1Which of these has the same dimensions as heat capacity?
Heat capacity and Boltzmann constant both have the dimensions [M L² T⁻² K⁻¹].
Heat and thermodynamicsClass 11, Thermal Properties of Matter
Dimensional formula of Heat capacity
[M L2 T-2 K-1]
Heat needed to raise the temperature of a whole body by one kelvin. Specific heat is per unit mass.
How to get the dimensional formula of heat capacity
- Start from the definition: heat capacity = heat / 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] / [K].
- Add the powers of each base quantity: [M L2 T-2 K-1].
Quantities with the dimensions [M L² T⁻² K⁻¹]
Equal dimensions do not make them the same quantity. Compare heat capacity with the others in the full grid.
Three questions on heat capacity
2What is the SI unit of heat capacity?
The SI unit of heat capacity is the joule per kelvin (J/K).
3Which one has different dimensions from the others?
Heat flow rate is [M L² T⁻³]. The other three are all [M L² T⁻² K⁻¹].
Heat capacity: quick answers
What is the dimensional formula of heat capacity?
The dimensional formula of heat capacity is [M L² T⁻² K⁻¹]. It comes from heat capacity = heat / temperature.
What is the SI unit of heat capacity?
The SI unit of heat capacity is the joule per kelvin (J/K).
Which quantities have the same dimensions as heat capacity?
Heat capacity shares [M L² T⁻² K⁻¹] with entropy, Boltzmann constant. Equal dimensions do not make them the same quantity.