Questions
8–10 MCQs per paper
Difficulty
Medium-Hard
Importance
Core — never skip
Overview
Thermodynamics is a core pillar of Mechanical Engineering that forms the backbone of thermal and power plant engineering in PSU exams. Aspirants must master the energy conversion cycles and state equations as they frequently appear in conceptual and numerical-heavy sections of papers like GATE, HPCL, and NTPC.
Laws of Thermodynamics
These fundamental laws define energy conservation, entropy, and the limits of thermal systems. In exams, focus on the Zeroth Law for temperature definitions, First Law for closed/open systems, and Second Law for entropy/efficiency bounds.
- Zeroth Law: Concept of temperature and thermal equilibrium
- First Law for cycle: cyclic integral of dQ = cyclic integral of dW
- Steady Flow Energy Equation: h1 + v1^2/2 + gz1 + Q = h2 + v2^2/2 + gz2 + W
- Clausius Inequality: cyclic integral of dQ/T <= 0
- Entropy Principle: dS >= dQ/T
Cycles: Carnot, Rankine, and Brayton
These cycles model the performance of heat engines and power plants. Expect heavy calculations regarding efficiency, work ratio, and back work ratio in Brayton and Rankine cycles.
- Carnot Efficiency: eta = 1 - (TL/TH)
- Rankine Cycle efficiency: Wnet/Qin = (h3-h4 - (h2-h1))/(h3-h2)
- Brayton Cycle efficiency: 1 - (1/rp)^((gamma-1)/gamma)
- Work Ratio for Gas Turbines: (W_turbine - W_compressor) / W_turbine
- Optimum Pressure Ratio for maximum work: rp = (Tp/Tc)^(gamma/(2*(gamma-1)))
IC Engines and Combustion Cycles
IC engine cycles compare theoretical performance based on compression ratios and heat addition types. Examiners often test the comparative efficiency of Otto, Diesel, and Dual cycles at the same compression ratio.
- Otto Efficiency: 1 - (1/r)^(gamma-1)
- Diesel Efficiency: 1 - [(1/r)^(gamma-1) * ((rho^gamma - 1)/(gamma*(rho - 1)))]
- Compression Ratio (r): Vc+Vs / Vc
- Cut-off Ratio (rho): V3/V2
- Mean Effective Pressure: Wnet / Vs
Refrigeration and Steam Tables
Refrigeration cycles focus on the Coefficient of Performance (COP) and refrigerant properties. Mastering Steam Tables is critical for solving Rankine cycle problems involving superheated or wet steam.
- VCR COP: (h1 - h4) / (h2 - h1)
- VCE COP: Cp(T2-T3) / (T1-T2)
- Enthalpy of wet steam: h = hf + x*hfg
- Entropy of wet steam: s = sf + x*sfg
- Tonnage of Refrigeration: 3.5 kW = 1 TR
Formula Sheet
dQ = dU + dW (First Law for closed systems)
eta = W_net / Q_in
Q = m*Cp*dT
PV = mRT
h = u + Pv
S = Sf + x*Sfg
COP_HP = 1 + COP_Ref
rp = P2/P1
W_net = Q1 - Q2
gamma = Cp/Cv
Exam Tip
Always identify the system boundaries first; for steady flow problems, the energy balance equation is your most reliable tool to solve for missing enthalpies or velocities.
Common Mistakes
- Confusing the specific heats (Cp and Cv) values, especially when dealing with air-standard cycles.
- Forgetting to convert temperatures into Kelvin during Carnot or efficiency calculations.
- Incorrectly identifying the cut-off ratio in Diesel cycles or confusing it with the expansion ratio.
More Revision Notes
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