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The van der Waals equation for 1 mole of gas is given by (p +av-2)(v -...

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Chemistry

The van der Waals equation for 1 mole of gas is given by (p+av-2)(v - b) = RT. In general, curves of p versus vforvarious values of T exhibit a maximum and a minimum at thetwopoints where (δp/δv)T = 0. The maximum and minumumcoalesceinto a single point on that curvewhere(δ2p/δv2)T = 0 inaddition to(δp/δv)T = 0. This point is calledthe \"critical point\"of the substance and its temperature,pressure, and molar volume aredenoted by Tc,pc, and vc,respectively.
    (a) Express a and b in terms of Tcandvc.
    (b) Express pc in termsofTc and vc.
    (c) Write the van der Waals equation in termsofthe reduced dimensionless variables T' ≡ T/Tc , v'≡v/vc , p' ≡ p/pc
This form should involve neither a nor b.

Answer & Explanation Solved by verified expert
3.8 Ratings (615 Votes)
Answer We have the van der walls equation PaV2VbRT 1 After rearrangement we get P RTVb aV2 2 At critical Temperature dPdV 0 and d2PdV2 0 Now starting from equation    See Answer
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