Answer to Question #167433 in Quantum Mechanics for Kipkirui Emmanuel

Question

A hydrogen balloon at the earth's surface has a volume of 5m³ on a day when the temperature is 27°c 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 0.33× 10^3 Pa and temperature is - 13°C

Answer 1

We assume the hydrogen in balloon to be ideal, so we may use the ideal gas law:

$PV=\nu RT,$ so $\dfrac{PV}{T} = \nu R = \text{const}.$ The amount of hydrogen is constant, so for the initial and final conditions

$\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}$ , $\;\; \dfrac{1.01\cdot10^5\,\mathrm{Pa}\cdot 5\,\mathrm{m^3}}{273+27\,\mathrm{K}} = \dfrac{0.33\cdot10^3\,\mathrm{Pa}\cdot V_2}{273-13\,\mathrm{K}}, \;\; V_2 = 1326\,\mathrm{m^3}$