Q1(b). Second virial coefficient A₂ and the Boyle temperature

Answer in brief

A₂ measures the interaction between pairs of molecules: negative at low T (attraction), zero at the Boyle temperature, positive at high T (repulsion); at A₂ = 0 the gas obeys Boyle's law widely.

Key points

• A₂ = (∂Z/∂p) at T, p → 0: the initial slope of the Z–p curve, unit Pa⁻¹.
• It is the first deviation from ideality, caused by interactions between pairs of molecules; A₂ < 0: attraction dominates; A₂ > 0: repulsion dominates.
• For a van der Waals gas A₂ = (b − a/RT)/RT; low T: A₂ large and negative, Z < 1.
• Moderate T: A₂ rises with T and passes through zero at TB; high T: A₂ > 0, repulsion wins.
• A₂ = 0 at the Boyle temperature: pVm = RT holds over a wide range of low and moderate pressure; for a van der Waals gas TB = a/Rb.