The equation of state of a real gas is given by ( p + ( a/ V2) ) (V - b) = RT where p, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the above equation is

Question

The equation of state of a real gas is given by ( p + ( a/ V2) ) (V - b) = RT where p, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the above equation is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

[ ( a/ V2 ) ] = [ p ] ∴ [ a ] = [ p V2 ] = [ ML - 1 T - 2 ] [ L6 ] = [ ML5 T - 2 ]

Q. The equation of state of a real gas is given by
$(p + \frac{a}{V ^{2}})$ $(V - b) = RT$
where $p, V$ and $T$ are pressure, volume and temperature respectively and $R$ is the universal gas constant. The dimensions of the constant $a$ in the above equation is ______

$[\frac{a}{V ^{2}}] = [p]$
$∴ [a] = [p V^{2}] = [M L^{- 1} T^{- 2}] [L^{6}] = [M L^{5} T^{- 2}]$

Q. The equation of state of a real gas is given by (p+V2a​) (V−b)=RT where p,V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the above equation is ______

[V2a​]=[p] ∴[a]=[pV2]=[ML−1T−2][L6]=[ML5T−2]

Q. The equation of state of a real gas is given by
$(p + \frac{a}{V ^{2}})$ $(V - b) = RT$
where $p, V$ and $T$ are pressure, volume and temperature respectively and $R$ is the universal gas constant. The dimensions of the constant $a$ in the above equation is ______

$[\frac{a}{V ^{2}}] = [p]$
$∴ [a] = [p V^{2}] = [M L^{- 1} T^{- 2}] [L^{6}] = [M L^{5} T^{- 2}]$