Question

Consider a small air pistol with a cylinder volume of 1 cm³ at 250 kPa, 27°C. The bullet acts as a piston initially held by a trigger. The bullet is released so the air expands in an adiabatic process. If the pressure should be 100 kPa as the bullet leaves the cylinder find the final volume and the work done by the air. 

Answer 1

C.V. Air. Assume a reversible, adiabatic process.

Energy Eq.  u₂ - u₁ = 0 − ₁w₂ ;

Entropy Eq  s₂ - s₁ = ∫ dq/T + ₁s_{2 gen} =  0 

State 1: (T₁,P₁)  State 2: (P₂, ?

So we realize that one piece of information is needed to get state 2.

Process: Adiabatic ₁q₂ = 0 Reversible ₁s₂ gen = 0

With these two terms zero we have a zero for the entropy change. So this is a constant s (isentropic) expansion process giving s₂ = s_1.