Dimensions of Specific Heat Capacity

Dimensional Formula of Specific Heat Capacity

The dimensional formula of Specific Heat Capacity is given by,

M0 L2 T-2 K-1

Where,

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

Derivation

Specific Heat Capacity (C) = Heat × [Mass × Temperature]-1.  . . . (1)

The dimensional formula of mass and temperature = [MLT0] and [MLTK1] . . . .(2)

Since, the dimensions of Heat Energy = Dimensions of Work Done

And, Work = Force × displacement

= M × a × displacement = [M] × [MLT-2] × [L]

∴ the dimensional formula of Heat energy = MLT-2 . . . . (3)

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

Specific Heat Capacity = Heat × [Mass × Temperature]-1

Or, C = [MLT-2] × [MLT0]-1 × [MLTK1]-1 = [M0 L2 T-2 K-1].

Therefore, specific heat capacity is dimensionally represented as [M0 L2 T-2 K-1].

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