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What is the equation to determine Boyle Temperature?

At low pressures, all gases behave

pV_{m} =
RT

However, at higher pressures gases deviate from the Ideal Gas Law, following a linear expansion of the form

pV_{m} = RT{1 +
Bīp + Cīp^{2} + ...}

pV_{m} = RT{1 +
B/V_{m} + C/V_{m}^{2} +
...}

The values of the *virial coefficients* B, C, ... depend on
temperature, and many gases have a particular temperature at which B = Bī =
0. This temperature is called the ** Boyle
Temperature**, T

T_{B} can be derived from the *va
n der Waals equation of state* for a real gas,

In order to do that, we express the van der Waals equation as

(1 *x*)^{-1} = 1 + *x* + *x*^{2} + ...

(TThus, the Boyle temperature may be found for any gas for which the critical temperature has been determined._{c}= 8a/27Rb is the critical temperature of the gas. For a derivation of the relationship of the critical constants to the van der Waals constants, see P.W. Atkins,Physical Chemistry, 3d Ed.page 31.)

Dan Berger | |

Bluffton College | |

http://cs.bluffton.edu/~berger |

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