Q1(b). Fugacity under repulsion

Answer in brief

Repulsion raises the escaping tendency and chemical potential relative to the ideal gas, giving φ=f/p>1 when the net residual contribution is positive.

Key points

• Define μ=μ°+RTln (f/p°) and the ideal reference at the same pressure as μ^id=μ°+RTln (p/p°). Hence μ-μ^id=RTln (f/p).
• At fixed temperature, ln φ=∫₀^p (Z-1) dp/p, where Z=pVₘ/(RT). Repulsive/excluded-volume effects tend to make Z>1.
• If the positive repulsive contribution dominates this integral, ln φ>0 and f>p.