Answer:
Hence , Ki = Kf
The gas is obeying the Boyle's law.
Explanation:
Given data:
The initial volume of the cylinder(in litres) = [tex]V_1[/tex] = 12.0 L
The initial pressure(in atmospheric pressure) = [tex]P_1[/tex]= 4.0 atm
The final pressure(in atmospheric pressure) = [tex]P_2[/tex] = 8.0 atm
The final volume of the cylinder(in litres) = [tex]V_2[/tex] = 6.0 L
First you need to know what Boyle's law is:
Boyle's law states that the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.
The Mathematical form of Boyle's law is:
[tex]P = \frac{k}{V}[/tex]
Where,
P = Pressure
V = Volume of the gas
k = Boyle's constant
According to the Boyle's law,
[tex]P_{1} = \frac{k_{i}}{V_{1}}[/tex]
[tex]=> k_{i} = P_{1}V_{1}[/tex]
Plug-in the values in the above equation, you would get:
[tex]k_{i} = 4.0 * 10.0 = 40[/tex]
The final pressure(in atmospheric pressure) = = 8.0 atm
The final volume of the cylinder(in litres) == 5.0 L
The Boyle's constant =[tex]k_{f}[/tex] = ?
According to the Boyle's law,
[tex]P_{2} = \frac{k_{f}}{V_{2}}[/tex]
[tex]=> k_{f} = P_{2}V_{2}[/tex]
Plug-in the values in the above equation, you would get:
[tex]k_{f} = 8.0 * 5.0 = 40[/tex]
in order to verify Boyle's law, the initial Boyle's constant should be EQUAL to the final Boyle's constant, meaning:
[tex]k_{i} = k_{f}[/tex]
Since,
[tex]k_{i} = 40\\k_{f} = 40[/tex]
Therefore,
40 = 40
Hence , Ki = Kf
The gas is obeying the Boyle's law.
