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1.Units, Dimensions and Measurement
medium
The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are
A
$M{L^5}{T^{ - 2}}$
B
$M{L^{ - 1}}{T^{ - 2}}$
C
${M^0}{L^3}{T^0}$
D
${M^0}{L^6}{T^0}$
Solution
(a) By principle of dimensional homogenity $\left[ {\frac{a}{{{V^2}}}} \right] = \left[ P \right]$
$\therefore $ $[a] = [P]\;[{V^2}] = [M{L^{ – 1}}{T^{ – 2}}]\; \times [{L^6}]$ = $[M{L^5}{T^{ – 2}}]$
Standard 11
Physics
