A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? Assume that the temperature remains constant
P1V1=P2V2
P1=103kpa
V1=30.0L
P2=25.0kpa
V2=?
(103kpa)(30.0l)=(25.0kpa)(v2)
v2 = 124l
P1V1 = P2V2
123.6
Well, well, it seems our helium-filled balloon is going on a little adventure! Don't worry, I've got your back and some funny answers for you too.
Now, let's calculate that volume change. We can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature remains constant. So, we have:
V1 x P1 = V2 x P2
Where:
V1 = initial volume (30.0 L)
P1 = initial pressure (103 kPa)
V2 = final volume (what we're trying to find)
P2 = final pressure (25.0 kPa)
Now, let's plug in the values and solve for V2:
30.0 L x 103 kPa = V2 x 25.0 kPa
1030 = 25V2
V2 = 1030 / 25
V2 ≈ 41.2 L
So, once our balloon rises to an altitude where the pressure is only 25.0 kPa, the volume of the helium will be approximately 41.2 liters. That's one stretchy balloon! Just hope it doesn't get too big, or we might start floating away too!
Did that answer pop your question?
To find the volume of the helium when the balloon rises to an altitude where the pressure is 25.0 kPa, you can use the combined gas law equation:
P1 × V1 / T1 = P2 × V2 / T2
Where:
P1 is the initial pressure (103 kPa)
V1 is the initial volume (30.0 L)
T1 is the initial temperature (assumed constant)
P2 is the final pressure (25.0 kPa)
V2 is the final volume (we want to find this)
T2 is the final temperature (assumed constant)
Since the temperature is constant, T1 = T2, and we can simplify the equation to:
P1 × V1 = P2 × V2
Now, let's plug in the given values:
103 kPa × 30.0 L = 25.0 kPa × V2
To find V2, rearrange the equation:
V2 = (103 kPa × 30.0 L) / 25.0 kPa
V2 = 123.6 L
Therefore, the volume of the helium when the balloon rises to an altitude where the pressure is 25.0 kPa is 123.6 L.