What are the dimensions of universal has constant if you use theta to denote temperature?

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Solution

We know ,

according to gases formula,
PV = nRT

where P is the pressure, V is the volume, n is the no of mole, R is gas constant and T is temperature.

now , R = PV/nT

dimension of pressure = [ML^-1T^-2]
dimension of volume = [ L^3 ]
dimension of mole = no dimension
dimension of temperature = [θ]

now , dimension of R =[ML^-1T^-2][L^3]/[K]
=[ ML²T⁻² θ⁻¹]

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