Topic: Message #1147155

[Gnarly4X]

Calculator police here....

We start with the ideal gas law: PV=NRT. R is a constant always, and we will assume that V is the same for the spare as for all 4 tires. We will also assume that ambient temperature stays the same over the course of the inflation.

The 10-ply, load range E spare is pumped up to 120 PSI. That means it contains PV/RT or 120*V/RT moles of gas. How many tires can we inflate from 8 to 25 PSI with this setup?

For convenience, I'm going to say that V/RT = C, some constant. A tire of volume V at 8 PSI contains 8*C moles of air, and at 25 PSI contains 25*C moles of air. We thus need 17*C moles of air to air up one tire. How many tires can we air up to 25 PSI? We have 95*C moles of air available before the spare is down to 25 PSI. Therefore, we can write

95C = nTires*17C

nTires = 95C/17C = 95/17 =~ 4.

Note: this assumes that tires do not change volume as they inflate: This is obviously wrong! However, certain aspects of this error tend to cancel each other out. To know how many tires you can really inflate this way, try it or calculate more carefully. However, 4 is all we care about usually and H8PVMNT already showed that it worked.

H8PVMNT, the calculator police is on your side....

How did you determine the volume of the tire? 

Gnarls.