a helium balloon containing 12m³ of gas at a pressure of 120kpa is released into the air. assuming that the temperature is constant, calculate the volume the balloon would have when the pressure inside the balloon has fallen to 40kpa. answer in m³.
a helium balloon containing 12m³ of gas at a pressure of 120kpa is released into the air. assuming that the temperature is constant, calculate the volume the balloon would have when the pressure inside the balloon has fallen to 40kpa. answer in m³.
answer: We can use the combined gas law to calculate the final volume of the helium balloon.
The combined gas law is given by:
(P1 x V1) / T1 = (P2 x V2) / T2
where:
P1 = initial pressure = 120 kPa
V1 = initial volume = 12 m³
T1 = initial temperature (assumed constant)
P2 = final pressure = 40 kPa
V2 = final volume (to be found)
T2 = final temperature (assumed constant)
Substituting the given values, we get:
(120 kPa x 12 m³) / T1 = (40 kPa x V2) / T2
Since the temperature is constant, T1 = T2 and we can simplify the equation to:
120 kPa x 12 m³ = 40 kPa x V2
Solving for V2, we get:
V2 = (120 kPa x 12 m³) / (40 kPa)
V2 = 36 m³
Therefore, when the pressure inside the balloon has fallen to 40 kPa, the balloon would have a volume of 36 m³.