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For a van der Waals gas, if Tc is the critical temperature and Tb is the Boyle temperature, which of the following relations between Tc and Tb is correct?

1. T_c = 8/27 T_b
2. T_c = 27/8 T_b
3. T_c = 4/27 T_b
4. T_c = 27/4 T_b

Correct answer: T_c = 8/27 T_b

Solution

For a van der Waals gas, the critical temperature is Tc = 8a/(27Rb) and the Boyle temperature is Tb = a/(Rb). Their ratio Tc/Tb = 8/27, giving Tc = (8/27)*Tb.

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