13. The volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 210 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 70 cubic inches.

4.67 pounds

Step-by-step explanation:

In order to find the answer we need to use the following formula:

V=k/P where:

V=volume

P=pressure of the gas

k = constant of proportionality

The above equation establishes that the volume is inversely proportional to the pressure of the gas.

Now, the problem gave us two situations, which are:

For a time 1, we have V1=210 cubic inches and P1=14 pounds, using the equation we have:

V1=k/P1

210 cubic inches=k * (14 pounds) which can be written as:

(210 cubic inches) / (14 pounds) = k

For time 2, we have V2=70 cubic inches and P2=P2 using the equation we have:

V2=k/P2

70 cubic inches=k*P2, using 'k-value' from above:

(70 cubic inches) = [ (210 cubic inches) / (14 pounds) ]*P2

(70 cubic inches) * (14 pounds) / (210 cubic inches) = P2

4.67 pounds = P2