Respuesta :
Answer: The quantity relating pressure and volume is [tex]PV=k[/tex] and the size of the tank must be [tex]1.92\times 10^3L[/tex]
Explanation:
To calculate the new volume, we use the equation given by Boyle's law. This law states that pressure is inversely proportional to the volume of the gas at constant temperature.
Mathematically,
[tex]P\propto \frac{1}{V}[/tex]
Or,
[tex]PV=k[/tex]
The equation given by this law is:
[tex]P_1V_1=P_2V_2[/tex]
where,
[tex]P_1\text{ and }V_1[/tex] are initial pressure and volume.
[tex]P_2\text{ and }V_2[/tex] are final pressure and volume.
We are given:
[tex]P_1=160atm\\V_1=12L\\P_2=1atm\\V_2=?L[/tex]
Putting values in above equation, we get:
[tex]160atm\times 12L=1atm\times V_2\\\\V_2=\frac{160\times 12}{1}=1920L=1.92\times 10^3L[/tex]
Hence, the size of the tank must be [tex]1.92\times 10^3L[/tex]
