1Which of these has the same dimensions as heat?
Heat and gravitational potential energy both have the dimensions [M L² T⁻²].
Heat and thermodynamicsClass 11, Thermodynamics
Dimensional formula of Heat
[M L2 T-2]
Energy that flows because of a temperature difference. It has the dimension of energy, not of temperature.
How to get the dimensional formula of heat
- Start from the definition: heat = work.
- 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].
- Put in the dimension of each part: [M L2 T-2].
- 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
- Internal energy
- Electric potential energy
- Work function
- Photon energy
- Binding energy
Equal dimensions do not make them the same quantity. Compare heat with the others in the full grid.
Three questions on heat
2What is the SI unit of heat?
The SI unit of heat is the joule (J).
3Which one has different dimensions from the others?
Ratio of specific heats is [M⁰ L⁰ T⁰]. The other three are all [M L² T⁻²].
An equation that uses heat
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]
Heat: quick answers
What is the dimensional formula of heat?
The dimensional formula of heat is [M L² T⁻²]. It comes from heat = work.
What is the SI unit of heat?
The SI unit of heat is the joule (J).
Which quantities have the same dimensions as heat?
Heat shares [M L² T⁻²] with work, energy, kinetic energy, potential energy, torque, torsional constant, gravitational potential energy, strain energy. Equal dimensions do not make them the same quantity.