Ideal Gas
This is a derivation to obtain an expression for for an ideal gas.
An ideal gas has the equation of state:
where
- P = pressure
- V = volume
- n = number of moles
- R = universal gas constant
- T = temperature
The ideal gas equation of state can be arranged to give:
- or
The following partial derivatives are obtained from the above equation of state:
The following simple expressions are obtained for thermal expansion coefficient :
and for isothermal compressibility :
One can now calculate for ideal gases from the previously-obtained general formula:
Substituting from the ideal gas equation gives finally:
where n = number of moles of gas in the thermodynamic system under consideration and R = universal gas constant. On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows:
This result would be consistent if the specific difference were derived directly from the general expression for .
Read more about this topic: Relations Between Heat Capacities
Famous quotes containing the words ideal and/or gas:
“The ideal of the self-sufficient American family is a myth, dangerous because most families, especially affluent families, do in fact make use of a range of services to survive. Families needing one or another kind of help are not morally deficient; most families do need assistance at one time or another.”
—Joseph Featherstone (20th century)
“Droning a drowsy syncopated tune,
Rocking back and forth to a mellow croon,
I heard a Negro play.
Down on Lenox Avenue the other night
By the pale dull pallor of an old gas light”
—Langston Hughes (1902–1967)