An ideal gas with a pressure of 1.00 atm at room temperature (300 K)is compressed from 500.0 cm³ to a final volume.The compression is adiabatic and the final pressure of the gas is 25.1 atm.What final volume of the gas?

Question

Quizplus · Accepted Answer

Using the adiabatic compression equation: PV^(gamma)=constant, where gamma is the heat capacity ratio of the gas. For an ideal gas, gamma=1+2/f, where f is the degrees of freedom (f=3 for monoatomic gas, and f=5 for diatomic gas). In this case, gamma=1.4, because air is mostly diatomic. 
Plugging in the given values, the equation becomes: 
(1.00 atm)(500.0 cm^3)^1.4 = (25.1 atm)V^1.4
Solving for V, we get V=44.3 cm^3, which is answer choice C.

An Ideal Gas with a Pressure of 1