Final answer:
Using Boyle's law, we find that when the pressure on a gas increases from 19 psi to 20 psi, the volume decreases from 480 cubic inches to 456 cubic inches, rounded to the nearest cubic inch.
Step-by-step explanation:
The volume of a gas is inversely proportional to the pressure applied to it, according to Boyle's law. This is often represented as PV = k, where P is pressure, V is volume, and k is a constant for a given amount of gas at a constant temperature. In this question, we are given an initial state where the volume (V1) is 480 cubic inches under a pressure (P1) of 19 pounds per square inch (psi), and we need to find the new volume (V2) when the pressure is increased to 20 psi (P2).
To solve, we set up the equation P1V1 = P2V2 since the product of the volume and pressure will remain constant if the temperature and amount of gas do not change. The equation is:
Calculate the constant: 19 psi * 480 cubic inches = k
Use the constant to find the new volume: k = P2 * V2, V2 = k / P2
Round off: Find V2 and round to the nearest cubic inch
Carrying out the calculations, we get the following:
19 psi * 480 cubic inches = 9120 cubic inch-psi (constant k)
V2 = 9120 cubic inch-psi / 20 psi
V2 = 456 cubic inches
Therefore, the new volume of the gas when the pressure is increased to 20 psi is 456 cubic inches, rounded to the nearest cubic inch.