Units And Dimensions Question 11

Question 11 - 01 February - Shift 1

$(P+\frac{a}{V^{2}})(V-b)=R T$ 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 $\frac{b^{2}}{a}$, will be :

(1) Bulk modulus

(2) Modulus of rigidity

(3) Compressibility

(4) Energy density

Show Answer

Answer: (3)

Solution:

Formula: Principle of homogeneity of dimensions

$[b]=[V]$

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

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