Question

Calculation of dimensional formula for specific gas constant and it's units

Answer 1

Answer:

Explanation:

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JEEUnits and DimensionsDimensions Of Gas Constant

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].