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].
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