1Which is the dimensional formula of specific heat capacity?
Specific heat capacity works out to [L² T⁻² K⁻¹].
Heat and thermodynamicsClass 11, Thermal Properties of Matter
Dimensional formula of Specific heat capacity
[L2 T-2 K-1]
Heat per unit mass per kelvin. Mass cancels, so only length, time and temperature remain.
How to get the dimensional formula of specific heat capacity
- Start from the definition: specific heat capacity = heat / (mass × 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] / ([M] × [K]).
- Add the powers of each base quantity: [L2 T-2 K-1].
Three questions on specific heat capacity
2What is the SI unit of specific heat capacity?
The SI unit of specific heat capacity is the joule per kilogram kelvin (J/(kg K)).
3Do specific heat capacity and solar constant have the same dimensions?
Specific heat capacity is [L² T⁻² K⁻¹] but solar constant is [M T⁻³].
An equation that uses specific heat capacity
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
Q = m c Δ(T)Q[M L2 T-2]=m c Delta T[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
Specific heat capacity: quick answers
What is the dimensional formula of specific heat capacity?
The dimensional formula of specific heat capacity is [L² T⁻² K⁻¹]. It comes from specific heat capacity = heat / (mass × temperature).
What is the SI unit of specific heat capacity?
The SI unit of specific heat capacity is the joule per kilogram kelvin (J/(kg K)).
Is specific heat capacity dimensionless?
No. Specific heat capacity has the dimensions [L² T⁻² K⁻¹].