Question

Give a solution to find the dimension formula of specific heat capacity ? And what is dimension formula of heat ?

Answer 1

Answer:

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 = [M1 L0 T0] and [M0 L0 T0 K1] . . . .(2)

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

And, Work = Force × displacement

= M × a × displacement = [M] × [M0 L1 T-2] × [L]

∴ the dimensional formula of Heat energy = M1 L2 T-2 . . . . (3)

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

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

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

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