Gaseous Equation of State Calculator

Dependent Variable		Units	Ideal Gas	van der Waals Gas	Dieterici Gas
	Pressure	atm bar Pa psi torr
	Volume	ft³ L m³ mL
	Temperature	K °C °F
	Moles	mol

Gas	custom He Ne Ar Kr Xe H2 N2 O2 CH4 NH3 H2O CO2 n-pentane n-hexane n-heptane n-octane Hg			van der Waals Parameters	Dieterici Parameters
PC (atm)			a (SI units)
VC (L/mol)			b (SI units)
TC (K)			TBoyle/TC
ZC (K)			ZC (calc)

Notes

T_Boyle/T_c

Any of the real gas equations of state can be written as a power series expansion. For the van der Waals equation, we have

PV RT

= 1 +

(

b -

a RT

)

1 V

+

b2

1 V2

+ ...

At the Boyle temperature T_Boyle intermolecular attractive and repulsive effects are balanced so that the terms linear in P (or 1/V) in the expansion to go to zero. The Boyle temperature for the van der Waals gas is then

TBoyle =

a bR

Inspection of the power series expansion for the Dieterici gas shows that

TBoyle =

(

a bR

)2/3

For most gases, experiment shows that the ratio of the Boyle temperature to the critical temperature is consistently about 2.75 (except for He).