the volume of a gas in a container varies inversely as the pressure on the gas. if a gas has a volume of 329329 cubic inches under a pressure of 66 pounds per square inch, what will be its volume if the pressure is increased to 77 pounds per square inch? round your answer to the nearest integer if necessary.

Question

19-12-2022
Mathematics

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the volume of a gas in a container varies inversely as the pressure on the gas. if a gas has a volume of 329329 cubic inches under a pressure of 66 pounds per square inch, what will be its volume if the pressure is increased to 77 pounds per square inch? round your answer to the nearest integer if necessary.

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Papreso Papreso · Answer 1 · 2022-12-19T12:39:12-05:00

The relationship between the volume of a gas and the pressure on the gas is described by the equation V ∝ 1/P, where V is the volume and P is the pressure. This equation means that the volume and pressure of a gas are inversely proportional, so if the pressure increases, the volume will decrease and vice versa.

To find the volume of the gas when the pressure is increased from 66 pounds per square inch to 77 pounds per square inch, you can use the formula for inverse proportionality to solve for the new volume:

V1/V2 = P2/P1

Plugging in the known values, you get:

V1/V2 = 77 pounds per square inch / 66 pounds per square inch

= 1.16

Rearranging the equation to solve for V2, you get:

V2 = V1 * (P1/P2)

= 329329 cubic inches * (66 pounds per square inch / 77 pounds per square inch)

= 329329 cubic inches * (0.86)

= 283590 cubic inches

Rounding this volume to the nearest integer, the volume of the gas when the pressure is increased to 77 pounds per square inch is approximately 283,590 cubic inches.