Question

A handheld pump for a bicycle has a volume of 25 cm³ when fully extended. You now press the plunger (piston) in while holding your thumb over the exit hole so that an air pressure of 300 kPa is obtained. The outside atmosphere is at P₀, T₀. Consider two cases: (1) it is done quickly (∼1 s), and (2) it is done very 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: 300 kPa, ?

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.

With constant s and constant heat capacity 

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

The process is then a reversible isothermal compression. 

 T₂ = T₀ = 298 K 

=> V₂ = V₁P₁/P₂ = 8.44 cm³