Question

The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 248 cubic inches under a pressure of 5 pounds per square inch what will be its volume of the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.

Answer 1

If two quentities (V, P) are very inversely, so

`\begin{gathered} V=(k)/(P) \\ OR \\ (V_1)/(V_2)=(P_2)/(P_1) \end{gathered}`

Where k is the constant of variation, we can get it by using the initial values of V and P

Let us use the second rule

Since V is 248 cubic inches when P is 5 pounds per square inch, then

`\begin{gathered} V_1=248 \\ P_1=5 \end{gathered}`

We need to find V when P = 7 pounds per square inch

`\begin{gathered} V_2=? \\ P_2=7 \end{gathered}`

Let us substitute these values in the second rule

`(248)/(V_2)=(7)/(5)`

By using cross multiplication

`\begin{gathered} V_2*7=248*5 \\ 7V_2=1240 \end{gathered}`

Divide both sides by 7

`\begin{gathered} (V_2)/(7)=(1240)/(7) \\ V_2=177.142857 \end{gathered}`

Round it to the nearest integer

`V_2=177in^3`

The volume of the gas is 177 cubic inches