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 ππ=ππ π to $$ππ^πΎ=ππ π$$
No. See the equation PV = nRT is valid for an ideal gas for any process.
In Adiabatic process, $$PV^πΎ = k β nRT$$where k is a constant.
However Ideal gas equation equally holds true. $$PV = nRT$$ here P,V and T are variable.
Why is only πΎ=πΆπ/πΆπ£ 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 $\endgroup$ Aug 26, 2020 at 4:57
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$\begingroup$ @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... $\endgroup$– PhilipAug 26, 2020 at 5:35
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$\begingroup$ @user270071 I agree with Philip on this one. $\endgroup$ Aug 26, 2020 at 5:37