# Engineering Q - dimensional analysis/conversions?

The pertinent variables in describing the behavior of a gas are taken as pressure (P, lbf/ft^2), volume (V, ft^3), number of moles (n, moles), and RT (ft-lbf/mole). On the basis of dimensional analysis, derive a relation among these variables. Note: You must formally derive your answer by following the procedure described in lecture.

I have no clue where to start.

Relevance

Dimensional analysis sounds scary, but it should be taught in high school. Basically, it means don't bother memorizing a bunch of stupid formulae, often you don't need them! Just include the units in your calculations, and make sure they work out.

So in this example, you have 4 variables:

P[lbf/ft^2]

V[ft^3]

n[mole]

RT[ft-lbf/mole]

"derive a relation among these variables" ... ie. write down an equals sign, try to make the right hand side (RHS) equal the left hand side (LHS). To start, just pick one variable for one side, and put the others on the other side

(1) P = VnRT

Now substitute the units and see what happens. Note: you can combine units by multiplying or dividing them out, just like numbers: ft * ft = ft^2 etc... Notice mole/mole=1, they cancel out

[lbf/ft^2] = [ft^3][mole][ft-lbf/mole] -------> [lbf/ft^2] = ft^4-lbf

Therefore, equation (1) is a complete lie because RHS does not equal LHS. Once you get the right equation, LHS = RHS like it should.

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