A cylinder contains 20 L of air at 1 atm.The ratio of C_p to C_V for air is 1.41.If this sample of air is compressed adiabatically to a volume of 5 L,the pressure after compression is approximately A)2.7 atm B)7.1 atm C)8.4 atm D)4.0 atm E)9.7 atm

Question

Quizplus · Accepted Answer

For adiabatic processes, $ P_1 V_1^\gamma = P_2 V_2^\gamma $. Given $ \gamma = 1.41 $, $ P_1 = 1 $ atm, $ V_1 = 20 $ L, and $ V_2 = 5 $ L, solve for $ P_2 $: $ P_2 = P_1 \times (V_1/V_2)^\gamma = 1 \times (20/5)^{1.41} \approx 7.1 $ atm.

A Cylinder Contains 20 L of Air at 1 Atm