Imagine the following design for a simple tire pump. The pump is filled with a volume Vi of air at atmospheric pressure pa and ambient temperature Ta. When you push the pump handle, the air is compressed to a new (smaller) volume Vf, raising its pressure. A valve is then opened, allowing air to flow from the pump into the tire until the remaining air in the pump reaches the pressure of the air in the tire, pt.

In this problem, you will consider whether you can get more air into the tire per pump cycle by pushing the pump handle quickly or slowly.

We will make the following simplifying assumptions:

The pressure of the air in the tire, pt, does not change significantly as air flows into the tire from the pump.

The temperature of the air in the pump does not change significantly while air is flowing into the tire (i.e., this is an isothermal process).

The air is mainly composed of diatomic molecules with =1.40.

part a

First imagine that you push the pump handle quickly, so that the compression of air in the pump occurs adiabatically. Find the absolute temperature Tf of the air inside the pump after a rapid compression from volume Vi to volume Vf, assuming an ambient temperature of Ta.

Express your answer in terms of Ta, Vi, Vf, and

part c

Now imagine that you push the pump handle slowly, so that the compression of air in the pump occurs isothermally. Find the absolute temperature Tf of the air inside the pump assuming an ambient temperature of Ta.