Answer to Question #167598 in Quantum Mechanics for Kevin

Question

 A hydrogen balloon at the Earths surface has a volume of on a day when the temperature is and the pressure 1 atm. What is the mass of hydrogen? The balloon rises and expands as the pressure drops. What would be the volume of the same number of molecules of hydrogen at an altitude of 40km where the pressure is and temperature is 

Answer 1

Complete problem:

A hydrogen balloon at the Earths surface has a volume 5.0 m³ of on a day when the temperature is 27 ºC and the pressure 1 atm. What is the mass of hydrogen? The balloon rises and expands as the pressure drops. What would be the volume of the same number of molecules of hydrogen at an altitude of 40 km where the pressure is 0.0032 atm and temperature is -13 ºC.

$V_1 = 5.0 \;m^3 \\ T_1 = 27 + 273 = 300 \;K \\ P_1 = 1 \;atm \\ T_2 = -13 + 273 = 260 \;K \\ P_2 = 0.0032 \;atm \\ \frac{V_1 \times P_1}{T_1} = \frac{V_2 \times P_2}{T_2} \\ V_2 = {V_1 \times P_1 \times T_2}{T_1 \times P_2} \\ = {5 \times 1 \times 260}{300 \times 0.0032} \\ = 1354.1 \;m^3$