Govt. Exams
Entrance Exams
Maxwell relations originate from the equality of mixed partial derivatives of thermodynamic potentials (∂²F/∂x∂y = ∂²F/∂y∂x), combined with Legendre transformations.
Throttling is isenthalpic (ΔH = 0) and occurs in expansion valves, regulators, and orifices. Used in refrigeration, HVAC systems. Entropy increases (irreversible) while enthalpy remains constant.
For reversible processes: dS = dq_rev/T. In an isolated system, dq = 0 (no heat transfer), therefore dS = 0. Entropy remains constant for reversible isolated processes.
B(T) is the second virial coefficient that accounts for molecular interactions. It corrects ideal gas behavior and is temperature-dependent, directly representing non-ideality.
For ideal solutions: ΔH_mix = 0 and ΔS_mix = -R(x₁ ln x₁ + x₂ ln x₂), so ΔG_mix = -TΔS_mix = RT(x₁ ln x₁ + x₂ ln x₂) < 0, making mixing spontaneous.
Partial molar volume V̄ᵢ = (∂V/∂nᵢ)T,P represents the actual volume increase when 1 mole of i is added. It varies with composition and differs from pure component molar volume.
At low T, attractive forces dominate (Z < 1). At high T, repulsive forces dominate (Z > 1). The Boyle temperature is where Z ≈ 1. Pressure and temperature both influence Z significantly.
In polytropic compression with n between 1 and γ, both T and P increase as volume decreases. Isentropic expansion decreases T and P. Throttling and isothermal keep T constant.
Residual properties (M^R) account for non-ideal behavior: M^R = M_real - M_ideal at same T and P. Essential for calculating properties of real gases and mixtures.
For isothermal process: dS = dq_rev/T = nR dV/V, integrating gives ΔS = nR ln(V₂/V₁). Temperature is constant, so entropy change depends only on volume change.
