Question

A weather balloon is designed to expand to a maximum radius of 16.2 m when in flight at its working altitude, where the air pressure is 0.0282 atm and the temperature is â65âC. If the balloon is filled at 0.873 atm and 21âC, what is its radius at lift-off?

Answer 1

Answer:

5.78971 m

Explanation:

$P_1$ = Initial pressure = 0.873 atm

$P_2$ = Final pressure = 0.0282 atm

$V_1$ = Initial volume

$V_2$ = Final volume

$r_1$ = Initial radius = 16.2 m

$r_2$ = Final radius

Volume is given by

$\frac{4}{3}\pi r^3$

From the ideal gas law we have the relation

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\\\Rightarrow \frac{0.873\times \frac{4}{3}\pi r_1^3}{294.15}=\frac{0.0282\frac{4}{3}\pi r_2^3}{208.15}\\\Rightarrow \frac{0.873r_1^3}{294.15}=\frac{0.0282\times 16.2^3}{208.15}\\\Rightarrow r_1=\frac{0.0282\times 16.2^3\times 294.15}{208.15\times 0.873}\\\Rightarrow r_1=5.78971\ m$

The radius of balloon at lift off is 5.78971 m