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 = [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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Pressure Gradient
• Dimensions of Current Density
• Dimensions of Impedance
• Dimensions of Linear Density
• Dimensions of Rotational Kinetic Energy

Heat Capacity