Let's say that the 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?
The general approach is to separate the variables which change on one side of an equation, and the variables which remain constant on the other side. Two equations can then be written which describe the situation before and after the change, and solved.
Pressure and temperature are changing in this problem, but the number of moles and volume is constant. Rearrange the ideal gas law to put the changing variables on one side and the constant ones on the other.
Now, we can have two "versions" of this equation. One applies to the sample before the change. Pressure and temperature are given a subscript one in this version. Another version of the equation applies to the sample after the change. Pressure and temperature are given a subscript two in the second version.
We don't need subscripts on n and V in the two versions because they don't change. Since the right-hand sides of those two equations are the same, we can set the left-hand sides equal to each other.
We are looking for P2, the pressure after the tire cools. Therefore, in the final step we solve for P2, plug in known values for P1, T1 and T2, and obtain the final answer of P2=2.59 atmospheres.