A monatomic ideal gas is compressed adiabatically to one-third of its initial volume. The resulting pressure will be
A) three times as large as the initial value.
B) less than three times as large as the initial value.
C) more than three times as large as the initial value.
D) equal to the initial value.
E) impossible to predict on the basis of this data.

Question

Quizplus · Accepted Answer

According to the adiabatic compression process, PV^(gamma)=constant, where P is pressure, V is volume, and gamma is the ratio of specific heats (Cp/Cv) for a monatomic ideal gas. As the gas is compressed to one-third of its initial volume, the final volume will be (1/3)V, and thus the final pressure will be P*(V/3)^gamma. Since gamma for a monatomic ideal gas is 5/3, we can simplify this expression to P*(1/3)^(5/3) = P*(1/27). Therefore, the final pressure will be 27 times the initial pressure, which is more than three times as large as the initial value. The correct choice is therefore C.

A Monatomic Ideal Gas Is Compressed Adiabatically to One-Third of Its