# Ideal Gas Equation of State

An equation of state is any equation that relates pressure, temperature, and specific volume.  Using an equation of state can be more practical than using property tables.  The reason for this is because even though property tables can provide very accurate information, they can be bulky as well as be vulnerable to typographical error.

### Ideal Gas Equation of State

There are several equations of state equations.  However, the most well known, and one of the simplest is the ideal gas equation of state.  The ideal gas equation allows us to predict the P-ν-T relation of an ideal gas quite accurately.  A form of the ideal gas equation can be seen below.

(Eq 1) $P=R\left(\frac{T}{ν}\right)$

$P$ = Absolute Pressure

$ν$ = specific volume

$R$ = gas constant

$T$ = Absolute Temperature

In the above equation the value for the gas constant is dependent on the gas.  However, the gas constant can be determined using the following equation.

(Eq 2) $R=\frac{R_u}{M}$

$R_u$ = universal gas constant

$M$ = molar mass

The list below represents the universal gas constant in different units.

• $8.31447~kJ/kmol·K$
• $8.31447~kPa·m^3/kmol·K$
• $0.0831447~bar·m^3/kmol·K$
• $1.98588~Btu/lbmol·R$
• $10.7316~psia·ft^3/lbmol·R$
• $1545.37~ft·lbf/lbmol·R$

In addition, there are several different ways that the ideal gas equation can be written.

(Eq 3) $V=mν→PV=mRT$

$V$ = volume

$m$ = mass

(Eq 4) $mR=(MN)R=NR_u→PV=NR_uT$

$N$ = mole number

(Eq 5) $V=N\bar{ν}→P\bar{ν}=R_uT$

$\bar{ν}$ =  molar specific volume

In reality an ideal gas is an imaginary substance.  However,  a real gas can behave like an imaginary gas when at low densities.  Hence, when the pressure is low, or the temperature is high,  the density of the gas will increase.  In turn, the P-ν-T relationship can be closely approximated for these conditions using the ideal gas equation of state.

In general, most gases, such as air, oxygen, nitrogen, etc, can be treated as an ideal gas with minimal error.  However, water vapors, and refrigerant vapors cannot.  When dealing with these substance you should use a property table for accuracy.