Answer: The pressure of the gas changes by a factor of 2
Explanation:
An isothermal expansion is a process in which a gas expands (or contracts), keeping a constant temperature.
On the other hand, the expression for an Ideal Gas is:
[tex]P.V=n.R.T[/tex] (1)
Where:
[tex]P[/tex] is the pressure of the gas
[tex]V[/tex] is the volume of the gas
[tex]n[/tex] the number of moles of gas
[tex]R[/tex] is the gas constant
[tex]T[/tex] is the absolute temperature of the gas
Now, if the temperature keeps constant, we can use Boyle's law, which relates the volume and pressure of a certain amount of gas maintained at a constant temperature:
[tex]P_{1}V_{1}=P_{2}V_{2}[/tex] (2)
Where [tex]P_{1}V_{1}[/tex] are the initial pressure and initial volume of the gas and [tex]P_{2}V_{2}[/tex] are the final pressure and final volume of the gas.
If:
[tex]P_{1}V_{1}=n.R.T[/tex] (3)
[tex]P_{2}V_{2}=n.R.T[/tex] (4) where [tex]V_{2}=2V_{1}[/tex]
Then:
[tex]P_{1}V_{1}=P_{2}(2V_{1})[/tex] (5)
[tex]\frac{P_{1}}{P_{2}}=\frac{2V_{1}}{V_{1}}[/tex] (6)
[tex]\frac{P_{1}}{P_{2}}=2[/tex] (7)
Finally:
[tex]P_{1}=2P_{2}[/tex] (8) This means the pressure of the gas changes by a factor of 2.
