Panel 10: Solving a problem with two variables:
An automobile tire is inflated to 3.0 atmospheres indoors
at a temperature of 302 Kelvin. The tire is then moved
outside, where the temperature is 261 Kelvin. Given this
data and assuming that the volume of the tire does not
change, what will be the resulting pressure in the tire?
Solution step 1: Rearrange PV=nRT to put the
changing variables on one side and the constant ones on the other:
P/T = nR/V
Solution step 2: Write two versions of this equation,
one for before the change and one for after the change:
Indoors: P1/T1 = nR/V
Outdoors: P2/T2 = nR/V
Solution step 3: Since the right-hand sides of the
previous two equations are the same, we can set the left-hand
sides equal to each other:
P1/T1 = nR/V = P2/T2
Solution step 4: Solve for P2:
P2 = P2T2/T1 = ( (3.00atm)(261K) ) / (302K) = 2.59atm