# Dimensions of Universal Gas Constant

## Dimensional Formula of Universal Gas Constant

The dimensional formula of Universal Gas Constant is given by,

M1 L2 T-2 K-1

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Since, P × V = nRT

Therefore, R = P × V × [nT]-1 . . . . . (1)

Where, P = pressure, V = volume, N = number of moles, T = temperature, R = Universal Gas Constant

The dimensional formula of volume = [M0 L3 T0] . . . . (2)

And, the dimensional formula of temperature = [M0 L0 T0 K1] . . . . (3)

Since, Pressure = Force × [Area]-1

= Mass × acceleration × [Area]-1 = [M] × [L1 T-2] × [L2]-1

∴ the dimensional formula of pressure = [M1 L-1 T-2] . . . . (4)

On substituting equation (2), (3) and (4) in equation (1) we get,

Universal Gas Constant = Presure × Volume × [n × Temperature]-1

Or, G = [M1 L-1 T-2] × [M0 L3 T0] × [M0 L0 T0 K1]-1 = [M1 L2 T-2 K-1].

Therefore, the Universal Gas Constant is dimensionally represented as [M1 L2 T-2 K-1].