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dedylja
2 months ago
7

A hydrogen-filled balloon to be used in high altitude atmosphere studies will eventually be 100 ft in diameter. At 150,000 ft, t

he 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
Engineering
1 answer:
mote1985 [299]2 months ago
5 0

Answer:

The calculated result is 11.7 ft

Explanation:

You can apply the combined gas law, which incorporates Boyle's law, Charles's law, and Gay-Lussac's Law, because hydrogen demonstrates ideal gas behavior under these specific conditions.

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

where the subscripts indicate "p" for pressure, "V" for volume, and "T" for temperature (in Kelvin) at varying moments. Let's denote t_1 as the balloon 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 represents the point at which the balloon is on the ground.

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

Based on the first equation

V_2 = \frac{p_1 V_1 T_2}{T_1 p_2}, we find

V_2 = 6701.07 ft^3 and consequently the radius turns out to be

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

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