# Homework Help: Bicycle pump!

1. Sep 17, 2008

### yossup

1. The problem statement, all variables and given/known data

A bicycle pump is a cylinder 20cm long and 3.0cm in diameter. The pump contains air at 21.0C and 1.0atm. If the outlet at the base of the pump is blocked and the handle is pushed in very quickly, compressing the air to half its original volume, how hot does the air in the pump become?

2. Relevant equations

PV=nRT
PV^gamma = PV^gamma

3. The attempt at a solution

So the intial volume is 1.55m^3. The final volume is .775m^3. And because the handle is pushed very quickly, the process is adiabatic. So I want to know what gamma is but do I use the one for di or triatomic? Then i just use the W = integral P dv?

2. Sep 17, 2008

### stewartcs

Air is composed mostly of Nitrogen and Oxygen (which are diatomic molecules). Thus, the specific heat ratio of air is assigned the value of 1.4.

Since the air is compressed quickly, you may assume it is adiabatic. At relatively low pressures air is also considered to behave as an ideal gas. If you further assume it is a reversible process then you end up with an isentropic process.

Do you know of any relationships that contain the volume, temperature, and specific heat ratio for an isentropic process?

CS

3. Sep 17, 2008

### yossup

Um...we haven't even gone over isentropic processes yet but is the equation your're talking about this? PdV + VdP = nRdT

4. Sep 17, 2008

### stewartcs

$$T_2 = T_1 \cdot \left(\frac{V_1}{V_2}\right)^{k-1}$$

where k is the specific heat ratio.

CS