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Thermodynamics & Energy Conversion

From transcript: 20ME330 Basic Thermodynamics (C) · 20ME410 Applied Thermodynamics (C) · 20ME58L Energy Conversion Lab (A)

Cheat sheet

Printable study sheet: formulas → definitions → topic notes → traps.

Formulas

1st law closed (common ME): Q − W = ΔU (check course sign!)
1st law open steady SFEE: h1+V1²/2+gz1+q = h2+V2²/2+gz2+w
Enthalpy H=U+PV ; h=u+Pv ; ideal gas Δh=cpΔT ; Δu=cvΔT ; cp−cv=R
Ideal gas PV=mRT = nℜT ; γ=cp/cv ; isentropic T2/T1=(V1/V2)^{γ−1}=(P2/P1)^{(γ−1)/γ}
2nd law: ΔS ≥ ∫δQ/T ; isolated S_gen≥0 ; Carnot η=1−Tc/Th
Entropy ideal gas: Δs = cv ln T2/T1 + R ln v2/v1 = cp ln T2/T1 − R ln P2/P1
Availability/exergy closed: Φ=(U−U0)−T0(S−S0)+P0(V−V0)
Otto η=1−r^{1−γ} ; Diesel η=1−(1/r^{γ−1})(ρ^γ−1)/(γ(ρ−1)) ; r=V1/V2, ρ=cutoff
Rankine: boiler→turbine→condenser→pump ; η = (Wt−Wp)/Qin
Refrigeration COP = Qc/W ; heat pump COP = Qh/W = 1+Qc/W
Relative humidity φ = Pv/Pg(T) ; specific humidity ω ≈ 0.622 Pv/(P−Pv)
Nozzle: h01=h+V²/2 ; throttling h≈const (Joule–Thomson)
Compressor polytropic: W = n/(n−1) m R (T2−T1) (ideal gas)
Mean effective pressure MEP related to work / displacement volume
1st law (closed): Q − W = ΔU (sign convention course-dependent)
1st law (open, SFEE): h + V²/2 + gz + q = h_e + … + w
2nd law: η_th ≤ 1 − Tc/Th (Carnot)
Ideal gas: PV = mRT ; Δu = cvΔT ; Δh = cpΔT
Otto: η = 1 − 1/r^(γ−1) ; Diesel: η = 1 − (1/r^(γ−1))((ρ^γ−1)/(γ(ρ−1)))
COP_ref = Q_c / W ; COP_HP = Q_h / W
Closed system (common textbook sign): ΔU = Q − W
Enthalpy H = U + PV ; h = u + Pv
Entropy balance: ΔS = ∫δQ_rev/T + S_gen (S_gen ≥ 0)
Isentropic ideal gas: T2/T1 = (V1/V2)^(γ−1) = (P2/P1)^((γ−1)/γ)
SFEE steady: h1 + V1²/2 + g z1 + q = h2 + V2²/2 + g z2 + w
Availability (closed, simple): Φ = (U−U0) − T0(S−S0) + P0(V−V0)

Definitions

System / surroundings / boundary
What you analyze; closed vs open (mass flow)
Property / state
Point function; path functions Q,W depend on process
Intensive / extensive
Independent of / scales with size
Quasi-equilibrium
System near equilibrium states — reversible idealization
Heat / work
Energy transfers across boundary — not stored as Q or W
Entropy
Disorder/quality metric; generation measures irreversibility
Exergy
Max useful work vs environment (T0,P0)
Dead state
Equilibrium with environment — zero exergy
Quality x
Vapor mass fraction in saturated mixture
Psychrometry
Moist air properties — AC design
State function
Property depending only on state (U, H, S) — not path
Reversible process
Quasi-static, no irreversibilities — upper bound on work
Availability / exergy
Useful work potential relative to environment
Quasi-static
Process proceeds through near-equilibrium states — idealization for reversible work
Relative humidity
Partial pressure of vapour / saturation pressure at same T

Topic-wise short notes

Study these first — one block per syllabus topic. Then read the deep notes below.

Zeroth, first & second laws

  • Zeroth: thermal equilibrium transitive — defines temperature.
  • 1st: energy conserved; Q and W are path functions; U is a property.
  • Sign convention: state yours (Q in +, W out + is common ME) before algebra.
  • 2nd: Kelvin–Planck / Clausius statements; equivalent.
  • Entropy: dS ≥ δQ/T ; equality for reversible; S_gen measures lost work.
  • Carnot between Th,Tc is max η for engines; max COP frameworks for ref/HP.

