Govt. Exams
Entrance Exams
For an adiabatic process: PV^γ = constant leads to TV^(γ-1) = constant when combined with ideal gas law.
For phase change at equilibrium: ΔS = ΔH/T = 6000 J / 300 K = 20 J/(mol·K). This applies at the melting point where both phases are in equilibrium.
In a cyclic process, the system returns to initial state, so ΔU = 0 (state function). From first law: Q = W. Heat absorbed equals work done by the system.
According to the second law of thermodynamics: ΔS_universe ≥ 0. For isolated systems, ΔS_system ≥ 0 (increases for irreversible, constant for reversible).
For gas mixtures: Cv(mix) = Σ(n_i × Cv_i)/Σn_i. The heat capacity is the weighted sum based on composition.
For ideal gases, μ_JT = 0 because they have no intermolecular forces. Real gases show non-zero values depending on temperature and pressure conditions.
Expansion in a rigid container is isochoric (constant volume), not isobaric. Phase changes and open systems typically occur at constant pressure.
In adiabatic process, Q = 0. Since ΔU = -W and W > 0 (expansion), ΔU < 0, so temperature decreases. Internal energy decreases as work is done by the gas.
Both relationships are true: Cp - Cv = R (molar basis) and Cp/Cv = γ. For monoatomic gas, γ = 5/3; for diatomic, γ = 7/5.
ΔU = Q - W = 1000 - 600 = 400 J. When work is done BY the system, it's subtracted from heat absorbed.
