(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A helium balloon has volume V_{0}and temperature T_{0}at sea level where the pressure is P_{0}and the air density is [itex]\rho_0[/itex]. The balloon is allowed to float up in the air to altitude y where the temperature is T. (a) Show that the volume occupied by the balloon is then V = V_{0}(T/T_{0})e^{cy}where [itex]c = \rho_0g/P_0[/itex]. (b) Show that the buoyant force does not depend on altitude y. Assume that the skin of the balloon maintains the helium pressure at a constant factore of 1.05 times greater than the outside pressure. [Hint: Assume that the pressure change with altitude is P = P_{0}e^{-cy}].

2. Relevant equations

The ideal gas law and the buoyant force equation.

3. The attempt at a solution

(a) is pretty simple since the hint gives it away. What concerns me is (b). Since the buoyant force on the balloon is equal to the weight of the volume of air displaced by the balloon, and since the volume depends on altitude, then it seems logical that the buoyant force depends on altitude. What gives?

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# Buoyant Force on a Helium Balloon

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