Boynton and Bramley equation of state: Difference between revisions

Latest revision as of 16:40, 2 December 2009

The Boynton and Bramley equation of state is given by ^[1]

\left(p+{\frac {a}{V^{2}}}\right)(V-b)={\frac {RT}{\left(1+{\frac {\psi ^{2}}{T^{2}}}\right)}}

where $\psi$ is a characteristic temperature. and where:

$p$ is the pressure,
$V$ is the volume,
$T$ is the absolute temperature,
$R$ is the molar gas constant; $R=N_{A}k_{B}$ , with $N_{A}$ being the Avogadro constant and $k_{B}$ being the Boltzmann constant.
$a$ and $b$ are constants that introduce the effects of attraction and volume respectively and depend on the substance in question.

For this equation at the critical point one has

{\frac {RT_{c}}{p_{c}V_{c}}}={\frac {8}{3}}\left(1+{\frac {\psi ^{2}}{T_{c}^{2}}}\right)

@@ Line 1: / Line 1: @@
 The '''Boynton and Bramley equation of state''' is given by <ref>[http://dx.doi.org/10.1103/PhysRev.20.46 W. P. Boynton and Arthur Bramley "A Modification of Van Der Waals' Equation", Physical Review '''20''' pp. 46-50 (1922)]</ref>
-:<math>\left( p + \frac{a}{v^2}\right) (v-b) = \frac{RT}{\left(1+ \frac{\psi^2}{T^2}\right)}</math>
+:<math>\left( p + \frac{a}{V^2}\right) (V-b) = \frac{RT}{\left(1+ \frac{\psi^2}{T^2}\right)}</math>
 where <math>\psi</math> is a characteristic [[temperature]]. and
 where:
 * <math> p </math> is the [[pressure]],
-* <math> v </math> is the volume,
+* <math> V </math> is the volume,
 * <math> T </math> is the absolute [[temperature]],
 * <math> R  </math> is the [[molar gas constant]]; <math> R = N_A k_B </math>, with <math> N_A </math> being the [[Avogadro constant]] and <math>k_B</math> being the [[Boltzmann constant]].
@@ Line 13: / Line 13: @@
 For this equation at the [[critical points | critical point]] one has
-:<math>\frac{RT_c}{p_cv_c} = \frac{8}{3}\left( 1 + \frac{\psi^2}{T_c^2}\right)</math>
+:<math>\frac{RT_c}{p_cV_c} = \frac{8}{3}\left( 1 + \frac{\psi^2}{T_c^2}\right)</math>
 ==References==
 <references/>
 [[category: Equations of state]]