The volume of the balloon will halve
Explanation:
Boyle's law states that for an ideal gas kept at constant temperature, the pressure of the gas is proportional to its volume. Mathematically,
[tex]pV=const.[/tex]
where
p is the gas pressure
V is the volume
The equation can also be rewritten as
[tex]p_1 V_1 = p_2 V_2[/tex]
And if we apply it to the gas inside the balloon in this problem (assuming its temperature is constant), we have:
[tex]p_1 = 101 kPa[/tex] is the initial pressure at sea level (the atmospheric pressure)
[tex]V_1[/tex] is the initial volume
[tex]p_2 = 202 kPa[/tex] is the final pressure
[tex]V_2[/tex] is the final volume
Substituting into the equation, we find:
[tex]V_2 = \frac{p_1 V_1}{p_2}=\frac{(101)V_1}{202}=\frac{V_1}{2}[/tex]
Which means that the volume of the balloon will halve.
Learn more about ideal gases:
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