Units Conversion By Factor-label - Checking Equations That Involve Dimensions

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 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 is 8.3145 Pa·m³/(mol·K)
• the temperature T is in kelvins (K)

mol (Pa)(m³) K (Pa)(m³) = ----- × ---------- × --- 1 (mol)(K) 1

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.