# Ideal gas equation for adiabatic process

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?

In an adiabatic expansion or compression of gases, does the ideal gas equation change from ππ=πππ to $$ππ^πΎ=ππ π$$

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

In Adiabatic process, $$PV^πΎ = k β nRT$$where k is a constant.

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

Why is only πΎ=πΆπ/πΆπ£ 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.

• 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 Aug 26, 2020 at 4:57
• @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... Aug 26, 2020 at 5:35
• @user270071 I agree with Philip on this one. Aug 26, 2020 at 5:37