Which terms are dimensionally homogeneous

Niederhauser, S. Wunderli, U. Feller, No Rationale for a redefinition of the mole. Chimia 63 , — CrossRef Google Scholar. Accessed 2 Dec Accessed 22 Nov Alberto N.

Conejo 1 1. Personalised recommendations. Cite chapter How to cite? ENW EndNote. Buy options. Now for the tricky part. Just because an equation is dimensionally homogeneous does not mean it is correct.

Take a look at the little example shown here. We KNOW that the equation for kinetic energy is valid. Therefore, we know that it must be dimensionally homogeneous. We can USE dimensional homogeneity to determine the dimensions of kinetic energy as shown here. If we had just derived an equation and we wanted to check to see if our result was dimensionally homogeneous, we would plug in the dimensions of each variable and see if each term in an addition, subtraction or equality operation has the same dimensions.

If the equation is not dimensionally homogeneous, we know we messed up the derivation. Well, that completes our discussion of dimensions and systems of units. Take a look at a bigger example problem. Then, review the lesson summary on the next page and try the quiz to make sure you really know what you are doing. Then move on to the next lesson: Systems, States and Properties. An example of an equation being dimensionally homogenous but inconsistent in units is if the units on one side of the equation are different than the other.

In these cases, usually the fix is to take the variable with the wrong units and use the appropriate conversion to assign the proper units to it. Differentiate dimensions and units dimensional homogeneity and unit consistency.

Understand dimensional homogeneity and unit consistency conceptually. In this section, we will explore the concept of homogeneity.