First slide

Dimensions of physical quantities

Question

For $n$ moles of gas, van der Waals' equation is $(p + \frac{a}{V^{2}}) (V - b) = n R T$
Find the dimensions of $a a n d b$ , where $p$ = pressure of gas, $V$ = volume of gas and $T$ = temperature of gas.

Moderate

A

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

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

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

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

Solution

$[b] = [V] = [L^{3}] \frac{[a]}{[V]^{2}} = [P] = [M L^{- 1} T^{- 2}] [a] = [{ML}^{5} T^{- 2}]$

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