Question

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.

Answer 1

4.67 pounds

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