A research balloon filled with helium (assumed ideal) is prepared at ground level
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A research balloon filled with helium (assumed ideal) is prepared at ground level, where the atmospheric pressure is 1.00 × 10⁵ Pa and the temperature is 293 K. At this level the balloon has a volume of 2.50 m³ and is in mechanical equilibrium with the surrounding air (i.e., the helium pressure equals the ambient pressure).
As the balloon ascends, it remains in pressure equilibrium with the surrounding atmosphere. The following data apply to two specific altitudes encountered during the ascent:
• Altitude A: atmospheric pressure 7.50 × 10⁴ Pa, temperature 268 K
• Altitude B: atmospheric pressure 5.00 × 10⁴ Pa, temperature 255 K
Assume the amount of helium in the balloon remains constant and ignore any diffusion of air into or out of the balloon.
(a) Calculate the volume of the helium at Altitude A.
(b) Without using the result from part (a), calculate directly the volume of the helium at Altitude B based on ground-level data and the given atmospheric conditions at Altitude B.
(c) The buoyant force on the balloon is proportional to the weight of the displaced air. Assuming the density of air at each altitude is proportional to the ratio of atmospheric pressure to absolute temperature, determine the ratio of the buoyant force at Altitude B to the buoyant force at ground level.
(d) Based on your calculation in part (c), discuss qualitatively whether the balloon’s ability to lift its payload increases, decreases, or remains the same as it rises to Altitude B. Support your answer with reasoning that refers to both the buoyant force and the weight of the helium.