Dimensional formula of Entropy

How to get the dimensional formula of entropy

1. Start from the definition: entropy = heat / temperature.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. displacement = length, so displacement is [L] = [L].
6. work = force × displacement, so work is [M L T^-2] × [L] = [M L² T^-2].
7. heat = work, so heat is [M L² T^-2] = [M L² T^-2].
8. Put in the dimension of each part: [M L² T^-2] / [K].
9. Add the powers of each base quantity: [M L² T^-2 K^-1].

Quantities with the dimensions [M L² T⁻² K⁻¹]

• Heat capacity
• Boltzmann constant

Equal dimensions do not make them the same quantity. Compare entropy with the others in the full grid.

Three questions on entropy

Related quantities

• Q Heat [M L² T⁻²]
• c Specific heat capacity [L² T⁻² K⁻¹]
• C Molar heat capacity [M L² T⁻² K⁻¹ mol⁻¹]
• L Latent heat [L² T⁻²]
• K Thermal conductivity [M L T⁻³ K⁻¹]
• dT/dx Temperature gradient [L⁻¹ K]