Govt. Exams
Entrance Exams
Entropy is a state function. ΔS is path-independent and same for all processes (reversible or irreversible) between fixed states.
At constant pressure: ΔH = Q_p (definition of enthalpy). From ΔU = Q - W and W = PΔV, we get Q = ΔH.
At high pressures, molecular volume effect (b term) dominates, making Z > 1. At moderate pressures, Z < 1 due to intermolecular attractions.
Raoult's law: P_i = x_i × P_i° for ideal solutions. Both statements A and C are equivalent for ideal solutions.
μ_JT = (∂T/∂P)_H. Negative coefficient means T increases with pressure drop (cooling requires very low T or high P).
For adiabatic process, Q = 0, so ΔU = W (first law). Temperature increases during compression.
From dG = -SdT + VdP, cross derivatives give (∂S/∂P)_T = -(∂V/∂T)_P, a Maxwell relation.
Second law: dS_universe ≥ 0. For isolated systems, dS_system ≥ 0. Equality holds for reversible adiabatic processes.
Throttling through a valve occurs at constant enthalpy (isenthalpic process). This explains cooling of real gases during expansion.
For constant external pressure, work is W = P_ext × ΔV. This is path-dependent work for irreversible processes.