Checking equations that involve dimensions
The factor-label method can also be used on any mathematical equation to check whether or not the dimensional units on the left hand side of the equation are the same as the dimensional units on the right hand side of the equation. Having the same units on both sides of an equation does not guarantee that the equation is correct, but having different units on the two sides of an equation does guarantee that the equation is wrong.
For example, check the Universal Gas Law This article outlines the historical development of the laws describing ideal gases. For a detailed description of the ideal gas laws and their further development, see Ideal gas, Ideal gas law and Gas equation of P·V = n·R·T, when:
- the pressure P is in pascals (Pa)
- the volume V is in cubic meters (m³)
- the amount of substance n is in moles (mol)
- the universal gas law constant R The gas constant is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy (i.e. the pressure-volume product) per kelvin per mole (rather than energy per kelvin per is 8.3145 Pa·m³/(mol·K)
- the temperature T is in kelvins (K)
(Pa) (m³) = (mol) [ (Pa·m³) / (mol · K) ] (K)
As can be seen, when the dimensional units appearing in the numerator and denominator of the equation's right hand side are cancelled out, both sides of the equation have the same dimensional units.
<<Table of Contents Many, if not most, parameters and measurements in the physical sciences and engineering are expressed as a numerical quantity and a corresponding dimensional unit; for example: 1000 kg/m³, 100 kPa/bar, 50 miles per hour, 1000 Btu/lb. Converting from one dimensional unit to another is often somewhat complex and being able to perform such | Next>> | Show All>>
