During an adiabatic compression, a volume of air decreases to 1/4 its original size. Calculate its final pressure if its original pressure was 1 atm. (Assume the air behaves like an ideal gas with γ = 1.4.)
A) 7.0 atm
B) 5.6 atm
C) 3.5 atm
D) 2.2 atm
E) 0.14 atm

Question

Quizplus · Accepted Answer

For an adiabatic process, PV^γ = constant. Thus, P_f * (V_i/4)^γ = P_i * V_i^γ, where P_i = 1 atm. Solving for P_f, we get P_f = P_i * (4)^γ = 1 atm * (4)^1.4 = 7.0 atm.

During an Adiabatic Compression, a Volume of Air Decreases to 1/4