Sources and References

Primary texts — Cengel, Y. A. and Boles, M. A. Thermodynamics: An Engineering Approach, 9th ed. McGraw-Hill, 2019. Incropera, F. P., DeWitt, D. P., Bergman, T. L., and Lavine, A. S. Fundamentals of Heat and Mass Transfer, 8th ed. Wiley, 2017.

Supplementary texts — Tester, J. W. et al. Sustainable Energy: Choosing Among Options, 2nd ed. MIT Press, 2012. Masters, G. M. Renewable and Efficient Electric Power Systems, 2nd ed. Wiley, 2013. Smil, V. Energy and Civilization: A History. MIT Press, 2017.

Online resources — MIT OpenCourseWare 22.081 Introduction to Sustainable Energy; MIT OCW 2.60J Fundamentals of Advanced Energy Conversion; IEA World Energy Outlook; IPCC Assessment Reports; NREL System Advisor Model documentation.

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Chapter 1: The First Law and Energy Balances

1.1 Forms of Energy

Macroscopic energy divides into kinetic, potential, and internal components. Internal energy \(U\) is the sum of microscopic translational, rotational, vibrational, and intermolecular potential energies. Enthalpy is defined as

\[ H = U + pV, \]

a convenience that absorbs the flow work term in open-system analysis. For an ideal gas, both \(U\) and \(H\) depend only on temperature.

1.2 Specific Heats

The specific heat at constant volume is \(c_v = (\partial u/\partial T)_v\); at constant pressure, \(c_p = (\partial h/\partial T)_p\). For ideal gases,

\[ c_p - c_v = R, \]

where \(R\) is the specific gas constant. The ratio \(\gamma = c_p/c_v\) governs adiabatic processes and acoustic speed. For air at room temperature, \(c_p \approx 1005\) J/(kg·K), \(c_v \approx 718\) J/(kg·K), \(\gamma \approx 1.4\).

For incompressible solids and liquids, \(c_p \approx c_v \equiv c\), and enthalpy change is simply \(\Delta h = c\,\Delta T + v\,\Delta p\), with the pressure term usually negligible.

1.3 Closed-System First Law

For a closed system between states 1 and 2,

\[ Q_{12} - W_{12} = \Delta U + \Delta KE + \Delta PE, \]

where \(Q\) is heat added and \(W\) is work done by the system. Sign conventions vary; we use heat positive when added, work positive when done by the system. On a rate basis,

\[ \dot Q - \dot W = \frac{dU}{dt}. \]

1.4 Open-System First Law

For a control volume with mass flows in and out,

\[ \frac{dE_{cv}}{dt} = \dot Q - \dot W + \sum_{in}\dot m_i\left(h_i + \tfrac{V_i^2}{2} + gz_i\right) - \sum_{out}\dot m_e\left(h_e + \tfrac{V_e^2}{2} + gz_e\right). \]

In steady state the left side vanishes. Most engineering devices (turbines, compressors, heat exchangers, nozzles) are analyzed with this equation plus mass conservation.

Chapter 2: Second Law, Entropy, and Efficiency

2.1 Kelvin-Planck and Clausius Statements

The Kelvin-Planck statement forbids a cyclic device that produces net work while exchanging heat with only one reservoir. The Clausius statement forbids a cyclic device that transfers heat from cold to hot without work input. The two are equivalent.

2.2 Carnot Efficiency

A heat engine operating reversibly between reservoirs at absolute temperatures \(T_H\) and \(T_C\) has efficiency

\[ \eta_{Carnot} = 1 - \frac{T_C}{T_H}. \]

A refrigerator has coefficient of performance \(\text{COP}_R = T_C/(T_H - T_C)\); a heat pump has \(\text{COP}_{HP} = T_H/(T_H - T_C)\). All real devices fall short of these limits.

2.3 Entropy

For a reversible process, \(dS = \delta Q/T\). The second law in its most general form is \(dS_{system} \ge \delta Q/T\), with equality for reversible processes. Entropy can be tabulated for substances as a function of state. The TdS relations give

\[ T\,ds = du + p\,dv, \qquad T\,ds = dh - v\,dp. \]

Isentropic processes (\(s = \text{const}\)) model ideal turbines, compressors, and nozzles; real devices are characterized by isentropic efficiency comparing actual work to ideal.

