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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

User Txema
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Answer:

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.

User Skawful
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