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:

• Dimensions of Acceleration Due To Gravity
• Dimensions of Density
• Dimensions of Linear Density
• Dimensions of Pressure Gradient
• Dimensions of Rotational Kinetic Energy