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Heat and thermodynamicsClass 11, Thermodynamics

Dimensional formula of Molar heat capacity

[M L2 T-2 K-1 mol-1]

SymbolC SI unitjoule per mole kelvin (J/(mol K))

Heat per mole per kelvin. It has the same dimension as the gas constant.

Derivation

How to get the dimensional formula of molar heat capacity

  1. Start from the definition: molar heat capacity = heat / (amount of substance × 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] / ([mol] × [K]).
  9. Add the powers of each base quantity: [M L2 T-2 K-1 mol-1].
Same dimensions

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

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

Practice

Three questions on molar heat capacity

1Which of these has the same dimensions as molar heat capacity?

2What is the SI unit of molar heat capacity?

3Do molar heat capacity and thermal resistance have the same dimensions?

Questions

Molar heat capacity: quick answers

What is the dimensional formula of molar heat capacity?

The dimensional formula of molar heat capacity is [M L² T⁻² K⁻¹ mol⁻¹]. It comes from molar heat capacity = heat / (amount of substance × temperature).

What is the SI unit of molar heat capacity?

The SI unit of molar heat capacity is the joule per mole kelvin (J/(mol K)).

Which quantities have the same dimensions as molar heat capacity?

Molar heat capacity shares [M L² T⁻² K⁻¹ mol⁻¹] with universal gas constant. Equal dimensions do not make them the same quantity.

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