Question

[P+a/(v square)] [v-b]=RT. :Here p is pressure a&b are constant. v is volume R is gas constant and T is temperature.Find the dimensions of [a] and[b].

Answer 1

(P + a/V2) (V - b) = RT
P is pressure, V is volume and T is temperature.
[P] = [F/A] = [MLT −2/L2] = [ML−1T −2]
[V] = [L3]

We cannot add or subtract quantities of different dimensions. Therefore
[P] = [a/V2] ⇒ [a] = [PV2] = [ML−1T −2 L6] = [M L5 T −2]
∴ [a] = [M L5 T −2]

Similarly,
[b] = [V] = [L3]

Answer 2

Answer:

The dimensions of a and b is [ML⁵T⁻²] and [L³].

Explanation:

Given that,

$(P+\dfrac{a}{V^2})(V-b)=RT$

Where, P = Pressure

V = Volume

T = Temperature

Pressure is the force upon area.

The dimension formula of pressure is

$P = \dfrac{F}{A}$

$P =\dfrac{[MLT^{-2}]}{[L^2]}$

$P = [ML^{-1}T^{-2}]$

The dimension formula of volume is

$V =[L^{3}]$

We cannot add or subtract quantities of different dimension.

Therefore,

$P =\dfrac{a}{V^2}$

$a=PV^2$

Put the dimension of P and V

$a =[ML^{-1}T^{-2}][L^{6}]$

$a=[ML^{5}T^{-2}]$

Similarly,

$b=V$

$b = [L^{3}]$

Hence, The dimensions of a and b is [ML⁵T⁻²] and [L³].