IDEAL GAS EQUATIONS

Notations and Units

Three forms of Equation of States (with java calculators)

Miscellaneous Equations

Notations and Units

Only use SI / metric units in the calculations.  Try the Unit Conversion Calculators at http://hurri.kean.edu/~yoh/calculations/units

Name	Notation	SI unit
pressure	p	Pa
temperature	T	K
specific volume		m3 kg-1
molar volume		m3 kmol-1
number in kilomole	N	kmol
density		kg m-3
volume	V	m3
mass	M	kg
molecular weight		kg kmol-1
Gas Constant  (specific heat capacity)	R	J deg-1 kg-1
Universal Gas Constant	R*	J deg-1 kmol-1

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Three forms of Equation of State of Ideal Gas

(1) First Form (Using Initial State and Partially Known Final State)

• Boyle's Law : when T is constant
• Charles' Law : when V is constant
 
Combing Boyle's Law and Charles' Law, if you know the initial condition (p₁, V₁, T₁) and any two of the final condition (p₂, V₂, T₂), we can always determine the third one.




where C depends on the mass of the gas (M) and kind of gas (specific gas constant R)




(2) Second Form (Using Gas Constant for a Specific Gas)

The constant C above depends on the mass of the gas because V depends on the mass (V is an extensive variable).  However, if we use specific volume (volume/mass) or density (mass/volume), the constant C in the above equation will become independent of the mass of the the gas, and we now label the constant as R, the gas constant for a specific kind of gas.






R is either given directly for the gas or R can be calculated if the molecular weight is known since






 

(3) Third Form (Using Universal Gas Constant)

The constant R above depends on the gas because specific volume (or density) of gases are different for different gases.  However, if we use molar volume (volume/kilomole), the ideal gas equation will become universal for all gases since all gases have the same molar volume at the same temperature and pressure (Avogador's Law). The constant R above will be replaced by R^*, the universal gas constant.

 Miscellaneous Equations

1. number of mole = Mass / molecular weight



2. number of mole = Volume / molar volume



3. specific volume = 1 / density

Report any errors in the calculators or send any suggestions to yoh@hurri.kean.edu 

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