An equation of state that has been used to model the behaviour of a fixed amount
ID: 811887 • Letter: A
Question
An equation of state that has been used to model the behaviour of a fixed amount of a real gas is
(P+a/V2) (V-b) =ZT
In the equation Z, a and b are constants, and P represents pressure, V represents volume, and T represents temperature. The constant Z depends on the amount of gas.
Consider what the dimensions of a and be are in terms of the fundamental quantities of mass(M), length(L), and time(T).
The answers are b : L3 a: ML5T-2
Can someone please explain why? I know the answers I need explanation for them please!
Explanation / Answer
as we know when there is addition or subtraction, the dimension should be same
so we can write,
the dimension of V and b will be same, {as, there is a term (V-b) }
V----> volume and it has a dimension of L3
=> b will also have the dimension L3
from the expression
(P+a/V2) we can say that the dimension of
[a/V2] = [P]........(I)
P ----> pressure = force / area = [MLT-2 ] / [L2 ] = [ML-1 T-2 ]
from (i)
=> [a/V2 ] = [P]
=> [a] = [P*V*V] = [ML-1 T-2 ]*[L3 ]2 = [ML-1 T-2 ]*[L6 ] = [ML5 T-2 ]
therefore,
[a] = [ML5 T-2 ]
and [b] = [L3 ]