Physics

Problem

At ground level (

1.00\times10^{5}\,\text{Pa}

and

15\,^{\circ}\text{C}

) a weather-service balloon is filled with helium until it forms a perfect sphere of diameter

2.00\,\text{m}

. The balloon material is flexible and can expand without limit; no helium escapes during the flight. When the balloon reaches an altitude of

10\,\text{km}

, the surrounding air pressure is

2.65\times10^{4}\,\text{Pa}

and the temperature is

-50\,^{\circ}\text{C}

. The molar mass of helium is

4.00\,\text{g mol}^{-1}

and the universal gas constant is

8.31\,\text{J mol}^{-1}\,\text{K}^{-1}

. (a) Determine the volume of the helium inside the balloon at ground level. (b) Calculate the volume of the helium when the balloon is at

10\,\text{km}

altitude. (c) Assuming the balloon remains spherical, find its diameter at that altitude. (d) Compute the density of the helium gas inside the balloon at

10\,\text{km}

. (e) Briefly describe how the change in gas density you calculated in part (d) affects the net buoyant force acting on the balloon as it ascends.

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