Question

A weather balloon has a volume of 45.0 L when released under conditions of 743 mm Hg and 24.0°C. What is the volume of the balloon at an altitude of 10,000 m where the pressure is 188 mm Hg and the temperature is 227 K?

Answer 1

The volume of the balloon at an altitude of 10,000 m is approximately 414.37 L.

Step-by-step explanation:

To find the volume of the balloon at an altitude of 10,000 m, we can use the combined gas law. The combined gas law relates the initial and final pressure, volume, and temperature of a gas.

The formula for the combined gas law is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)

Using the given values:
Initial pressure (P1) = 743 mm Hg
Initial temperature (T1) = 24.0°C = 297.15 K
Initial volume (V1) = 45.0 L
Final pressure (P2) = 188 mm Hg
Final temperature (T2) = 227 K
Final volume (V2) = ?

Plugging in the values into the formula:
(743 mm Hg * 45.0 L) / (297.15 K) = (188 mm Hg * V2) / (227 K)

Solving for V2:
V2 = (743 mm Hg * 45.0 L * 227 K) / (188 mm Hg * 297.15 K)

V2 ≈ 414.37 L

The volume of the balloon at an altitude of 10,000 m is approximately 414.37 L.