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Ideal Gas Law

Unlike liquids, the density of gases are greatly effected by changes of pressure or changes in temperature.  This reason for this is because gas in a compressible fluid.  To determine how the density of a gas would change due to change in pressure or temperature the ideal gas law can be used.

(Eq 1) $ρ=\frac{P}{RT}$

$ρ$ = Density

$P$ = Pressure

$R$ = Gas Constant

$T$ = Temperature

Ideal Gas Law Calculator

Density

Pressure

Gas Constant

Absolute Temperature

Answer:

The ideal gas law is the equation of state for a hypothetical gas. Due to this fact the ideal gas law will only give an approximate value for real gases under normal condition that are not currently approaching qualification.  The approximate value is generally accurate under many conditions.  However there are several limitations.  This is due to the fact that the ideal gas law makes the assumption that gas particles have no volume and are not attracted to each other.  In reality if you were to put enough pressure on gas molecules they would start to form a liquid, which in turn will cause the inaccuracies in your calculation.

Absolute  Pressure

To use the ideal gas law effectively you will need to use the absolute pressure of the gas not the gage pressure.  The gage pressure of a gas would be the pressure that you read off of a pressure gage.  Absolute pressure on the other hand is a combination of gage pressure and atmospheric pressure.

(Eq  2) $P_{abs}=P_{atm}+P_{gage}$

Absolute Temperature

Just like with pressure, when using the ideal gas law you must use absolute temperature.  This means that you cannot use the Celsius scale or the Fahrenheit scale.  Instead you must convert Celsius to Kelvin, or convert Fahrenheit to Rankin.  Both the Kelvin temperature scale and Rankin Temperature scale are absolute temperature scales.  The reason why is because there lowest value is absolute zero, meaning there are no negative values on these two scales.

(Eq 3) $T_{Kelvin}=T_{Celsius}+273$

(Eq 4) $T_{Rankin} = T_{Fahrenheit}+460$

Gas Constant

Finally, the R value seen in the ideal gas law equation represents the gas constant. Refer to the table below to view gas constants for different gases.

 

Gas

Gas Constant

English Units

$\left(\frac{ft·lb}{slug·^oR}\right)$

Gas Constant

SI Units

$\left(\frac{J}{kg·K}\right)$

Air (Standard) 1.716 X 103 2.869 X 102
Carbon Dioxide 1.130 X 103 1.889 X 102
Helium 1.242 X 104 2.077 X 103
Hydrogen 2.466 X 104 4.124 X 103
Methane 3.099 X 103 5.183 X 102
Nitrogen 1.775 X 103 2.968 X 102
Oxygen 1.554 X 103 2.598 X 102

Example

Helium that is currently captured in container has a density of $15 \frac{kg}{m^3}.  The temperature of the helium within the container 300 K.  Determine the absolute pressure of the helium within the container.  If the outside of the container is at 1 ATM what is gage pressure of helium inside the container.

Solution

 $ R = 2.077 e 3$

Step 1:  Determine the absolute pressure of the helium.

$P_{abs} = ρRT = 15(2.077e3)(300) =9.35e6~Pa = 92.3 ATM $

Step 2:   Determine the gage pressure of the helium.

$ P_{gage} = 92.3 – 1 = 91.3 ATM$

 

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