Question

A hydrogen-filled balloon to be used in high altitude atmosphere studies will eventually be 100 ft in diameter. At 150,000 ft, the pressure is 0.14 lb/in2 and the temperature is - 67°F. Assume the balloon is spherical in shape. What is the diameter of the hydrogen balloon at the ground at 14.7 lb/in2 and 68°F

Answer 1

Answer:

The answer is 11.7 ft

Explanation:

You can use the combined gas law from Boyle's law, Charles's law, and Gay-Lussac's Law. Only because hydrogen behaves like an ideal gas for this conditions.

$\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$

where the subscripts denote the pressure "p", volume "V" and the temperature "T" (in Kelvin) at two different times. Let's consider $t_1$ as the balloom at 150,000 ft so

$p_1 = 0.14 \ lb/in^2$

$V_1 = \frac{4}{3} \pi R_1^3 = 523598.77 \ ft^3$

and $T_1 = -67^\circ F = 218.15\ K$.

Then, $t_2$ is the moment when the balloon is on the ground.

$p_2 = 14.7 \ lb/in^2$ and  $T_2 = 68^\circ F = 293.15\ K$.

From the first equation,

$V_2 = \frac{p_1 V_1 T_2}{T_1 p_2}$, then

$V_2 = 6701.07 ft^3$ and the radius would be  

$R_2 = \sqrt[3]{\frac{3 V_2}{4 \pi}} = 11.7 \ ft$.