Adiabatic Process (Reversible)

An adiabatic change by definition, is one which does not allow any transfer of heat, i.e., q = 0 , it follows from the 1st law,

ΔU = − W

dU = − dW

Let only mechanical work of expansion or contraction is involved, dW = PdV. Moreover,

dU= CVdT

∴ CVdT = − PdV

For a system of 1 mole of an ideal gas, expanding adiabatically and reversibly from temp T1 to T2 and volume V1 to V2, we have

Adiabatic work:

W = – CvT = −Cv(T2 − T1) = Cv (T1 − T2)

Where T1,T2 are initial and final temperatures.

For 1 mole of gas T = PV/R

Hence adiabatic work

Slope of PV curve in adiabatic & isothermal expansion.

For isothermal expansion of the gas, PV = K

The slope of the PV curve will be obtained from

For the adiabatic expansion of the gas PVγ = K’

∴ P = K’/Vγ

In the both the changes the slope is negative, since γ , is greater than 1 , the slope in the adiabatic P − V curve will be large than that in the isothermal one.

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