# Bicycle tire easy exercise

1. Feb 21, 2012

### zezima1

1. The problem statement, all variables and given/known data
A bicycle tire is to start with flat and has a pressure of one atmosphere. It is then pumped such that the pressure is 4atm, when the air inside the tire has the same temperature as before.
a) How much air has been pumped into the bicycle tire?
b) What is the temperature of the air inside the tire just after it has been pumped (assume no heat escapes during the compression).

2. Relevant equations
Ideal gas law
pV = nRT
V*T^(f/2) = constant

3. The attempt at a solution
For the first one I thought this:
Since T is the same before and after but pressure is 4 times a much n must be 4 times as much as before the pumping. Is this correct?

Is so, good. Next we have b). Here I want to use the equations for adiabatic compression but I'm unsure if I'm doing it well. I thought the pressure one would be hard to use since the 4atm is after heat has escaped. Instead I thought that the volume before must have filled up a space of 4 times as much as after, since the amount of molecules is quadropled. Then knowing this we can write an expression for Tfinal = Tf:
Vf*Tf^(5/2) = Vi*Ti^(5/2)
where I've used that normal air has on average about 5 DOF. IS THIS APPROACH CORRECT?