Govt. Exams
For Carnot refrigerator: COP = T_c/(T_h - T_c) = 250/(300-250) = 250/50 = 5
Q = nC_vΔT. 5000 = 2 × (5/2) × 8.314 × ΔT. ΔT = 5000/(5 × 8.314) = 5000/41.57 ≈ 120.2 K. Final T = 300 + 120.2 ≈ 380 K
From PV² = constant: P₁V₁² = P₂V₂². P₂/P₁ = (V₁/V₂)² = (V/2V)² = 1/4
In a reversible process, total entropy change = 0. ΔS_system + ΔS_surroundings = 0. This is the definition of a reversible process.
For diatomic gas, C_v = (5/2)R. ΔU = nC_vΔT = 4 × (5/2) × 8.314 × (400-300) = 10 × 8.314 × 100 = 8314 × 2 = 16628 J
For isothermal compression: W = -nRT ln(V_f/V_i) = nRT ln(V_i/V_f). 2300 = n × 8.314 × 400 × ln(10/5) = n × 8.314 × 400 × 0.693. n = 2300/(2300) = 1 mole
Efficiency of Carnot engine = 1 - T_c/T_h = 1 - 300/500 = 0.4 = 40%. Work = Efficiency × Q_h = 0.4 × 5000 = 2000 J
Using conservation of moles: n_A = 2PV/RT, n_B = PV/RT. Total moles = 3PV/RT. Final pressure = (3PV/RT)RT/(2V) = 1.5P
At constant P: Q = ΔU + PΔV, so more heat is needed to produce same temperature rise. Relation: Cp - Cv = R
An open system allows both mass and energy exchange with surroundings (e.g., a boiling kettle), while a closed system allows only energy exchange