First slide

Dimensions of physical quantities

Question

In the formula, $p = \frac{n R T}{V - b} e^{\frac{a}{R T V}}$ , find the dimensions of $a a n d b$ , where $p$ = pressure, $n$ = number of moles, $T$ = temperature, $V$ = volume and $R$ = universal gas constant.

Moderate

A

$[a] = [{ML}^{5} T^{2} {mol}^{- 1}], [b] = [L^{3}]$
B

$[a] = [{ML}^{- 5} T^{- 2} {mol}^{- 1}], [b] = [L^{3}]$
C

$[a] = [{ML}^{3} T^{- 2} {mol}^{- 1}], [b] = [L^{4}]$
D

$[a] = [{ML}^{5} T^{- 2} {mol}^{- 1}], [b] = [L^{3}]$

Solution

$[\frac{a}{R T V}] = [M^{0} L^{0} T^{0}] ∴ [a] = [R T V] = [\frac{p V^{2}}{n}] = [{ML}^{5} T^{- 2} {mol}^{- 1}] [b] = [L^{3}]$

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