1Which of these has the same dimensions as ratio of specific heats?
Ratio of specific heats and angle both have the dimensions [M⁰ L⁰ T⁰].
Heat and thermodynamicsClass 11, Thermodynamics
Dimensional formula of Ratio of specific heats
[M0 L0 T0]
C_p divided by C_v, a pure number such as 5/3 or 7/5. It is why γ can appear as a plain factor in v = sqrt(γP/ρ).
How to get the dimensional formula of ratio of specific heats
- Start from the definition: ratio of specific heats = molar heat capacity / molar heat capacity.
- 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-1 mol-1] / [M L2 T-2 K-1 mol-1].
- Add the powers of each base quantity: [M0 L0 T0].
Quantities with the dimensions [M⁰ L⁰ T⁰]
- Angle
- Solid angle
- Coefficient of friction
- Coefficient of restitution
- Relative density
- Strain
- Poisson's ratio
- Reynolds number
- Emissivity
- Sound level
- Relative permittivity
- Magnetic susceptibility
- Relative permeability
- Power factor
- Quality factor
- Refractive index
- Magnification
Equal dimensions do not make them the same quantity. Compare ratio of specific heats with the others in the full grid.
Three questions on ratio of specific heats
2Which of these has no dimensions at all?
Ratio of specific heats is a ratio, so every power in its dimensional formula is zero.
3Which one has different dimensions from the others?
Coefficient of linear expansion is [K⁻¹]. The other three are all [M⁰ L⁰ T⁰].
An equation that uses ratio of specific heats
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
v = sqrt(γ P / ρ)v[L T-1]=sqrt(gamma P / rho)[L T-1]Dimensionally consistentEvery term is [L T-1]
v = velocity
Ratio of specific heats: quick answers
What is the dimensional formula of ratio of specific heats?
The dimensional formula of ratio of specific heats is [M⁰ L⁰ T⁰]. It comes from ratio of specific heats = molar heat capacity / molar heat capacity.
What is the SI unit of ratio of specific heats?
Ratio of specific heats has no unit, because it is a pure number.
Is ratio of specific heats dimensionless?
Yes. Ratio of specific heats is a ratio of like quantities, so every power in its dimensional formula is zero: [M⁰ L⁰ T⁰].