Obtain the dimensional equation for universal gas constant. - Vidyadip

MCQ

Obtain the dimensional equation for universal gas constant.

A
$[\text{ML}^2\text{T}^{-2}]\text{ mol }^{-1}\text{K}^{-1}$
B
$[\text{M}^2\text{LT}^{-1}\text{mol }^{-2}\text{K}^{-2}]$
C
$[\text{ML}^{2}\text{L}\text{T}^{-1}\text{ mol}^{-1}\text{K}^{-1}]$
D
$[\text{ML}^{3}\text{L}\text{T}^{-1}\text{ mol}^{-1}\text{K}^{-2}]$

✓

Answer

$[\text{ML}^2\text{T}^{-2}]\text{ mol }^{-1}\text{K}^{-1}$

Explanation:

According to ideal gas equation for universal gas constant.

i.e., pV = nRT, where n is the number of moles of gases.

$\text{R}=\frac{(\text{p})(\text{V})}{(\text{n})(\text{T})}=\frac{[\text{ML}^{-1}\text{T}^2][\text{L}^3]}{{[\text{mol}][\text{K}]}}$

$=[\text{ML}^2\text{T}^{-2}\text{mol}^{-1}\text{K}^{-1}]$

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