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Deduce the Van der Waals equation for re...

Deduce the Van der Waals equation for real gases at (a) low presssure and (b) high pressure.

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Van der Waals equation for one mole of real gas is `(P + (a)/(V_(2))) (V-b) = RT`
(a) At low pressure where molar volume of the gas is very high, b is neglible when compared with molar volume V.
`V - b = V`
`(P + (a)/(V_(2))) V = RT (or) PV + (a)/(V) = RT `
`(PV)/(RT) + (a)/(RTV) =1`
`(PV)/(RT) = 1 - (a)/(RTV) (or) z = 1 - (a)/(RTV)`
(b) At high pressure, `(a)/(V^(2))` can be neglected when compared with P
`P + (a)/(V^(2)) = P (or) P (V-b) = RT`
`PV - Pb = RT (or) (PV)/(RT) = 1 + (pb)/(RT)`
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