Calculating Temperature Rise of Air in Bicycle Pump

[yossup]

Homework Statement

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?

Homework Equations

PV=nRT
PV^gamma = PV^gamma

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?

 

[stewartcs]

Homework Statement

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?

Homework Equations

PV=nRT
PV^gamma = PV^gamma

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?

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

 

[yossup]

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

 

[stewartcs]

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

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

where k is the specific heat ratio.

CS