Aphysical system is described by a law fEPA0 where E P and A

Aphysical system is described by a law f(E,P,A)=0, where E, P, and A are energy, pressure, and area, respectively.

Show that P A^3/2 /E = Const.

Solution

Energy [E] = [M L^2 T^-2]

Pressure [P] = [M L^-1 T^-2]

Area [A] = [L^2]

Given E^a*P^b*A^c = constant

[M L^2 T^-2]^a * [M L^-1 T^-2]^b [L^2]^c = k

[M^(a+b) L^(2a-b+2c) T^(-2a-2b)] = k

a+b = 0

2a-b+2c = 0

-2a-2b = 0

solving these three equation

a = -1, b = 1, c = 3/2

P*A^(3/2)/E = k