Weather balloons are high altitude balloons that are capable of reaching an alti

Question

Weather balloons are high altitude balloons that are capable of reaching an altitude of 40 km (or 25 miles). They are usually filled with hydrogen or helium gas. One such balloon is filled with air that is initially at a temperature of 307 K and at atmospheric pressure. This particular balloon can expand to a maximum diameter of 28 m when it reaches an altitude where the pressure and temperature are 0.028 atm and 190 K respectively. Determine the diameter of the balloon at lift off. (answer in m)

Explanation / Answer

Apply ideal gas equation to the initial and final states of ballon

P1 V1/T1 = P2 V2/T2

1atm ( V1)/ 307 K = ( 0.028 atm ( 4/3 * pi ( 28/2)^3/190 K

1atm ( V1)/ 307 K = ( 0.028 atm ( 11488.213) /190 K

V1 = 519.75 m^3

4/3 pi (r1)^3 = 519.75 m^3

r1= 4.98 m

diameter D1 = 2r1 = 2( 4.98 m) =9.96 m

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