The equation of-state of some gases can be expressed as ( p+(a/V2) )(V-b)=RT where, p is the pressure, V the volume, T the absolute temperature and a and b are constants. The dimensional formula of a is

Question

The equation of-state of some gases can be expressed as ( p+(a/V2) )(V-b)=RT where, p is the pressure, V the volume, T the absolute temperature and a and b are constants. The dimensional formula of a is (A)  [ML5T-2]  (B)  [M-1L5T-2]  (C)  [ML-1T-2]  (D)  [ML-5T-2]

Tardigrade Admin · Accepted Answer

In the equation p, V and T are pressure, volume and temperature respectively.

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

Dimensions of

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

will be same as that of pressure.

∴

Dimensions of

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

dimensions of p

\Rightarrow

Dimensions of

a =

dimensions of

p \times

dimensions of

V^{2}

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

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

Q. The equation of-state of some gases can be expressed as
$(p + \frac{a}{V ^{2}}) (V - b) = RT$
where, p is the pressure, V the volume, T the absolute temperature and a and b are constants. The dimensional formula of a is

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

$[M^{- 1} L^{5} T^{- 2}]$

$[M L^{- 1} T^{- 2}]$

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

Q. The equation of-state of some gases can be expressed as (p+V2a​)(V−b)=RT where, p is the pressure, V the volume, T the absolute temperature and a and b are constants. The dimensional formula of a is

[ML5T−2]

[M−1L5T−2]

[ML−1T−2]

[ML−5T−2]

In the equation p, V and T are pressure, volume and temperature respectively. (p+V2a​)(V−b)=RT Dimensions of V2a​ will be same as that of pressure. ∴ Dimensions of V2a​= dimensions of p ⇒ Dimensions of a= dimensions of p× dimensions of V2 =[ML−1T−2][L6] =[ML5T−2]

Q. The equation of-state of some gases can be expressed as
$(p + \frac{a}{V ^{2}}) (V - b) = RT$
where, p is the pressure, V the volume, T the absolute temperature and a and b are constants. The dimensional formula of a is

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

$[M^{- 1} L^{5} T^{- 2}]$

$[M L^{- 1} T^{- 2}]$

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