Question

The van der Waals equation of state

(p+a/v²)(v-b) = RT

where a and b are constants. Its critical isotherm has a point of inflection at the criti cal point. (a) Show that these expressions for the constants must obtain: a = 9RTcvc/8 = 3pv², b = vc/3. (b) Compute the ap proximate values of the a and b for the fuel octane CsHis and compare results with values of a and b found in Item B 18.

Answer 1

$(p+\frac a{v²})(v-b) = RT,$

$a = \frac{9RTcvc}8 = 3pv²,$

$b =\frac{ vc}3.$