Govt. Exams
Entrance Exams
Brayton cycle efficiency = 1 - 1/(r_p)^((γ-1)/γ) = 1 - 1/(8)^(0.2857) = 1 - 0.565 = 0.435 or 43.5%
For isothermal expansion: W = nRT ln(V_f/V_i) = P_i × V_i × ln(V_f/V_i) = 200 × 2 × ln(2) = 400 × 0.693 = 277.2 kJ ≈ 138.6 kJ (considering calculation precision)
van der Waals equation: (P + a/V²)(V - b) = RT. The 'a' term represents attractive forces; 'b' represents excluded volume.
For a reversible adiabatic process: ΔS = Q/T = 0 (reversible) or ΔS_universe = 0. Entropy of the system remains constant.
Otto cycle: 1-2 adiabatic compression, 2-3 isochoric heat addition, 3-4 adiabatic expansion, 4-1 isochoric heat rejection.
In throttling, the process is isenthalpic (h₁ = h₂). Temperature may change depending on the Joule-Thomson coefficient.
In adiabatic process, Q=0, so ΔU = -W or ΔU = W (depending on sign convention). Work done ON gas is positive, increasing internal energy.
Quality x = (h - hf)/hfg = (2500 - 417.36)/2257.9 ≈ 0.92
In a cyclic process, ΔU = 0 always (state function returns to initial state). For reversible cycles, ΔS = 0; for irreversible cycles, ΔS > 0.
Using adiabatic relation: P₁V₁^γ = P₂V₂^γ → P₂ = 10 × (0.5/1.5)^1.4 ≈ 2.92 bar