Answer to Question #188814 in Classical Mechanics for Robin

Question

The air in a hot air balloon has been heated to 100 degrees Celsius, and has the same pressure as the air. The balloon is approximately spherical, with a radius of 10 m. How much weight (including the balloon and its basket) can the balloon lift? The answer can be rounded to the nearest ten power.

Answer 1

$$W=\Delta \rho g V\\W=\frac{4}{3}\pi(1.205 -0.946)(9.8)(10)^3=10600\ J$$