A helium-filled weather balloon has a volume of 547 L at 14.9°C and 755 mmHg. It is released and rises to an altitude of 8.24 km, where the pressure is 306 mmHg and the temperature is –33.1°C.
The volume of the balloon at this altitude is
L.
To find the volume of the balloon at this altitude, we can use the combined gas law equation:
(P1V1/T1) = (P2V2/T2)
Where:
P1 = 755 mmHg
V1 = 547 L
T1 = 14.9°C + 273.15 = 287.05 K
P2 = 306 mmHg
V2 = ?
T2 = -33.1°C + 273.15 = 240.05 K
Now we can plug in the values and solve for V2:
(755 mmHg * 547 L) / 287.05 K = (306 mmHg * V2) / 240.05 K
V2 = (755 * 547 * 240.05) / (306 * 287.05)
V2 = 36022816.09 / 87589.3
V2 ≈ 411.45 L
Therefore, the volume of the balloon at this altitude is approximately 411.45 L.