Govt. Exams
Entrance Exams
At same T and P, the chemical potential per molecule is identical. Internal energy and entropy depend on amount (volume), heat capacity depends on mass.
ΔG = ΔH - TΔS = -200 - (300)(50/1000) = -200 - 15 = -185 kJ/mol
Free expansion is an irreversible process. For the isolated system, ΔS_universe > 0. The gas entropy increases as volume increases.
At equilibrium phase transition (melting point), ΔG = 0. This is the condition for phase equilibrium at constant T and P.
For monatomic gas: Cv = (3/2)R, Cp = (5/2)R. Therefore γ = Cp/Cv = (5/2)/(3/2) = 5/3 ≈ 1.67
COP = Q_cold/W. Therefore, Q_cold = COP × W = 5 × 100 = 500 J
In adiabatic compression (q=0), work is done on gas, increasing both P and T without heat exchange. Other processes would have different P-T relationships.
For isothermal process: W = nRT ln(V_f/V_i) = nRT ln(P_i/P_f). Since ΔU = 0, q = W.
Second law of thermodynamics: For an isolated system, ΔS ≥ 0 (entropy increases for irreversible processes, constant for reversible).
At constant pressure, supplied heat does two things: increases internal energy and does expansion work. Hence Cp > Cv by amount R.