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?
Assuming temp is constant?
75kPa*V=101kPa*980
solve for V
To determine the volume of the gas inside the balloon at its highest altitude, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional, assuming the temperature remains constant.
Let's denote the initial pressure and volume of the gas as P₁ and V₁, respectively, and the final pressure and volume at the ground level as P₂ and V₂, respectively.
According to Boyle's Law, we have:
P₁ * V₁ = P₂ * V₂
Given:
P₁ = 75,000 Pa
V₁ is unknown
P₂ = 1 atm or 101,325 Pa
V₂ = 980 m^3 = 980,000 dm^3
We need to convert the units of pressure and volume to be consistent. Since 1 dm^3 = 1 L, we can rewrite V₂ as 980,000 L or 980,000 dm^3.
Let's substitute the given values into Boyle's Law:
75,000 Pa * V₁ = 101,325 Pa * 980,000 dm^3
Now, we can solve for V₁:
V₁ = (101,325 Pa * 980,000 dm^3) / 75,000 Pa
Calculating this expression, we have:
V₁ = 1322 dm^3
Therefore, the volume of the gas inside the balloon at its highest altitude was approximately 1322 cubic meters.