In a gas equation, for one mole of real gas (p+(a/V2))(V-b)=R T dimensions of constants a and b are :

Question

In a gas equation, for one mole of real gas (p+(a/V2))(V-b)=R T dimensions of constants a and b are : (A) [L2],[M L4 T-2] (B) [L],[M L2 T-2] (C) [M L5 T-2],[L3] (D) none of these

Tardigrade Admin · Accepted Answer

We know that only dimensions of similar quantities can be added or subtracted. Given,

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

Dimensions of

V =

Dimensions of

b [b] = [L^{3}]

Dimensions of

\frac{a}{V ^{2}}

=Dimensions of pressure

P

\Rightarrow

Dimensions of

a =

Dimensions of

P \times V^{2}

Dimensions of

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

\Rightarrow [a] = [M L^{5} T^{- 2}]

Q. In a gas equation, for one mole of real gas $(p + \frac{a}{V ^{2}}) (V - b) = RT$ dimensions of constants $a$ and $b$ are :

$[L^{2}], [M L^{4} T^{- 2}]$

$[L], [M L^{2} T^{- 2}]$

$[M L^{5} T^{- 2}], [L^{3}]$

none of these

Q. In a gas equation, for one mole of real gas (p+V2a​)(V−b)=RT dimensions of constants a and b are :

[L2],[ML4T−2]

[L],[ML2T−2]

[ML5T−2],[L3]

none of these

We know that only dimensions of similar quantities can be added or subtracted. Given, (P+V2a​)(V−b)=RT Dimensions of V= Dimensions of b[b]=[L3] Dimensions of V2a​ =Dimensions of pressure P ⇒ Dimensions of a= Dimensions of P×V2 Dimensions of [a]=[ML−1T−2][L6] ⇒[a]=[ML5T−2]

Q. In a gas equation, for one mole of real gas $(p + \frac{a}{V ^{2}}) (V - b) = RT$ dimensions of constants $a$ and $b$ are :

$[L^{2}], [M L^{4} T^{- 2}]$

$[L], [M L^{2} T^{- 2}]$

$[M L^{5} T^{- 2}], [L^{3}]$