Weather balloons are high altitude balloons that are capable

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 299 K and at atmospheric pressure. This particular balloon can expand to a maximum diameter of 36 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.

Solution

given

P1 = 1 atm

T1 = 299 k

P2 = 0.028 atm

T2 = 190 K

d2 = 36 m

let V1 and V2 are the initial and final volumes.

and d1 is the d diameter of the balloon at lift off

use Ideal gas equation,

P1*V1/T1 = P2*V2/T1

V1 = V2*(P2/P1)*(T2/T1)

= V2*(0.028/1)*(190/299)

= V2*0.0175

(4/3)*pi*R1^3 = (4/3)*pi*R2^3*0.0175

R1^3 = R2^3*0.0175

(d1/2)^2 = (d2/2)^2*0.0175

d1 = d2*sqrt(0.0175)

= d2*0.1330

= 36*0.1330

= 4.788 m