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?
Physics - bobpursley, Saturday, February 18, 2012 at 6:21pm
Assuming temp is constant?
75kPa*V=101kPa*980
solve for V
Where did you get the 101kpa.
I am getting v2=p1v1/p2
(6000)(980m^3) divided by 75000 = 78.4 m^3
101kPa is atmospheric pressure.
6000 is in meters, of little use here. I don't know why you did that.
To find the volume of the gas inside the balloon at its highest altitude, you can use the ideal gas equation: PV = nRT, where P is the pressure of the gas, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
However, in this case, we can assume that the temperature remains constant. So the equation can be simplified to P1V1 = P2V2, where P1 and V1 are the pressure and volume at the highest altitude, and P2 and V2 are the pressure and volume when the balloon reaches the ground.
Given:
P1 = 75,000 Pascals
V2 = 980 m^3 (when the balloon reaches the ground)
P2 = atmospheric pressure, which is approximately 101,000 Pascals
To find V1, we rearrange the equation:
V1 = P2 * V2 / P1
Plugging in the values:
V1 = (101,000 * 980) / 75,000
V1 ≈ 1314.67 m^3
Therefore, the volume of the gas inside the balloon at its highest altitude was approximately 1314.67 m^3.