A partially inflated weather balloon at ground level contains moles of helium
PHYSICS · Multi-part · GCSE · Physics · Particle Model of Matter · Particle Model of Matter
Problem
A partially inflated weather balloon at ground level contains n moles of helium, modeled as an ideal gas, at pressure P0 and temperature T0. As the balloon rises through a certain layer of the atmosphere, measurements show that the ambient temperature remains directly proportional to the ambient pressure, obeying T=kP, where k is a constant for that layer. Assume the balloon skin is perfectly flexible so that its internal gas is always in equilibrium with the surroundings and that no gas escapes.
(a) Starting from the ideal-gas equation, derive an expression for the balloon volume V as a function of the ambient pressure P during this portion of the ascent. Express V in terms of n, k, and P.
(b) The initial volume at ground level is V0. By what factor does the balloon’s volume change when the ambient pressure falls to 31P0?
(c) On clearly labeled axes, sketch the qualitative shape of a plot of V versus P for P varying from P0 down to 31P0. Mark the initial and final points corresponding to parts (a) and (b).
(d) Using proportional reasoning based on your expression from part (a), explain whether the balloon’s volume changes more rapidly with respect to pressure at higher altitudes or at lower altitudes within this pressure range.