Question

To what pressure must a gas be compressed in order to get into a 3.00 cubic foot tank the entire weight of a gas that occupies 400.0 cu. ft. at standard pressure?

Answer 1

Hint: At standard temperature and pressure the pressure is 1 atm.
There is a relationship between pressure and volume and it can be expressed by using Boyle’s law and it as follows.
\[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\]
${{P}_{1}}$ = Initial pressure
${{V}_{1}}$ =initial volume
${{P}_{2}}$ = final pressure
${{V}_{2}}$ = final volume

Complete Solution :
- In the question it is given that a gas is compressed in order to get into a 3. Cu. foot tank.
- The total tank occupies 400.0 cu. foot at standard pressure.
- The given data in the question is as follows.
${{P}_{1}}$ = Initial pressure = 1atm
${{V}_{1}}$ =initial volume = 400 cu. foot
${{P}_{2}}$ = final pressure
${{V}_{2}}$ = final volume = 3.00 cu. ft.

- By using Boyle’s law we can find the final pressure of the gas and it is as follows.
\[\begin{align}
  & {{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}} \\
 & 1\times 400={{P}_{2}}\times 3 \\
 & {{P}_{2}}=\dfrac{400}{3} \\
 & {{P}_{2}}=133.3 atm \\
\end{align}\]
- Therefore 133.3 atm of pressure is required to compress the gas in order to get into a 3.00 cubic foot tank the entire weight of a gas that occupies 400.0 cu. ft. at standard pressure

Note: Volume and pressure are inversely proportional to each other. If the volume of the gas increases then the pressure is going to decrease and if the pressure increases then the volume of the gas decreases. Temperature and volume are directly proportional to each other. If the temperature of the gas increases then the volume of the gas also increases and vice versa.