Respuesta :
Answer:
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.
Step-by-step 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.
[tex]$v \propto \frac{1}{p}$[/tex]
Where volume is represented by v and pressure is represented by p.
Remove the proportionality and place a constant say k.
[tex]$v=\frac{k}{p}$[/tex]
Substitute the given values of nitrogen that v=29.5 and
p=2000 and calculate the value of k from above equation.
[tex]$\begin{aligned}&29.5=\frac{k}{2000} \\&\Rightarrow k=29.5 \times 2000 \\&\Rightarrow k=59000\end{aligned}$[/tex]
Step 2 of 2
Substitute the value p=14.7 and above calculated k value in the equation
[tex]$\begin{aligned}&v=\frac{k}{p} . \\&v=\frac{59000}{14.7} \\&\Rightarrow v=4013.6\end{aligned}$[/tex]
