At ground level ( and ) a weather-service balloon is filled with helium until it…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

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.

Related theory

Browse the problem library