Govt. Exams
Entrance Exams
At constant T and P, spontaneity is determined by Gibbs free energy: ΔG < 0 for spontaneous process, ΔG = 0 for equilibrium, ΔG > 0 for non-spontaneous process.
In van der Waals equation (P + a/V²)(V - b) = RT, 'a' accounts for intermolecular attractive forces and 'b' represents excluded molecular volume. Both are positive constants.
Cₚ - Cᵥ = R (for ideal gas). At constant P, supplied heat does both internal energy and expansion work. At constant V, all heat goes to internal energy only.
Maximum efficiency is Carnot efficiency: η_max = 1 - T_cold/T_hot = 1 - 300/500 = 0.40 = 40%. No heat engine can exceed this efficiency.
For reversible processes, ΔS = Q_rev/T. For irreversible processes, ΔS > Q_irrev/T. This is the Clausius inequality: dS ≥ dQ/T.
ΔS_vap = ΔH_vap/T = 40660 J/mol / 373 K ≈ 109 J/mol·K. This follows Trouton's rule (~85-105 J/mol·K for most liquids).
From ΔG = ΔH - TΔS, for ΔG < 0 at all T: ΔH < 0 (exothermic) and ΔS > 0 (entropy increases). This is a spontaneous process at all temperatures.
For isothermal process of ideal gas, W = nRTln(V₂/V₁) = nRTln(P₁/P₂). This is derived from the first law with ΔU = 0 for isothermal ideal gas process.
Gibbs Free Energy (G = H - TS) is the appropriate thermodynamic potential for processes at constant T and P. ΔG = 0 at equilibrium and ΔG < 0 for spontaneous processes.
In a CSTR, conversion depends on residence time (τ = V/Q). When volumetric flow rate Q doubles while V remains constant, residence time τ decreases by half. Since conversion X_A = kτ/(1+kτ) for first-order reaction, decreased τ leads to decreased conversion. This is a fundamental principle in reactor design for 2024-25 competitive exams.
