Question

A handheld pump for a bicycle has a volume of 2 in.³ when fully extended. You now press the plunger (piston) in while holding your thumb over the exit hole so an air pressure of 45 lbf/in.² is obtained. The outside atmosphere is at Po, To. Consider two cases:

(1) it is done quickly (~1 s), and

(2) it is done slowly (~1 h).

a.  State assumptions about the process for each case.

b.  Find the final volume and temperature for both cases. 

Answer 1

C.V. Air in pump. Assume that both cases result in a reversible process.

State 1: P₀, T₀

State 2: 45 lbf/in.², ?

One piece of information must resolve the ? for a state 2 property.

Case I) Quickly means no time for heat transfer

Q = 0, so a reversible adiabatic compression.

Case II) Slowly, time for heat transfer so T = constant = T₀.

The process is then a reversible isothermal compression.

T₂ = T₀ = 536.7 R => V₂ = V₁P₁/P₂ = 0.653 in³