Dimensional formula of Internal energy

How to get the dimensional formula of internal energy

1. Start from the definition: internal energy = heat.
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].
9. Add the powers of each base quantity: [M L² T^-2].

Quantities with the dimensions [M L² T⁻²]

• Work
• Energy
• Kinetic energy
• Potential energy
• Torque
• Torsional constant
• Gravitational potential energy
• Strain energy
• Heat
• Electric potential energy
• Work function
• Photon energy
• Binding energy

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

Three questions on internal energy

Related quantities

• C Heat capacity [M L² T⁻² K⁻¹]
• 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]