Question

A pressure vessel that has a volume of 10m3 is used to store high-pressure air for operating a supersonic wind tunnel. If the air pressure and temperature inside the vessel are 20 atm and 300K, respectively: What is the mass of air stored in the vessel

Answer 1

The mass of air stored in the vessel is 235.34 kilograms.

Step-by-step explanation:

Let supossed that air inside pressure vessel is an ideal gas, The density of the air (
`\rho`), measured in kilograms per cubic meter, is defined by following equation:

`\rho = (P\cdot M)/(R_(u)\cdot T)` (1)

Where:

`P` - Pressure, measured in kilopascals.

`M` - Molar mass, measured in kilomoles per kilogram.

`R_(u)` - Ideal gas constant, measured in kilopascal-cubic meters per kilomole-Kelvin.

`T` - Temperature, measured in Kelvin.

If we know that
`P = 2026.5\,kPa`,
`M = 28.965\,(kg)/(kmol)`,
`R_(u) = 8.314\,(kPa\cdot m^(2))/(kmol\cdot K)` and
`T = 300\,K`, then the density of air is:

`\rho = ((2026.5\,kPa)\cdot \left(28.965\,(kg)/(kmol) \right))/(\left(8.314\,(kPa\cdot m^(2))/(kmol\cdot K) \right)\cdot (300\,K))`

`\rho = 23.534\,(kg)/(m^(3))`

The mass of air stored in the vessel is derived from definition of density. That is:

`m = \rho \cdot V` (2)

Where
`m` is the mass, measured in kilograms.

If we know that
`\rho = 23.534\,(kg)/(m^(3))` and
`V = 10\,m^(3)`, then the mass of air stored in the vessel is:

`m = \left(23.534\,(kg)/(m^(3)) \right)\cdot (10\,m^(3))`

`m = 235.34\,kg`

The mass of air stored in the vessel is 235.34 kilograms.