Question

the pressure p,volume v and absolute temperature t of a real gas are related as (p+av^-2)*(v-b)=rt. a,b and r are constant what are the dimensions of a?

Answer 1

Since aV^-2 is added to P, the dimension of aV^-2 is same as Pressure.

Dimension of Pressure = kg m/s² /m² = kg/ ms² = [M^1 L^-1 T^-2]
Let dimension of a = [M^p L^q T^r]
Dimension of aV^-2 =  [M^p L^q T^r] * [M^0 L^-6 T^0] = [M^p L^(q-6) T^r]

Since [M^p L^(q-6) T^r] = [M^1 L^-1 T^-2]

p = 1
q-6 = -1 ⇒ q = 5
r = -2

So dimension of a is [M L^5 T^-2]
It's unit will be kg m⁵ /s²