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1.Units, Dimensions and Measurement
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The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{b\theta }}{l}$ Where $P$ is the pressure, $V$ the volume, $\theta $ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is
A
$[M{L^5}{T^{ - 2}}]$
B
$[{M^{ - 1}}{L^5}{T^{ 2}}]$
C
$[M{L^{ - 5}}{T^{ - 1}}]$
D
$[M{L^{ 5}}{T^{ 1}}]$
(AIPMT-1996)
Solution
(a) By the principle of dimensional homogenity
$[P] = \left[ {\frac{a}{{{V^2}}}} \right] \Rightarrow [a] = [P] \times [{V^2}] = [M{L^{ – 1}}{T^{ – 2}}]\,[{L^6}]$
= $[M{L^5}{T^{ – 2}}]$
Standard 11
Physics
