A high-altitude balloon contains 97.5 L of helium gas at 95.8 kPa. What is the volume when the balloon rises to an altitude where the pressure is only 21.5 kPa? (Assume that the temperature remains constant.)
P*V = constant at constant T.
It's somebody's Law. Boyle's?
P1*V1 = P2*V2
You aleady know P1, P2 and V1.
Solve for V2.
no its Charles' Law
To find the volume of the balloon at a different pressure, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is constant.
Boyle's Law equation: P₁V₁ = P₂V₂
Where:
P₁ = Initial pressure = 95.8 kPa
V₁ = Initial volume = 97.5 L
P₂ = Final pressure = 21.5 kPa (the pressure at a higher altitude)
V₂ = Final volume (what we need to find)
We can rearrange the Boyle's Law equation to solve for V₂:
V₂ = (P₁V₁) / P₂
Now we can substitute the values into the equation:
V₂ = (95.8 kPa * 97.5 L) / 21.5 kPa
First, we cancel out the units of kPa:
V₂ = (95.8 * 97.5 L) / 21.5
Now, we can calculate the final volume:
V₂ = 4377.75 L / 21.5
V₂ ≈ 203.17 L
Therefore, the volume of the balloon when it rises to an altitude with a pressure of 21.5 kPa is approximately 203.17 L.