A cylinder with a piston contains 2.00 liters of an ideal monatomic gas at 1.00 atm and 275 K.The gas is subject to an adiabatic compression and its pressure increases to four times its initial pressure.What is the volume after the compression?

Question

Quizplus · Accepted Answer

Since the process is adiabatic, we have 
PV^γ=constant, where γ=Cp/Cv=5/3 for a monatomic gas.
At the initial state, P1V1^γ = nRT1 which gives us n = P1V1 / RT1 = 0.0832 mol (using R = 8.31 J/mol K). 
When the pressure becomes 4P1, the final volume is V2 = V1 (P1/P2)^1/γ = 0.866 L. 
Thus the answer is C, 0.87 liters.

A Cylinder with a Piston Contains 2