The dimensions of universal gas constant are

Options

(a) [ML²T⁻²θ⁻¹]
(b) [M²LT⁻²θ]
(c) [ML³T⁻²θ⁻¹]
(d) None of these

Correct Answer:

[ML²T⁻²θ⁻¹]

Explanation:

According to Ideal gas equation,  PV = nRT
where P is the pressure, V is the volume, n is the no of moles, R is gas constant and T is temperature.
now , R = PV/nT
dimension of pressure = [ML⁻¹T⁻²]
dimension of volume = [ L³ ]
dimension of mole = no dimension
dimension of temperature = [ θ]

So , dimension of R =[ML⁻¹T⁻²][L³]/[θ]
=[ ML²T⁻²θ⁻¹]