Chapter 3: Power and Refrigeration Cycles

3.1 Rankine Cycle

Steam power plants follow the Rankine cycle: pump feedwater to high pressure, boil in a steam generator, expand through a turbine, condense, repeat. Ideal Rankine efficiency is

\[ \eta = \frac{w_{turbine} - w_{pump}}{q_{in}}. \]

Modern supercritical plants with reheat and regenerative feedwater heating achieve thermal efficiencies above 45%.

3.2 Brayton Cycle

Gas turbines follow the Brayton cycle: compress air, burn fuel in a combustor, expand through a turbine. Ideal Brayton efficiency with pressure ratio \(r_p\) is

\[ \eta = 1 - r_p^{(1-\gamma)/\gamma}. \]

Combined-cycle plants use Brayton exhaust heat to drive a Rankine bottoming cycle, achieving overall efficiencies above 60%.

3.3 Vapour Compression Refrigeration

Reverse the Rankine cycle: a compressor raises refrigerant pressure, a condenser rejects heat to the environment, an expansion valve drops pressure, and an evaporator absorbs heat from the cold space. COPs of three to five are typical for air conditioners and heat pumps, meaning one unit of electrical work delivers three to five units of thermal transfer.

Chapter 4: Heat Transfer

4.1 Conduction

Fourier’s law states \(\dot q''_x = -k\,dT/dx\). For steady one-dimensional conduction through a plane wall of thickness \(L\) and conductivity \(k\) with surface temperatures \(T_1\) and \(T_2\),

\[ \dot Q = \frac{kA(T_1 - T_2)}{L}. \]

Composite walls combine resistances \(R = L/(kA)\) in series or parallel. The general unsteady equation is

\[ \frac{\partial T}{\partial t} = \alpha\nabla^2 T + \frac{\dot q_{gen}}{\rho c}, \]

with thermal diffusivity \(\alpha = k/(\rho c)\).

4.2 Convection

Newton’s law of cooling gives \(\dot q'' = h(T_s - T_\infty)\), where \(h\) is the convective heat transfer coefficient. Free convection in still air has \(h\) around 5 to 25 W/(m²·K); forced convection raises it to hundreds or thousands. Dimensionless groups (Nusselt, Reynolds, Prandtl, Grashof) correlate data; for turbulent flow in pipes the Dittus-Boelter equation is

\[ \text{Nu} = 0.023\,\text{Re}^{0.8}\text{Pr}^{n}. \]

4.3 Radiation

A black body emits power per unit area \(\sigma T^4\), with \(\sigma = 5.67 \times 10^{-8}\) W/(m²·K⁴). Real surfaces have emissivity \(\varepsilon < 1\). Net radiation exchange between two surfaces depends on geometry through view factors. Radiation dominates at high temperatures and in vacuum.

Chapter 5: Phase Change in Environmental Systems

5.1 Latent Heat

Phase transitions absorb or release latent heat at constant temperature. Water has \(h_{fg} = 2257\) kJ/kg at 100 °C and \(h_{sf} = 334\) kJ/kg at 0 °C. Evapotranspiration cools vegetated surfaces; freezing lakes release 334 J per gram of water frozen, buffering arctic temperatures.

5.2 Psychrometrics

Moist air is a mixture of dry air and water vapour. The ratio of water vapour mass to dry air mass is humidity ratio \(\omega\); relative humidity is the ratio of partial pressure of water to its saturation pressure at the same temperature. The dew point is the temperature at which saturation occurs. Cooling coils that lower air below dew point condense moisture and dehumidify simultaneously.

Chapter 6: Renewable Energy Technologies

6.1 Solar Thermal and Photovoltaic

Solar irradiance at the top of the atmosphere averages 1361 W/m²; at clear-sky ground level with the sun overhead, about 1000 W/m². Flat-plate solar thermal collectors heat water with efficiencies of 40 to 70 percent.

