.

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  • Understanding of adiabatic processes in thermodynamics
  • Familiarity with the ideal gas law
  • Knowledge of calculus, specifically integration techniques
  • Concept of the adiabatic condition PV^\gamma=constant
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thenewbosco
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hello the problem is as stated:
a cylinder containing n moles of an ideal gas undergoes an adiabatic process. using W=-\int Pdv and using the condition PV^\gamma=constant, show that the work done is:
W=(\frac{1}{\gamma - 1}(PfVf - PiVi) where Pf is final pressure, Pi is initial pressure...
I tried substituting that P=\frac{constant}{V^\gamma} into the integral, and evaluating from Vi to Vf, but this still leaves the gamma as an exponent. how can i go about solving this one?
thanks
 
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thenewbosco said:
hello the problem is as stated:
a cylinder containing n moles of an ideal gas undergoes an adiabatic process. using W=-\int Pdv and using the condition PV^\gamma=constant, show that the work done is:
W=(\frac{1}{\gamma - 1}(PfVf - PiVi) where Pf is final pressure, Pi is initial pressure...
I tried substituting that P=\frac{constant}{V^\gamma} into the integral, and evaluating from Vi to Vf, but this still leaves the gamma as an exponent. how can i go about solving this one?
thanks

Replace back V^{\gamma} by constant/P.

ehild
 

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