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

\[\frac{p_1\cdot V_1}{T_1}=\frac{p_0\cdot V_0}{T_0}\]
in terms of radius, this becomes
\[\frac{p_1\cdot r_1^3}{T_1}=\frac{p_0\cdot r_0^3}{T_0}\]
You know that \(p_0 = \) 1 atm and \(r_0= 22.9\) cm. You will need a table or a formula to give you the pressure (\(p_1\)) and temperature (\(T_1\)) at 1210 m, 2210 m, and at 5210 m elevation. Then solve for \(r_1\).