Thermodynamics and Heat Transfer
Thermodynamics accounts for energy and its transformations; heat transfer describes how thermal energy actually moves. Together they underpin engines, refrigerators, heat pumps, and every thermal system, governed by the first law (energy is conserved) and the second law (some conversions are impossible). Careful use of absolute temperature is essential throughout.
The first law and energy balances
The first law is conservation of energy. For a closed system, ΔU = Q − W: the change in internal energy equals heat added minus work done by the system. For an open system (control volume) at steady state, energy in equals energy out, including enthalpy, kinetic, and potential terms. Sensible heating without phase change follows Q = m·c·ΔT; raising 2 kg of water (c = 4.18 kJ/kg·K) by 10°C needs Q = 2·4.18·10 = 83.6 kJ. Getting the sign convention right — heat in positive, work out positive — is the recurring first-law discipline.
Ideal-gas behavior
Many FE gas problems use the ideal-gas law, P·V = n·R·T (universal R = 8.314 J/mol·K) or the mass form P·V = m·R_specific·T, where R_specific = R/M. For air R_specific = 0.287 kJ/kg·K, so 2 kg at 300 K and 100 kPa occupies V = m·R·T/P = 2·0.287·300/100 ≈ 1.72 m³. At fixed temperature, pressure and volume are inversely related (Boyle's law): double the pressure and the volume halves. Temperatures in every gas relation must be absolute — kelvin or rankine, never Celsius.
The second law, entropy, and processes
The second law says heat flows spontaneously only from hot to cold and that no cyclic engine can convert heat entirely into work; entropy of an isolated system never decreases. Entropy change for a reversible process is ΔS = Q_rev/T. Common idealized processes include isothermal (constant T), isobaric (constant P), isochoric (constant V), and isentropic (reversible adiabatic, ΔS = 0). For isentropic compression of an ideal gas, T·P^((1−k)/k) is constant; air (k = 1.4) compressed from 100 to 200 kPa rises from 300 K to T = 300·(200/100)^(0.4/1.4) ≈ 366 K.
Cycles: engines, refrigerators, and heat pumps
A reversible Carnot engine between absolute temperatures T_hot and T_cold has the maximum possible efficiency η = 1 − T_cold/T_hot — between 600 K and 300 K that ceiling is 1 − 300/600 = 0.50, or 50%. No real engine beats it. For a Carnot refrigerator, the coefficient of performance is COP_ref = T_cold/(T_hot − T_cold); for a Carnot heat pump, COP_hp = T_hot/(T_hot − T_cold) = COP_ref + 1. A heat pump maintaining a house at 300 K from 270 K outdoor air has COP_hp = 300/30 = 10. The universal trap is inserting Celsius where kelvin is required.
Conduction, convection, and radiation
Heat moves by three modes. Conduction through a plane wall follows Fourier's law, Q = k·A·ΔT/L, where k is thermal conductivity and L the thickness — a thicker or less conductive wall passes less heat. Convection between a surface and a moving fluid is Newton's law of cooling, Q = h·A·ΔT, with h the convection coefficient. Radiation from a surface scales with the fourth power of absolute temperature, Q = ε·σ·A·T⁴ (Stefan–Boltzmann σ = 5.67×10⁻⁸ W/m²·K⁴). Series conduction resistances add like electrical resistors, R = L/(k·A), which lets composite walls be solved by a thermal-circuit analogy.
Phase change and latent heat
Adding heat to a substance at its melting or boiling point changes phase at constant temperature; the energy is latent heat, Q = m·L, where L is the latent heat of fusion or vaporization. A heating curve therefore shows sloped sensible-heating segments (Q = m·c·ΔT) connected by flat latent plateaus. Water's large latent heat of vaporization (about 2,260 kJ/kg) is why boiling absorbs far more energy than simply heating the liquid. Forgetting the latent term when a process crosses a phase boundary underestimates the total heat required.
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