What is the volume of air in an air chamber 4" in diameter and 12" long at a pressure of 80 psig if the chamber is initially filled with air at atmospheric pressure (14.7 psi)?

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Quizplus · Accepted Answer

The volume of air in the chamber can be calculated using the ideal gas law, which in this context simplifies to Boyle's Law since the temperature is constant. Boyle's Law states that P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. The initial pressure is atmospheric pressure, 14.7 psi, and the final pressure is 80 psig, which is gauge pressure. To use Boyle's Law, we need to convert gauge pressure to absolute pressure by adding atmospheric pressure: 80 psig + 14.7 psi = 94.7 psi absolute. The volume of the cylinder (V1) can be calculated using the formula for the volume of a cylinder, V = πr^2h, where r is the radius (half the diameter) and h is the height (length). The radius is 2 inches (half of 4 inches), and the height is 12 inches. So, V1 = π(2^2)(12) = π(4)(12) = 48π cubic inches. Using Boyle's Law to find V2 (the volume at the new pressure), we get V2 = (P1V1)/P2 = (14.7*48π)/94.7. Since we're looking for an equivalent volume at the original atmospheric pressure to compare, we calculate the volume at the higher pressure and then understand it in terms of the space it would occupy at atmospheric pressure. The calculation simplifies to finding the initial volume since the pressure ratio adjusts the volume directly. The actual calculation of V2 gives us the volume at the new pressure, but since we're asked for the volume in cubic inches at the original condition (which implicitly means how much more air or the equivalent volume of air at atmospheric pressure), we directly use the initial volume calculation, which is 48π cubic inches. Converting 48π to a decimal gives us approximately 150.8 cubic inches at atmospheric pressure. However, the question seems to be asking for how the volume of air changes due to compression, which would be reflected in the change in conditions, not directly calculable without considering the change in conditions. The correct approach involves understanding the relationship between pressure and volume changes, but the provided options and explanation seem to mismatch typical calculations for these conditions. The explanation provided aims to clarify the process, but it appears there may be a misunderstanding in the question's intent or a misinterpretation in the explanation process.

What Is the Volume of Air in an Air Chamber