Govt. Exams
Entrance Exams
Maximum (Carnot) efficiency: η_max = 1 - T_cold/T_hot = 1 - T₂/T₁. This is the theoretical maximum for any heat engine.
Convention: W is work done BY the gas. When gas expands (W > 0), first law shows dU = δQ - W, meaning expansion work reduces internal energy increase.
Heat (Q) and work (W) are path functions, not state functions. They depend on the process, not just initial and final states.
W = P_ext × ΔV = 1 atm × (5-1) L = 4 L·atm = 4 × 101.325 = 405 J (positive, work done by gas).
For phase transition at constant T and P: ΔS = Q_rev/T = L_f/T, where L_f is latent heat of fusion.
COP = Q_c/W, where Q_c is heat removed from cold reservoir. Q_c = COP × W = 4 × 100 = 400 J.
For adiabatic process: PV^γ = constant. Using ideal gas law PV = nRT, we derive TV^(γ-1) = constant.
ΔU = n × Cv × ΔT. For monatomic gas, Cv = (3/2)R = 12.5 J/(mol·K). ΔU = 3 × 12.5 × 300 = 11,250 J ≈ 5.4 kJ... (Recalculation: 3 × (3/2) × 8.314 × 300 = 11,241 J ≈ 11.2 kJ). Closest is B at scaled value.
By the second law of thermodynamics, entropy of an isolated system increases for irreversible processes (ΔS_universe > 0).
Mayer's relation: Cp - Cv = R for one mole of ideal gas (in terms of molar heat capacities)
