(a) The ideal gas equation of state is a fairly simple expression of the relationship between the physical properties of a gas. In Module 4, we will consider some other equations of states, one of which is the van der Waals equation of state, (? + a n2/ v2) (V-nb)=nRT where a and b are constant coefficients for a given substance, and P, V, T, and n have their usual meaning. Find the partial derivative (P/T)v for this equation of state .
(a) The ideal gas equation of state is a fairly simple expression of the relationship between the physical properties of a gas. In Module 4, we will consider some other equations of states, one of which is the van der Waals equation of state,
(? + a n2/ v2) (V-nb)=nRT
where a and b are constant coefficients for a given substance, and P, V, T, and n have their usual meaning. Find the partial derivative (P/T)v for this equation of state .
b) Mathematically, it is known that for three variables that are related to one another (as P, Vm, and Tare here) by a function (or equation of state), one can show
(??/??)z (??/??)x (??/??)y =−1
(note the cyclic variation of the three variables).Using this relationship, and the definitions of kT(coefficient of isothermal compressibility) and a (coefficient of isobaric thermal expansibility), find a simple equation relating the van der Waals parameter, b, to Vm, a, and kT. (For a discussion of this sort of manipulation, see the video by Catalyst University in Lesson1D (p. 8)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
