Question

It's 32°F (0°C) outside under normal atmospheric conditions (1 atm) at a stunt

Answer 1

The volume of the balloon is approximately 2652 liters.

How to determine the volume occupied by the gas in a balloon

Let suppose that flammable hydrogen behaves ideally. GIven the molar mass ($M$), in kilograms per kilomole, and mass of the gas ($m$), in kilograms. The volume occupied by the gas ($V$), in cubic centimeters, is found by the equation of state for ideal gases:

$V = \frac{m\cdot R_{u}\cdot T}{P\cdot M}$   (1)

Where:

• $R_{u}$ - Ideal gas constant, in kilopascal-cubic meters per kilomole-Kelvin.
• $T$ - Temperature, in Kelvin
• $P$ - Pressure, in kilopascals

If we know that $m = 0.239\,kg$, $R_{u} = 8.314\,\frac{kPa\cdot m^{3}}{kmol\cdot K}$, $T = 273.15\,K$, $P = 101.325\,kPa$ and $M = 2.02\,\frac{kg}{kmol}$, then the volume of the balloon is:

$V = \frac{(0.239\,kg)\cdot \left(8.314\,\frac{kPa\cdot m^{3}}{kmol\cdot K} \right)\cdot (273.15\,K)}{\left(101.325\,kPa\right)\cdot \left(2.02\,\frac{kg}{kmol} \right)}$

$V = 2.652\,m^{3}$ ($2652\,L$)

The volume of the balloon is approximately 2652 liters. $\blacksquare$

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