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For a van der Waals gas the Boyle temperature is given by

A $T_{B} = \frac{a}{R b}$
B $T_{B} = \frac{2 a}{R b}$
C $T_{B} = \frac{8 a}{27 R b}$
D $T_{B} = \frac{a}{27 R b ^{2}}$

Answer: A

The Boyle temperature is the temperature at which the second virial coefficient

b - a / RT

vanishes, giving

T_{B} = a / R b

.

2 a / R b

is the inversion temperature and

8 a /27 R b

the critical temperature.

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