Question

A child loses his balloon, which rises slowly into the sky.

a) If the balloon is 22.9 cm in diameter when the child loses it, what is its diameter at an altitude of 1210 m? Assume that the balloon is very flexible and so surface tension can be neglected.

b) And what is the diameter of the same balloon at an altitude of 2210 m?

c) And what is the diameter of the same balloon at an altitude of 5210 m?

Answer 1

This depends on the temperature and pressure outside of the balloon, and these depend on the atmospheric conditions. You'll need to know what sort of approximations (or model) for the atmosphere is being used.

But...

The basic physics is the ideal gas law: V = n R T / P where:
n = number of moles of gas in the balloon (probably a constant)
R = Ideal gas constant
T = temperature of the gas in the balloon (equal to the atmosphere outside) IN KELVIN
P = pressure of the atmosphere outside the balloon.