Question

What do you mean by Boyle temperature ? Give its expression and its relation with inversion temperature.

Answer 1

"“Boyle temperature” in thermodynamics denotes the “temperature” at which a “non-ideal” gas “behaves” most like an “ideal gas”.  

At Boyle temperature, by setting the “compressibility factor” Z to 1, We get

${ T }_{ b }=\frac { a }{ { R }_{ b } }$

Where a and b are “Van der Waals” parameters.

$p = RT(\frac { 1 }{ { V }_{ m } } \quad +\quad \frac { { B }_{ 2 }(T) }{ { V }^{ 2 }m } \quad +\quad \frac { { B }_{ 3 }(T) }{ { V }^{ 3 }m } \quad +....)$

This is the “virial equation”.  

This temperature is formally defined as the “temperature” for which the “second virial coefficient” ${ B }_{ 2 }(T)$equals to 0 and at “this temperature” that the “attractive forces” and the “repulsive forces” reacting on the “gas particles” “balance out”.  

In any case, when there is lower pressures, the “second virial coefficient” will be the “only relevant” one because the “remaining concern terms” of “higher order” on the pressure. We then have $\frac { dz }{ dp } =\quad 0$, if p = 0. Then Z is the compressibility factor."