Photovoltaics convert photons to electron-hole pairs across a semiconductor junction. Silicon’s bandgap of 1.12 eV limits single-junction theoretical efficiency (Shockley-Queisser limit) to about 33 percent; commercial modules achieve 18 to 22 percent. Output depends on irradiance and temperature; higher cell temperature reduces efficiency by about 0.4% per °C.

6.2 Wind Energy

The kinetic energy flux through an area \(A\) in wind of speed \(V\) is

\[ \dot E_k = \tfrac{1}{2}\rho A V^3. \]

A wind turbine cannot extract all of this energy without stopping the wind; the Betz limit bounds the fraction extractable at \(16/27 \approx 59.3\%\). Real turbines achieve power coefficients of 0.4 to 0.5. The cubic dependence on wind speed makes site selection critical; a doubling of wind speed multiplies power by eight.

6.3 Hydroelectric

The gravitational potential energy per unit mass of water at height \(H\) above the turbine is \(gH\). Power output is

\[ P = \rho g Q H \eta, \]

with flow rate \(Q\) and efficiency \(\eta\) typically above 90%. Hydroelectric provides roughly 16% of global electricity, the largest renewable source.

6.4 Geothermal

Ground-source heat pumps exploit the stable temperature of deep soil (roughly equal to mean annual air temperature) as a heat source in winter and heat sink in summer, achieving seasonal COPs of 3 to 5. Deep geothermal uses hot rock or hydrothermal reservoirs to drive Rankine cycles directly. Enhanced geothermal systems (EGS) fracture hot dry rock to create artificial reservoirs.

6.5 Biomass, Biofuels, and Tidal

Biomass combustion is carbon-neutral in theory if the carbon was sequestered by growth within a short cycle; life-cycle analyses must account for land use change and fossil inputs to cultivation. Liquid biofuels include ethanol (from sugar or starch fermentation) and biodiesel (from transesterified triglycerides). Tidal energy uses predictable lunar-driven sea-level oscillations; barrage schemes like La Rance (France) and emerging tidal stream turbines deploy hydrokinetic conversion.

Chapter 7: Non-Renewable Energy

7.1 Fossil Fuels

Fossil fuels remain the dominant primary energy source. Coal combustion produces roughly 900 g CO\(_2\) per kWh of electricity at 40% efficiency; natural gas produces about 400 g CO\(_2\) per kWh at 55% efficiency due to higher H/C ratio and combined-cycle operation. Petroleum is primarily a transportation fuel, with refinery outputs (gasoline, diesel, jet) tailored to engine demand.

7.2 Nuclear Fission

Uranium-235 fission releases about 200 MeV per nucleus, equivalent to roughly 80 TJ per kilogram of fuel, a factor of \(10^6\) above fossil energy density per mass. Pressurized water reactors, boiling water reactors, and CANDU heavy-water reactors are the dominant civilian designs. Waste management, proliferation, and capital cost remain the principal challenges.

Chapter 8: Environmental Implications and Policy

8.1 Greenhouse Gases and Climate

Atmospheric CO\(_2\) has risen from roughly 280 ppm pre-industrial to over 420 ppm today. The radiative forcing of CO\(_2\) is approximately \(\Delta F = 5.35\ln(C/C_0)\) W/m². Methane is about 28 times more potent than CO\(_2\) per unit mass over a century, but shorter-lived. Global warming potential (GWP) provides a common unit (CO\(_2\)-equivalent) for comparing gases.

8.2 Policy Instruments

Carbon pricing (tax or cap-and-trade) internalizes the externality of emissions. Renewable portfolio standards mandate fractional supply from renewables. Feed-in tariffs guarantee a purchase price for renewable generation. Building codes and appliance standards improve end-use efficiency. The economics of each depends on discount rate, electricity market structure, and political willingness to bear transition costs.

8.3 Life-Cycle Assessment

Every energy technology has upstream (manufacturing, fuel extraction) and downstream (operation, end-of-life) environmental impacts. Life-cycle CO\(_2\) per kWh ranges from about 10 to 50 g for wind and hydro, 40 to 80 g for solar PV, 10 to 20 g for nuclear, 400 to 500 g for combined-cycle gas, and 800 to 1000 g for coal. Rational energy policy requires comparing on a life-cycle basis rather than nameplate efficiency.