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