1Which is the dimensional formula of thermal conductivity?
Thermal conductivity works out to [M L T⁻³ K⁻¹].
Heat and thermodynamicsClass 11, Thermal Properties of Matter
Dimensional formula of Thermal conductivity
[M L T-3 K-1]
From the rate of heat flow H = KA ΔT/l, solved for K.
How to get the dimensional formula of thermal conductivity
- Start from the definition: thermal conductivity = heat × length / (time × area × temperature).
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- displacement = length, so displacement is [L] = [L].
- work = force × displacement, so work is [M L T-2] × [L] = [M L2 T-2].
- heat = work, so heat is [M L2 T-2] = [M L2 T-2].
- Put in the dimension of each part: [M L2 T-2] × [L] / ([T] × [L2] × [K]).
- Add the powers of each base quantity: [M L T-3 K-1].
Three questions on thermal conductivity
2What is the SI unit of thermal conductivity?
The SI unit of thermal conductivity is the watt per metre kelvin (W/(m K)).
3Do thermal conductivity and entropy have the same dimensions?
Thermal conductivity is [M L T⁻³ K⁻¹] but entropy is [M L² T⁻² K⁻¹].
Thermal conductivity: quick answers
What is the dimensional formula of thermal conductivity?
The dimensional formula of thermal conductivity is [M L T⁻³ K⁻¹]. It comes from thermal conductivity = heat × length / (time × area × temperature).
What is the SI unit of thermal conductivity?
The SI unit of thermal conductivity is the watt per metre kelvin (W/(m K)).
Is thermal conductivity dimensionless?
No. Thermal conductivity has the dimensions [M L T⁻³ K⁻¹].