Govt. Exams
Entrance Exams
Clausius-Clapeyron equation (d ln P/dT = ΔH_vap/RT²) applies specifically to phase equilibria and shows direct relationship between vapor pressure and temperature.
For a spontaneous process at constant T and P, ΔG must be negative. ΔG = 0 indicates equilibrium, and ΔG > 0 indicates non-spontaneous process.
First Law: ΔU = Q - W. Q = +500 J (absorbed), W = +200 J (work by system). ΔU = 500 - 200 = 300 J. Positive indicates internal energy increases.
For constant volume: W = 0, so Q = ΔU from first law (ΔU = Q - W). This is isochoric process where all heat goes to internal energy change.
At constant pressure, ΔH = qₚ (heat at constant pressure). This is the definition of enthalpy and its primary application.
A reversible adiabatic process has constant entropy (dS = 0), which defines an isentropic process. This is a fundamental concept in thermodynamics.
ΔU = Q - W = 100 - 60 = 40 J (First Law of Thermodynamics)
This is the van der Waals equation where 'a' accounts for intermolecular forces and 'b' for molecular volume
η_Carnot = 1 - (T_C/T_H) = 1 - (300/600) = 0.5 = 50%
At equilibrium, ΔG = 0, which means ΔG° = -RT ln(K), and when ΔG° = 0, K = 1 (equilibrium)