1Which of these has the same dimensions as universal gas constant?
Universal gas constant and molar heat capacity both have the dimensions [M L² T⁻² K⁻¹ mol⁻¹].
Fundamental constantsClass 11, Kinetic Theory
Dimensional formula of Universal gas constant
[M L2 T-2 K-1 mol-1]
The R in PV = nRT. It has the dimension of molar heat capacity.
How to get the dimensional formula of universal gas constant
- Start from the definition: universal gas constant = pressure × volume / (amount of substance × 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].
- area = length × length, so area is [L] × [L] = [L2].
- pressure = force / area, so pressure is [M L T-2] / [L2] = [M L-1 T-2].
- volume = length3, so volume is [L]3 = [L3].
- Put in the dimension of each part: [M L-1 T-2] × [L3] / ([mol] × [K]).
- Add the powers of each base quantity: [M L2 T-2 K-1 mol-1].
Quantities with the dimensions [M L² T⁻² K⁻¹ mol⁻¹]
Equal dimensions do not make them the same quantity. Compare universal gas constant with the others in the full grid.
Three questions on universal gas constant
2What is the SI unit of universal gas constant?
The SI unit of universal gas constant is the joule per mole kelvin (J/(mol K)).
3Do universal gas constant and Coulomb constant have the same dimensions?
Universal gas constant is [M L² T⁻² K⁻¹ mol⁻¹] but Coulomb constant is [M L³ T⁻⁴ A⁻²].
An equation that uses universal gas constant
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
P V = n R TPV[M L2 T-2]=nRT[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
Universal gas constant: quick answers
What is the dimensional formula of universal gas constant?
The dimensional formula of universal gas constant is [M L² T⁻² K⁻¹ mol⁻¹]. It comes from universal gas constant = pressure × volume / (amount of substance × temperature).
What is the SI unit of universal gas constant?
The SI unit of universal gas constant is the joule per mole kelvin (J/(mol K)).
Which quantities have the same dimensions as universal gas constant?
Universal gas constant shares [M L² T⁻² K⁻¹ mol⁻¹] with molar heat capacity. Equal dimensions do not make them the same quantity.