Properties & ideal gas

  • Two independent intensive props fix simple compressible state.
  • Steam: compressed liquid / sat mix (x) / superheat — use correct table.
  • Ideal gas: u(T), h(T) only; pv=RT; isentropic relations with γ.
  • Real gas: compressibility Z; charts when near saturation/critical.
  • Specific heats: cp, cv; γ; polytropic n between isothermal & adiabatic limits.

Gas power cycles

  • Otto (SI): const-V heat add; η↑ with r; knock limits r.
  • Diesel (CI): const-P heat add; cutoff ratio ρ; higher r possible.
  • Dual: both; Brayton: gas turbine; regeneration/intercool/reheat options.
  • Cold air-standard: constant cp — exam estimates only.
  • MEP, BSFC, volumetric efficiency for real engines.

Vapour power & refrigeration

  • Rankine: pump work small vs turbine; improve via superheat/reheat/regen.
  • Irreversibilities: boiler ΔT, turbine η_is, condenser subcooling, pipe losses.
  • VCR: evaporator absorbs Qc; compressor work; condenser rejects; TXV/throttle h≈const.
  • COP_ref=Qc/W; COP_HP=Qh/W; never call COP an 'efficiency' % without care.
  • Psychrometrics: DB/WB/DP, φ, ω, enthalpy — cooling coils & towers.

Exergy & availability

  • Exergy is useful work potential vs environment (T0,P0).
  • Destroyed exergy = T0 S_gen — target for improvements.
  • Throttling destroys exergy even though h constant.

Exam traps & quick notes

Comprehensive notes

Properties, processes, and ideal gas

A property depends only on state (P, T, v, u, h, s). A process is a path between states. Intensive properties are independent of mass; extensive scale with mass. For an ideal gas, Pv = RT (or PV = mRT), u = u(T) only, h = h(T) only, with Δu = cvΔT and Δh = cpΔT. Real gases need compressibility charts or tables when near saturation or at high pressure.

Common processes: isochoric (V const), isobaric (P const), isothermal (T const), adiabatic (Q=0), isentropic (adiabatic + reversible). Polytropic PV^n = const interpolates many machines. Sketch P–v and T–s diagrams in interviews — they show work and heat geometrically.

Pitfall: mixing sign conventions (heat into system positive vs some engineering texts). State yours. Project tie: energy conversion lab trials (engines/compressors) are where BSFC and efficiency become tangible.

External: LearnThermo ↗ NPTEL Basic Thermodynamics ↗

First & second laws; Carnot

First law for a closed system balances heat, work, and energy change. For open systems use the steady-flow energy equation with enthalpy and shaft work. Second law introduces irreversibility and the Carnot limit η = 1 − Tc/Th between two reservoirs. Clausius inequality and entropy generation quantify “how irreversible.”

Exergy (availability) measures useful work potential relative to the environment — useful when comparing devices beyond first-law efficiency alone. Throttling (h≈const) is highly irreversible: temperature may drop (Joule–Thomson) but exergy is destroyed.

External: MIT OCW Thermo ↗

Gas & vapour power cycles; refrigeration

Otto: isentropic compression → const-V heat addition → isentropic expansion → const-V heat rejection. η = 1 − r^(1−γ). Diesel: const-P heat addition; cut-off ratio ρ appears in η. Dual blends both. Brayton models gas turbines (const-P heat add/reject). Rankine is the vapour power cycle — use steam tables; improve with superheat, reheat, regeneration.

Vapour-compression refrigeration: COP = Q_c/W; heat pumps use Q_h/W. Discuss refrigerants at high level (safety, GWP) without pretending regulatory expertise you don’t have.

External: NASA Brayton ↗

Likely interview questions (thermo)

Q: Does higher compression ratio always help?
A: In Otto air-standard yes for η, but real SI engines knock — limited by fuel octane and combustion. Diesel uses higher r because fuel is injected into hot air.

Q: Why is isentropic efficiency used for turbines/compressors?
A: Compares actual work to ideal reversible adiabatic work between same pressures — captures irreversibilities in one number.

Q: Throttling in AC — why?
A: Expansion device drops pressure; roughly isenthalpic; enables low evaporator temperature for heat pickup.

External: Thermodynamics interview topics (NPTEL) ↗