Mixed ConceptsMediumQuestion 5048
Question
Using Θ for temperature and N for amount of substance, what are the dimensions of the molar gas constant R?
- A[ML²T⁻²Θ⁻¹N⁻¹]Correct
- B[MLT⁻²Θ⁻¹]
- C[ML²T⁻²N⁻¹]
- D[ML²T⁻¹Θ⁻¹N⁻¹]
Correct answer
[ML²T⁻²Θ⁻¹N⁻¹]
Explanation
In PV = nRθ, pressure × volume has energy dimensions [ML²T⁻²]. Divide by amount [N] and temperature [Θ] to obtain [ML²T⁻²Θ⁻¹N⁻¹]. The SI unit is J mol⁻¹ K⁻¹; unit symbols and dimension symbols are different.