Dimensions of Gas Constant

Dimensional Formula of Gas Constant

The dimensional formula of Gas Constant is given by,

[M1 L2 T-2 K-1]

Where,

  • M = Mass
  • L = Length
  • T = Time

Derivation

⇒ Pressure × Volume = Total moles × Temperature × Gas Constant

∴ Gas Constant = Pressure × Volume × [Total moles × Temperature]-1 . . . . . (1)

The dimensional formula of temperature and volume = [M0 L0 T0 K1] and [M0 L3 T0] . . . . (2)

Since, Pressure = Force × [Area]-1 

P = M × a × [Area]-1 = [M × LT-2 × L-2]

∴ the dimensions of pressure = [M1 L-1 T-2] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Gas Constant = Pressure × Volume × [Total moles × Temperature]-1

Or, G = [M1 L-1 T-2] × [L3] × [K1]-1 = [M1 L2 T-2 K-1].

Therefore, the gas constant is dimensionally represented as [M1 L2 T-2 K-1].

⇒ Check Other Dimensional Formulas:

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