Determine dimensions and si units of constants?
I am am trying to work out the dimensions and si units of the constants a and b in the following equation.
(P + a/V^2) (V - b) = RT
- KeplJoeyLv 710 years agoFavorite Answer
Multiplying out the LHS using FOIL yields
PV - Pb + a/V^3 - ab/V^2
For this addition of quantities to be meaningful, we must have that all four carry the same dimensions.
This suggests that b carries the same dimensions as volume, m^3 in SI units.
Also a/V^2 must have the same dimensions as P,
So, [a/V^2] = [P], or [a]/[V^2] = [P], so [a] = [P][V^2].
Note that pressure is force divided by area, or mass times acceleration divided by Area.
So [P] = [M][L][T]^2/[L]^2 = [M][T]^2/[L], which in SI units is the kg s^2/m
And [V]^2 = ([L]3)^2 = [L]^6 which in SI units is m^6
So [a] = [P][V]^2
which in SI units is kg m^5 s^2.