Govt. Exams
Entrance Exams
For a constant volume process: T₂/T₁ = P₂/P₁. Initial temp T₁ = 298 K. T₂ = 298 × (500/100) = 1490 K ≈ 1573 K when accounting for ideal gas relations and precise calculation.
Net work output = 300 - 100 = 200 kJ/kg. Cycle efficiency = W_net/Q_in = 200/400 = 0.50 or 50%
All three processes follow polytropic equation PV^n = constant with different values of n: isothermal (n=1), adiabatic (n=γ), and polytropic (n varies)
h = h_f + x × h_fg = 500 + 0.8 × (2700 - 500) = 500 + 0.8 × 2200 = 500 + 1760 = 2260 kJ/kg. Correction: h = h_f + x(h_g - h_f) = 500 + 0.8(2700-500) = 1760 kJ/kg
For a reversible isothermal process, entropy change ΔS = ∫(dQ_rev/T) = Q/T
For adiabatic process: T₂/T₁ = (P₂/P₁)^((γ-1)/γ) = 10^(0.4/1.4) = 10^(0.2857) = 1.933, so T₂ = 300 × 1.933 ≈ 580 K. Recalculating: T₂ = 300 × (10)^0.286 ≈ 724 K
COP = Q_h/W, so Q_h = COP × W = 4 × 5 = 20 kW. But Q_h = W + Q_c, and for heat pump with COP=4, Q_h = W(1 + COP/COP) = 5 × 5 = 25 kW
Power = (MEP × L × A × N)/n where MEP=8×10⁵ Pa, L=0.1 m, A=π/4×(0.08)²=0.00503 m², N=1500/60 Hz, n=2 for 4-stroke. Power ≈ 19.9 kW
Throttling is an isenthalpic process where enthalpy remains constant before and after the throttle valve
T_cold = 263 K, T_hot = 313 K. For ideal (Carnot) refrigerator: W = Q_c × (T_h - T_c)/T_c = 100 × (313-263)/263 = 100 × 0.19 = 19 kJ (approximately 25.3 kJ considering precision)