Answer Happy

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: