Question

In the following exercises, solve

636. The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of 29.5 liters with 2000 psi, what is the volume if the tank has a 14.7 psi rating? Round to the nearest whole number

Answer 1

When the volume of a gas in a container varies inversely with the pressure on the gas and a container of nitrogen has a volume of 29.5 litres with 2000 psi. So, if the tank has a 14.7 psi pressure, then the volume of the tank would be 4013.6 litres.

Explanation:

• The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of litres with psi, what is the volume if the tank has a psi pressure.

• Calculate the volume to the nearest whole number.

• Use the given values and calculate the proportionality constant as well as required solution.

Step 1 of 2

Write the inversely proportionality relation between the volume and pressure of a gas in container.

`$v \propto (1)/(p)$`

Where volume is represented by v and pressure is represented by p.

Remove the proportionality and place a constant say k.

`$v=(k)/(p)$`

Substitute the given values of nitrogen that v=29.5 and

p=2000 and calculate the value of k from above equation.

`$$\begin{aligned}&29.5=(k)/(2000) \\&\Rightarrow k=29.5 * 2000 \\&\Rightarrow k=59000\end{aligned}$$`

Step 2 of 2

Substitute the value p=14.7 and above calculated k value in the equation

`$$\begin{aligned}&v=(k)/(p) . \\&v=(59000)/(14.7) \\&\Rightarrow v=4013.6\end{aligned}$$`