Prove that for an adiabatic process TVγ-1 constant.

1.	Prove that for an adiabatic process TVγ-1 constant.
Answer» We know that for an adiabatic process PV^γ = constant ……(1) For an ideal gas, \(\frac{PV}{T}\) = constant, C …….(2) ∴ P = \(\frac{C.T}{V}=\) ........(3) using equation (3) in (1), \((\frac{C.T}{T})V^γ\) = constant. i.e. T.V^γ-1 = constant.

Answer»

We know that for an adiabatic process

PV^γ = constant ……(1)

For an ideal gas, \(\frac{PV}{T}\) = constant, C …….(2)

∴ P = \(\frac{C.T}{V}=\) ........(3)

using equation (3) in (1),

\((\frac{C.T}{T})V^γ\) = constant.

i.e. T.V^γ-1 = constant.

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Prove that for an adiabatic process TVγ-1 constant.

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