A weather balloon with a volume of 3.86934 L is released from Earth’s surface at sea level.What volume will the balloon occupy at an altitude of 20.0 km, where the air pressure is 10 kPa?
Answer in units of L
Assuming the T is constant (which it will not be) use p1v1 = p2v2
I know I'm suppose to use 3.86934 as the first volume and 10 kPa as the second pressure, but what am I suppose to use as the first pressure? Am I suppose to use 20.0 km?
No, 20 km is a distance, not a pressure. The problem says the balloon is relesed at sea level on earth's surface. Pressure at sea level is 101.325 kPa or 1 atm or 14.7 lb/sq ft. Since you are using kPa for the second P you should use first P in the same units.
Oh okay, thankyou!
To find the volume of the balloon at an altitude of 20.0 km, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
In this case, we are given the initial volume of the balloon (V1 = 3.86934 L) and the pressure at the given altitude (P2 = 10 kPa). We want to find the final volume (V2) of the balloon.
First, we need to calculate the number of moles of gas at the initial altitude (n1) using the formula:
n1 = (P1 * V1) / (R * T1)
At sea level, the temperature is typically around 298 K.
Now we can rearrange the ideal gas law equation to solve for the final volume (V2):
V2 = (n1 * R * T2) / P2
At an altitude of 20.0 km, the temperature (T2) is significantly lower than at sea level due to the decrease in atmospheric pressure.
The exact value of the ideal gas constant (R) depends on the units used for pressure, volume, and temperature. The commonly used value of R is 0.0821 L·atm/(mol·K). So we will use this value in our calculation.
Substituting the known values into the equation, we get:
V2 = (n1 * R * T2) / P2
Let's calculate the final volume (V2) using the given values.