Obtain the dimensional equation for universal gas constant. - Vidyadip

MCQ

Obtain the dimensional equation for universal gas constant.

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

✓

Answer

(a) $\left[ M L ^2 T^{-2} mol^{-1} K^{-1}\right]$
Explanation: According to ideal gas equation for universal gas constant. i.e., $pV = nRT$, where n is the number of moles of gases.
$
\begin{aligned}
& R=\frac{(p)(V)}{(n)(T)}=\frac{\left[ML^{-1} T^{-2}\right]\left[L^3\right]}{[mol][K]} \\
& =\left[ML^2 T^{-2} mol^{-1} K^{-1}\right]
\end{aligned}
$

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