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 296 K and at atmospheric pressure. This particular balloon can expand to a maximum diameter of 24 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.
__________ m

Explanation / Answer

at lift off

T1 = 296 K

P1 = 1 atm

let d1 is the diamtere at lift off.

V1 = (4/3)*pi*(d1^3/8)

at 40 km height

T2 = 190 K

P2 = 0.028 atm

V2 = (4/3)*pi*(24^3/8)

Now Apply

P1*V1/T1 = P2*V2/T2

1*(4/3)*pi*(d1^3/8)/296 = 0.028*(4/3)*pi*(24^3/8)/190

d1^3/296 = 0.028*24^3/190

d1 = 24*(0.028*296/190)^(1/3)

= 8.45 m <<<<<<<<<<-----------------Answer

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