A hot air balloon is hovering at an altitude of 6000 meters. The pilot decides that it is time to descend and turns off the balloon's burners. Once the balloon reaches the ground, the gas inside the balloon occupies 980 m^3 and is at atmospheric pressure. If the pressure of the gas inside of the balloon was 75,000 Pascals at its highest altitude, what was the volume of the gas at that time? A hot air balloon is hovering at an altitude of 6000 meters. The pilot decides that it is time to descend and turns off the balloon's burners. Once the balloon reaches the ground, the gas inside the balloon occupies 980 m^3 and is at atmospheric pressure. If the pressure of the gas inside of the balloon was 75,000 Pascals at its highest altitude, what was the volume of the gas at that time?
To find the volume of the gas inside the balloon at its highest altitude, we can use Boyle's Law, which states that the pressure and volume of a given amount of gas are inversely proportional at a constant temperature.
Mathematically, Boyle's Law can be expressed as:
P1 * V1 = P2 * V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, the initial volume is unknown, and the final volume is given as 980 m^3. The initial pressure is given as 75,000 Pascals, and the final pressure is atmospheric pressure.
Let's set up the equation:
(75,000 Pascals) * V1 = (atmospheric pressure) * (980 m^3)
Since atmospheric pressure is approximately 101,325 Pascals, we can substitute it into the equation:
(75,000 Pascals) * V1 = (101,325 Pascals) * (980 m^3)
Now we can solve for V1:
V1 = (101,325 Pascals * 980 m^3) / 75,000 Pascals
V1 ≈ 1311.04 m^3
Therefore, at its highest altitude, the volume of the gas inside the balloon was approximately 1311.04 m^3.