   Chapter 10, Problem 37P

Chapter
Section
Textbook Problem

A weather balloon is designed to expand to a maximum radius of 20 m at its working altitude, where the air pressure is 0.030 atm and the temperature is 200 K. If the balloon is filled at atmospheric pressure and 300 K, what is its radius at liftoff?

To determine
The radius of the balloon at liftoff ( r1 ).

Explanation

Given Info: The maximum radius of the balloon ( r1 ) is 20 m where pressure is P2=0.030atm and temperature is T2=200K . The balloon is then filled at pressure P1=1.0atm and temperature T1=300K .

From Ideal gas equation,

P1V1=nRT1       (I)

P2V2=nRT2       (II)

• V1 and V2 are the volumes of balloon at different pressures and temperatures
• n is the number of moles which is constant

Divide Equation (II) by (I) and re-arrange,

V1V2=(P2P1)(T1T2)

The volume is proportional to the cube of the radius. Therefore,

(r1r2)3=(P2P1)(T1T2)

• r1 and r2 are the radii of balloon at different pressures and temperatures

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