Question

The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 360 cubic inches under a pressure of 15 pounds per square inch, what will be its volume if the pressure is increased to 19 pounds per square inch? Round your answer to the nearest integer if necessary.

Answer 1

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Explanation:

The relationship between the volume (V) of a gas and the pressure (P) on the gas can be expressed as an inverse variation or proportionality:

V ∝ 1/P

This means that the product of volume and pressure is constant. You can write this as: (V)*(P) = k

Where "k" is a constant. We can find the value of "k" using the initial values:

Initial volume (V1) = 360 cubic inches

Initial pressure (P1) = 15 pounds per square inch

(V1) * (P1) = k

360 * 15 = k

k = 5400

Now that we have found the constant "k," we can use it to find the new volume (V2) when the pressure (P2) is increased to 19 pounds per square inch:

(V2) * (P2) = k

V2 * 19 = 5400

Now, solve for V2:

V2 = 5400 / 19 ≈ 284.21 (rounded to two decimal places)

So, when the pressure is increased to 19 pounds per square inch, the volume of the gas will be approximately 284 cubic inches (rounded to the nearest integer).