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

We can use the combined gas law to determine the volume of the balloon at a higher altitude. The combined gas law relates the pressure, volume, and temperature of a gas:

(P1 x V1) / T1 = (P2 x V2) / T2

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

We are given the initial pressure (P1 = 761 mmHg), volume (V1 = 56.0 L), and temperature (T1 = 23.1 °C = 296.25 K) of the gas, and the final pressure (P2 = 0.0772 atm), and temperature (T2 = -6.97 °C = 266.18 K) of the gas. We can solve for V2, the final volume of the gas:

(P1 x V1) / T1 = (P2 x V2) / T2

V2 = (P1 x V1 x T2) / (P2 x T1)

V2 = (761 mmHg x 56.0 L x 266.18 K) / (0.0772 atm x 296.25 K)

V2 = 2,040 L (rounded to three significant figures)

Therefore, the volume of the weather balloon at the higher altitude is approximately 2,040 L.