A helium-filled weather balloon has a 1.2 m radius at liftoff where air pressure is 2 atm and the temperature is 278 K.When airborne,the temperature is 227 K,and its radius expands to 2 m.What is the pressure at the airborne location?

Question

Quizplus · Accepted Answer

The combined gas law can be used to solve this problem:

(P1V1/T1) = (P2V2/T2)

First, we need to convert the radius to volume using the formula for the volume of a sphere:

V1 = (4/3)π(1.2 m)^3 = 7.239 m^3     (at liftoff)
V2 = (4/3)π(2 m)^3 = 33.51 m^3       (airborne)

Next, we can plug in the given values:

(P1V1/T1) = (P2V2/T2)
(2 atm)(7.239 m^3)/(278 K) = P2(33.51 m^3)/(227 K)

Simplifying gives:

P2 = (2 atm)(7.239 m^3)(227 K)/(33.51 m^3)(278 K) = 0.353 atm

Therefore, the answer is C.

A Helium-Filled Weather Balloon Has a 1