Question

A gas‑filled weather balloon has a volume of 56.0 L

at ground level, where the pressure is 761 mmHg
and the temperature is 23.1 ∘C.
After being released, the balloon rises to an altitude where the temperature is −6.97 ∘C
and the pressure is 0.0772 atm.
What is the weather balloon's volume at the higher altitude?

Answer 1

To determine the weather balloon's volume at the higher altitude, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas.

P1V1/T1 = P2V2/T2

where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.

Converting the initial conditions to SI units:

P1 = 761 mmHg = 101.325 kPa
V1 = 56.0 L
T1 = 23.1 + 273.15 = 296.25 K

Converting the final conditions to SI units:

P2 = 0.0772 atm * 101.325 kPa/atm = 7.84 kPa
T2 = -6.97 + 273.15 = 266.18 K

Solving for V2:

V2 = V1 * P1 * T2 / (P2 * T1)
V2 = 56.0 * 101.325 * 266.18 / (7.84 * 296.25)
V2 = 122.7 L

Therefore, the weather balloon's volume at the higher altitude is 122.7 L.