First slide

Dimensions of physical quantities

Question

The equation of the state of some gases can be expressed as $(P + \frac{a}{V^{2}}) = \frac{b θ}{V}$ , where P is the pressure, V the volume, $θ$ the absolute temperature, and a and b are constants. The dimensional formula of a is

Moderate

A

$[M L^{5} T^{- 2}]$
B

$[M^{- 1} L^{5} T^{2}]$
C

$[M L^{- 1} T^{- 2}]$
D

$[M L^{- 5} T^{- 2}]$

Solution

By the principle of dimensional homogeneity,
$\begin{array}{l} [P] = [\frac{a}{V^{2}}] \\ \Rightarrow [a] = [P] \times [V^{2}] = [M L^{- 1} T^{- 2}] [L^{6}] = [M L^{5} T^{- 2}] \end{array}$

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