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In an adiabatic expansion or compression of gases, does the ideal gas equation change from $PV=nRT$ to $PV^{\gamma} = nRT$? If so, then why as pressure and volume are inversely related in both the cases and the only difference is in their heat exchange process with the surroundings? Why is only $\gamma = C_{p}/C_{v}$ used in the equation as neither volume nor pressure is constant here?

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In an adiabatic expansion or compression of gases, does the ideal gas equation change from 𝑃𝑉=𝑛𝑅𝑇 to $$𝑃𝑉^𝛾=𝑛𝑅𝑇$$

No. See the equation PV = nRT is valid for an ideal gas for any process.

In Adiabatic process, $$PV^𝛾 = k β‰  nRT$$where k is a constant.

However Ideal gas equation equally holds true. $$PV = nRT$$ here P,V and T are variable.

Why is only 𝛾=𝐢𝑝/𝐢𝑣 used in the equation as neither volume nor pressure is constant here?

See in the cases of ideal gases, Cp and Cv are treated as constants.Even though P and V are not constant, heat capacity at constant Pressure and constant Volume - Cp and Cv are constants for ideal gas.And their ratio is called Adiabatic Index or Gamma.


P.S. If you still have any doubt,comment below.

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  • $\begingroup$ In adiabatic process P.V is not constant as temperature is not the same but PV/T =nR =constant PV^gamma =k. Is V/T is same as V^gamma $\endgroup$
    – user270071
    Commented Aug 26, 2020 at 4:57
  • $\begingroup$ @user270071 Just because two quantities are constant, it doesn't mean that they are the same! The two quantities that you're comparing don't even have the same dimension... $\endgroup$
    – Philip
    Commented Aug 26, 2020 at 5:35
  • $\begingroup$ @user270071 I agree with Philip on this one. $\endgroup$
    – Tony Stark
    Commented Aug 26, 2020 at 5:37

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