(P+(a/V2))(V-b)=R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of (b2/a), will be:

Question

(P+(a/V2))(V-b)=R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of (b2/a), will be: (A) Bulk modulus (B) Compressibility (C) Modulus of rigidity (D) Energy density

Tardigrade Admin · Accepted Answer

[b]=[V] [(a/b2)]=[P] ∴ [(b2/a)]=(1/[P])=(1/[B])=[K]

Q. $(P + \frac{a}{V ^{2}}) (V - b) = RT$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b ^{2}}{a}$ , will be:

Bulk modulus

Compressibility

Modulus of rigidity

Energy density

$[b] = [V]$
$[\frac{a}{b ^{2}}] = [P]$
$∴ [\frac{b ^{2}}{a}] = \frac{1}{[ P ]} = \frac{1}{[ B ]} = [K]$

Q. (P+V2a​)(V−b)=RT represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a,b,R are the constants. The physical quantity, which has dimensional formula as that of ab2​, will be: