5  Fossil Energy—Conversion Technologies

“We have burned our way to prosperity. The question now is whether we can innovate our way to sustainability without burning our way to catastrophe.”

Chapter 4 traced the full energy chain from nuclear fusion in the Sun, through photosynthesis and geological concentration, to the fossil fuel deposits we extract today. We saw that fossil fuels represent time-integrated ancient sunlight, accumulated over hundreds of millions of years and concentrated by geological processes into deposits with power densities 1,000-10,000× higher than the original photosynthesis that captured the energy.

This chapter addresses the next question: how do we extract that stored energy from chemical bonds, and what are the fundamental limits on extraction? The answer involves combustion chemistry, thermodynamic cycles, and engineering compromises refined over two centuries.

5.1 The Chemistry of Combustion

5.1.1 The Basic Reaction

All fossil fuel combustion follows the same basic pattern: hydrocarbons react with oxygen to produce carbon dioxide, water, and heat. The general form for any hydrocarbon \(C_nH_m\) is:

\[C_nH_m + \left(n + \frac{m}{4}\right)O_2 \rightarrow nCO_2 + \frac{m}{2}H_2O + \text{heat}\]

For methane, the primary component of natural gas: \[CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O + 890 \text{ kJ/mol}\]

For octane, a representative gasoline component: \[C_8H_{18} + 12.5O_2 \rightarrow 8CO_2 + 9H_2O + 5,470 \text{ kJ/mol}\]

The heat released—the enthalpy of combustion—depends on breaking carbon-carbon and carbon-hydrogen bonds while forming carbon-oxygen and hydrogen-oxygen bonds. Since C-O and H-O bonds are stronger than C-C and C-H bonds, the reaction releases energy.

5.1.2 Higher and Lower Heating Values

When we quote the energy content of a fuel, we must specify whether the water produced remains as vapor or condenses to liquid. The difference matters:

  • Higher Heating Value (HHV): Assumes water condenses, capturing the latent heat of vaporization
  • Lower Heating Value (LHV): Assumes water remains as vapor, losing that latent heat to the exhaust

For natural gas, HHV = 55.5 MJ/kg while LHV = 50.0 MJ/kg—a 10% difference. Most efficiency calculations use LHV because most exhaust streams are hot enough to keep water as vapor. But condensing boilers can capture some of that latent heat, achieving apparent efficiencies above 100% when quoted on an LHV basis.

NoteBack-of-Envelope: Why Natural Gas is “Cleaner”

Per unit of energy released, different fuels emit different amounts of CO2:

Fuel Carbon content Energy content kg CO2/GJ
Coal (bituminous) 75% C 27 MJ/kg 95
Petroleum 85% C 42 MJ/kg 73
Natural gas 75% C 50 MJ/kg 56

Natural gas emits 40% less CO2 per unit energy than coal, primarily because methane has a higher hydrogen-to-carbon ratio (4:1 vs. roughly 0.8:1 for coal). Some of the energy comes from burning hydrogen to water rather than carbon to CO2.

This is why “coal-to-gas switching” reduces emissions—but only by 40%, not to zero. Natural gas is a bridge, not a destination.

5.1.3 The Combustion Air Requirement

Complete combustion requires oxygen. Since air is only 21% oxygen, substantial volumes of air must flow through any combustion system. For methane:

\[CH_4 + 2O_2 + 7.5N_2 \rightarrow CO_2 + 2H_2O + 7.5N_2\]

That nitrogen passes through the combustion chamber, absorbing heat and diluting the exhaust. At high temperatures, some nitrogen reacts with oxygen to form nitrogen oxides (\(NO_x\)), a major air pollutant. Managing this trade-off—hot enough for efficiency, cool enough to limit \(NO_x\)—is a central challenge in combustion engineering.

Real combustion systems run with excess air to ensure complete fuel oxidation. Insufficient air produces carbon monoxide (toxic) and unburned hydrocarbons (wasted fuel). Typical excess air ranges from 10% for well-controlled gas burners to 50% for coal combustion with varying particle sizes.

5.2 The Steam Cycle: Converting Heat to Work

5.2.1 Why We Need Cycles

Combustion produces heat. But we want electricity, which requires mechanical rotation to drive generators. The thermodynamic challenge is converting thermal energy (random molecular motion) into work (directed macroscopic motion).

The Second Law tells us this conversion can never be complete. Some heat must be rejected to a cold reservoir. The Carnot limit sets the maximum efficiency:

\[\eta_{Carnot} = 1 - \frac{T_{cold}}{T_{hot}}\]

For a power plant rejecting heat to the atmosphere (300 K) while operating at 600°C (873 K): \[\eta_{Carnot} = 1 - \frac{300}{873} = 66\%\]

Real cycles achieve roughly half the Carnot limit due to irreversibilities.

5.2.2 The Rankine Cycle

The workhorse of thermal power generation is the Rankine cycle, which uses water as the working fluid. The cycle has four stages:

  1. Compression (Pump): Liquid water at low pressure is pumped to high pressure. Compressing a liquid requires little work because liquids are nearly incompressible.

  2. Heat Addition (Boiler): High-pressure water passes through the boiler, absorbing heat from combustion. The water vaporizes and becomes superheated steam.

  3. Expansion (Turbine): High-pressure, high-temperature steam expands through a turbine, doing work on the rotating blades. Pressure and temperature drop as the steam expands.

  4. Heat Rejection (Condenser): The low-pressure steam passes through a condenser, where cooling water (or air) removes the remaining heat. The steam condenses back to liquid, completing the cycle.

The efficiency of a simple Rankine cycle is: \[\eta = \frac{W_{turbine} - W_{pump}}{Q_{in}} = \frac{(h_3 - h_4) - (h_2 - h_1)}{h_3 - h_2}\]

where \(h\) represents specific enthalpy at each state point.

5.2.3 Improving the Rankine Cycle

Modern coal and gas-steam plants incorporate several refinements:

Superheat: Rather than expanding saturated steam, the boiler heats steam well above its saturation temperature. This increases the average temperature of heat addition, improving efficiency and reducing moisture content in the turbine exhaust (wet steam damages turbine blades).

Reheat: Steam partially expands through a high-pressure turbine, then returns to the boiler for reheating before completing expansion through a low-pressure turbine. This further increases average heat-addition temperature.

Regeneration (Feedwater Heating): Steam extracted from intermediate turbine stages heats the feedwater before it enters the boiler. This reduces the heat input needed from fuel combustion.

A modern supercritical coal plant operating at 600°C and 300 bar achieves: \[\eta_{actual} \approx 45\%\]

This is about 68% of the Carnot limit—a testament to two centuries of engineering refinement.

ImportantTrilemma Tension: Efficiency vs. Cooling Water

Higher thermal efficiency reduces fuel consumption and emissions per kWh (Sustainability). But all thermal plants must reject waste heat. A 1,000 MW coal plant at 40% efficiency produces 1,500 MW of waste heat that must go somewhere.

Once-through cooling withdraws roughly 150 liters per kWh from rivers or lakes (most is returned, but warmer). Cooling towers reduce withdrawal but evaporate about 2 liters per kWh. The visible steam plumes from cooling towers are often mistaken for pollution; they are simply water vapor condensing in cold air.

Water-stressed regions face a genuine trilemma conflict: efficient thermal generation requires water that may have competing agricultural or municipal uses (Equity), and warm water discharge harms aquatic ecosystems (Sustainability). This is one reason why thermal plants are increasingly controversial even when they burn natural gas rather than coal.

5.3 The Combined Cycle: Gas Turbines Plus Steam

5.3.1 The Brayton Cycle

While steam plants dominate coal generation, natural gas enables a different approach: the gas turbine, operating on the Brayton cycle.

The Brayton cycle also has four stages, but using gas as the working fluid:

  1. Compression: Air is compressed to 15-30 times atmospheric pressure
  2. Heat Addition: Fuel is injected and burned in the compressed air
  3. Expansion: Hot combustion gases expand through a turbine, producing work
  4. Heat Rejection: Exhaust gases exit to the atmosphere

The key advantage: gas turbines operate at much higher temperatures than steam turbines, with modern units reaching 1,500°C at the turbine inlet. The Carnot limit for such a cycle: \[\eta_{Carnot} = 1 - \frac{300}{1773} = 83\%\]

But simple-cycle gas turbines achieve only 35-40% efficiency because the exhaust gases are still extremely hot (500-600°C). All that remaining thermal energy exits up the stack.

5.3.2 Combined Cycle Gas Turbines (CCGT)

The breakthrough insight: use the hot gas turbine exhaust to generate steam for a Rankine cycle. This “combined cycle” captures energy that would otherwise be wasted.

A typical combined cycle plant:

  • Gas turbine (Brayton): converts 38% of fuel energy to electricity
  • Heat recovery steam generator: captures exhaust heat
  • Steam turbine (Rankine): converts another 22% of original fuel energy to electricity
  • Overall efficiency: 60%

Modern combined cycle plants routinely achieve 60-63% efficiency, far exceeding any other thermal generation technology. The best units (GE’s 9HA, Siemens’ HL-class) reach 64%.

NoteBack-of-Envelope: CCGT Emissions

A 60%-efficient combined cycle plant burning natural gas:

  • Fuel input: 6.0 GJ per MWh electricity
  • Natural gas: 56 kg CO2 per GJ
  • Emissions: \(6.0 \times 56 = 336\) kg CO2/MWh

A 38%-efficient coal plant:

  • Fuel input: 9.5 GJ per MWh
  • Coal: 95 kg CO2 per GJ
  • Emissions: \(9.5 \times 95 = 900\) kg CO2/MWh

Switching from coal to gas combined-cycle reduces emissions by 63%—from 900 to 336 kg CO2/MWh. This is partly the fuel (40% less carbon per unit energy) and partly the efficiency (60% vs 38%).

But even the best gas plant emits 336 kg CO2/MWh. Zero-carbon electricity requires something other than fossil combustion.

5.3.3 Flexibility and Grid Integration

Beyond efficiency, combined cycle plants offer operational flexibility increasingly valuable in grids with variable renewables:

  • Start-up time: 30-60 minutes from cold start (vs. 6-8 hours for large coal plants)
  • Ramp rate: 8-10% of capacity per minute
  • Part-load efficiency: Remains above 50% even at 50% load

This flexibility explains why gas plants are often described as “partners” to renewables. When solar and wind output drops, gas turbines can ramp up quickly to fill the gap. This partnership has real limits—covered in Module 4 on grid integration—but it explains the appeal of natural gas as a “transition fuel.”

5.4 Internal Combustion: The Transportation Challenge

5.4.1 The Otto Cycle

While power plants generate electricity from stationary combustion, transportation requires mobile power sources. The internal combustion engine (ICE) has dominated surface transportation for over a century, operating on thermodynamic cycles quite different from stationary power plants.

The spark-ignition (gasoline) engine operates on the Otto cycle:

  1. Intake: Air-fuel mixture drawn into the cylinder
  2. Compression: Piston compresses the mixture (compression ratio 8:1 to 12:1)
  3. Combustion: Spark ignites the mixture; rapid pressure rise pushes the piston down
  4. Exhaust: Piston pushes burned gases out

The theoretical efficiency of the Otto cycle depends on compression ratio: \[\eta_{Otto} = 1 - \frac{1}{r^{\gamma-1}}\]

where \(r\) is the compression ratio and \(\gamma\) is the specific heat ratio (1.4 for air). For a compression ratio of 10: \[\eta_{Otto} = 1 - \frac{1}{10^{0.4}} = 60\%\]

But real gasoline engines achieve only 25-30% efficiency. Why the gap?

  • Part-load operation (the biggest factor): Engines are sized for peak power but usually operate at partial load. At partial throttle, the engine must work against the intake vacuum, wasting 10-15% of fuel energy just pumping air.
  • Heat transfer: Cylinder walls absorb energy from the hot combustion gases, losing roughly 10-15% of fuel energy to the cooling system.
  • Friction: Pistons, bearings, valve trains, and accessories consume 5-10% of output.
  • Incomplete combustion: Not all fuel burns completely, losing 2-5%.
  • Exhaust losses: Hot exhaust at ~600°C carries away significant energy that could theoretically do work.

Why not just increase the compression ratio? Higher compression means higher efficiency, but gasoline engines face a physical limit: knock. At high compression, the air-fuel mixture gets so hot that it auto-ignites before the spark plug fires, causing a destructive pressure wave (the “pinging” sound). This limits practical gasoline compression ratios to about 10-12:1. Premium fuel resists knock better but still limits compression to roughly 14:1.

Modern engines push these boundaries with remarkable results:

Table 5.1: Modern gasoline engine achievements
Engine Compression Ratio Peak Thermal Efficiency
Ford EcoBoost 2.3L 10:1 ~30%
Toyota Dynamic Force 2.5L 13:1 41%
Mazda Skyactiv-X (SPCCI) 16.3:1 ~43%
F1 Mercedes-AMG PU 18:1 >50%

Toyota’s 41% result comes from Atkinson-cycle operation and extreme combustion optimization. Mazda’s Skyactiv-X blurs the line between Otto and Diesel by using “spark-controlled compression ignition.” The F1 engine achieves over 50% at a single design point, but only under race conditions with exotic materials and unlimited development budget.

5.4.2 The Diesel Cycle

Diesel engines operate differently: they compress air alone (to much higher ratios, 15:1 to 22:1), then inject fuel into the hot compressed air. The fuel self-ignites without a spark. Because there is no premixed air-fuel charge, there is no knock limit, allowing much higher compression.

Table 5.2: Diesel efficiency by application
Application Compression Ratio Ideal Efficiency Real Efficiency
Car diesel 18:1 56% 35-40%
Truck diesel 20:1 58% 40-45%
Marine diesel 22:1 60% 45-50%

The largest marine diesels are engineering marvels. The Wartsila-Sulzer RTA96-C, with a 1-meter bore, produces 80 MW and achieves 51.7% thermal efficiency, the highest of any heat engine in commercial service. These two-stroke behemoths succeed because they face no weight constraints, operate at a single design point, and have enormous cylinders (low surface-to-volume ratio minimizes heat loss).

The trade-off: higher diesel combustion temperatures produce more nitrogen oxides (NOx). The Dieselgate scandal (2015) revealed that achieving both low NOx and high efficiency simultaneously was so difficult that Volkswagen cheated the emissions tests. The resulting regulatory backlash collapsed diesel car sales in Europe from 60% to 16% of new registrations.

5.4.3 Efficiency Across All Cycles

Table 5.3: Thermal efficiency comparison across thermodynamic cycles
Cycle Application Typical Efficiency Why
Rankine Coal/nuclear plants 33-45% Limited by steam temperatures
Brayton Gas turbines 35-42% High exhaust temperature
Combined (CCGT) Gas plants 58-64% Brayton + Rankine together
Otto Gasoline cars 25-30% Knock limits compression, part-load
Diesel Trucks, ships 35-50% Higher compression, no throttling

The key insight: stationary plants beat mobile engines because they can optimize for a single operating point, use larger components (lower surface losses), and reject heat to abundant cooling water. Mobile engines must compromise across a wide range of speeds and loads.

NoteBack-of-Envelope: The Electrification Advantage

Even when electricity comes from fossil fuels, electric vehicles can be more efficient than gasoline cars because of the efficiency gap between stationary and mobile heat engines.

Gasoline car (well-to-wheels): Refining 85% \(\times\) engine 25% = 21% overall

EV charged from CCGT: Generation 60% \(\times\) transmission 93% \(\times\) charging 90% \(\times\) motor 90% = 43% overall

EV charged from coal: Generation 38% \(\times\) transmission 93% \(\times\) charging 90% \(\times\) motor 90% = 28% overall

The EV wins in every scenario because it replaces a 25%-efficient mobile engine with a 60%-efficient stationary plant plus a 90%-efficient electric motor. This is a thermodynamic argument, not an emissions argument. As the grid decarbonizes, the EV’s advantage grows further.

In CO2 terms: a gasoline car emits 180-220 g/km. An EV on the average US grid emits 100-150 g/km. An EV on CCGT power emits 70-90 g/km. And the EV gets cleaner over time as the grid improves, while the gasoline car is locked in.

TipFramework Connection: Why Transportation is Harder Than Electricity

The Principle → Technology gap differs dramatically between sectors:

Electricity: Large, stationary plants can optimize around a single operating point. Combined cycle plants achieve 60% efficiency because engineers can design for baseload operation with ideal temperatures and pressures.

Transportation: Vehicles must operate across a wide range of speeds and loads, from idling in traffic to climbing mountains. No single design point is optimal. Weight and volume constraints prevent using the most efficient thermodynamic cycles. The result: even the best internal combustion vehicles convert only 25-30% of fuel energy to motion.

This fundamental asymmetry—electricity can be 60% efficient, transportation only 25%—explains why electrifying transportation via batteries or hydrogen makes thermodynamic sense even when the electricity comes from fossil fuels. A 60%-efficient gas plant feeding an 85%-efficient electric motor (51% overall) beats a 25%-efficient gasoline engine.

5.5 Refining: From Crude to Products

5.5.1 Why Refining Matters

Crude oil as extracted is nearly useless. It’s a complex mixture of thousands of hydrocarbon compounds with boiling points ranging from -40°C to over 600°C. Transforming this raw material into useful products—gasoline, diesel, jet fuel, plastics feedstock—requires the sophisticated chemical engineering of refineries.

5.5.2 Distillation: Separating by Boiling Point

The first refining step exploits the fact that different hydrocarbons boil at different temperatures. Crude oil is heated to 350-400°C and fed into a distillation column. As vapors rise through the column, they cool. Compounds condense at different heights depending on their boiling points:

Product Boiling range Carbon atoms Uses
LPG < 40°C C3-C4 Heating, cooking
Gasoline 40-200°C C5-C12 Spark-ignition engines
Kerosene/Jet 150-275°C C10-C16 Aviation, heating
Diesel 200-350°C C14-C20 Compression-ignition engines
Residual > 350°C C20+ Heavy fuel oil, asphalt

The problem: crude oil doesn’t naturally contain the right proportions of each product. Demand for gasoline and diesel far exceeds what simple distillation yields. Additional processes convert less valuable fractions into more valuable ones.

5.5.3 Cracking: Breaking Large Molecules

Fluid catalytic cracking (FCC) breaks large molecules into smaller ones. Heavy gas oil (too heavy for diesel) passes over a hot catalyst at 500-550°C, breaking carbon-carbon bonds to produce gasoline-range molecules. This single process produces about 45% of all gasoline.

Hydrocracking uses hydrogen at high pressure (100-200 bar) to crack heavy molecules while simultaneously removing sulfur and nitrogen. The hydrogen “caps” the broken bonds, producing cleaner fuels with lower emissions.

5.5.4 Reforming: Rearranging Molecules

Not all molecules crack well. Catalytic reforming rearranges molecular structures without changing carbon numbers. Straight-chain alkanes become branched or aromatic compounds with higher octane ratings, suitable for modern high-compression engines.

Reforming also produces hydrogen as a byproduct—about 1-2% of crude oil throughput. This hydrogen feeds hydrocracking and desulfurization processes, making modern refineries largely self-sufficient in hydrogen.

5.5.5 The Energy Cost of Refining

Refining consumes energy—about 6-8% of the crude oil processed. This “process energy” shows up in several forms:

  • Heating crude to distillation temperatures
  • Compressing gases for hydrocracking
  • Generating steam for various processes
  • Pumping fluids through kilometers of piping

When calculating the carbon footprint of gasoline, this refining energy must be included. The full “well-to-wheel” analysis adds roughly 20% to the direct combustion emissions.

ImportantTrilemma Tension: Refinery Complexity and Communities

Modern refineries are marvels of chemical engineering, processing 500,000+ barrels per day with remarkable efficiency. But they are also major sources of local pollution, concentrated in specific communities.

In the United States, refineries cluster along the Gulf Coast (Texas, Louisiana), the Los Angeles basin, and the San Francisco Bay Area. These facilities emit volatile organic compounds, particulate matter, and sulfur oxides. The communities living nearby—often lower-income and minority—bear health costs that don’t appear in gasoline prices (Equity).

This geographic concentration creates political economy dynamics: the jobs and tax revenues benefit one set of stakeholders while the health costs fall on another. The energy transition will need to address both the workers whose livelihoods depend on refineries and the communities whose health has been compromised by them.

5.6 The Carbon Debt Problem

5.6.1 Committed Emissions

Every coal plant, gas turbine, and refinery represents a decades-long commitment to carbon emissions. A coal plant built today will operate for 40+ years. A new refinery will process crude oil for 50 years. The vehicles on the road today will burn gasoline for 15-20 years.

This “committed emissions” or “carbon debt” creates a profound challenge. Even if we stopped building new fossil fuel infrastructure today, the existing stock would continue emitting for decades.

The International Energy Agency estimates that if all existing fossil fuel infrastructure operates for its expected lifetime, cumulative emissions would exceed 650 billion tons of CO2—more than the remaining carbon budget for limiting warming to 1.5°C.

5.6.2 The Age of Infrastructure

The age profile of fossil fuel infrastructure varies dramatically by region:

Young infrastructure (China, India, Southeast Asia): Much of the coal fleet was built in the last 20 years. Average age of Chinese coal plants: 14 years. These plants have 25+ years of expected remaining life.

Middle-aged infrastructure (United States, Europe): Average age of U.S. coal plants: 40+ years. Many are approaching retirement anyway, making closure less economically disruptive.

Stranded asset risk: Retiring fossil fuel infrastructure before the end of its economic life destroys value—for utilities, for investors, for workers. This is the “stranded assets” problem. It creates powerful opposition to aggressive decarbonization timelines.

NoteBack-of-Envelope: The Coal Phase-Out Math

Global coal capacity: ~2,100 GW Annual coal generation: ~10,000 TWh Coal plant average remaining life: 25 years Coal emissions: ~900 kg CO2/MWh

If we operate this fleet to end-of-life: \[10,000 \text{ TWh/yr} \times 25 \text{ yr} \times 0.9 \text{ kg/kWh} = 225 \text{ Gt CO~2~}\]

The remaining carbon budget for 1.5°C is roughly 300 Gt. Coal alone could consume 75% of it.

This arithmetic explains why Smil is skeptical about rapid transitions. But it also explains why climate advocates push for early retirement of coal plants—even accepting the economic losses.

5.6.3 The Natural Gas Dilemma

Natural gas occupies an awkward position in the energy transition. It’s cleaner than coal—60% lower CO2 per kWh, much lower air pollution. Combined cycle plants are efficient and flexible. Gas has enabled significant emissions reductions in countries that switched from coal (U.S., UK).

But natural gas is not zero-carbon. If the world builds out gas infrastructure as extensively as it built coal infrastructure, we lock in emissions incompatible with climate goals.

The dilemma:

  • Near-term: Gas displacing coal reduces emissions now
  • Long-term: Gas infrastructure commits to emissions for decades
  • Methane leakage: Natural gas is primarily methane, a potent greenhouse gas. Leaks during production, processing, and distribution erode or potentially eliminate the climate benefit versus coal

Studies disagree sharply on methane leakage rates. Official estimates hover around 1-2%; some field measurements suggest 3-4% or higher in certain basins. At 3% leakage, the 20-year climate impact of gas may equal coal.

5.7 Looking Forward

This chapter has examined how we extract energy from fossil fuels—the combustion chemistry, the thermodynamic cycles, the conversion efficiencies. Several themes emerge:

Efficiency matters but has limits: Two centuries of engineering have brought coal plants to 45% efficiency and combined cycles to 64%. Further improvements are possible but incremental. The fundamental constraint is thermodynamic.

Infrastructure locks in emissions: Fossil fuel systems are capital-intensive and long-lived. Decisions made today commit emissions for decades. This is the core tension between climate urgency and economic reality.

Transportation is harder than electricity: The 60% efficiency achievable in stationary power plants drops to 25% in mobile applications. This asymmetry argues for electrifying transportation even when electricity comes from fossil fuels.

Module 2 continues by examining the solar and wind alternatives that could eventually displace fossil combustion. But those alternatives must compete with a formidable incumbent: two centuries of optimization, trillions of dollars of installed infrastructure, and deeply embedded supply chains. Understanding what we’re replacing—its strengths as well as its problems—is essential to understanding why the transition is difficult.

5.8 Key Concepts

  • Heating values: Higher (HHV) includes water condensation; Lower (LHV) assumes vapor exhaust
  • Rankine cycle: The four-stage steam cycle underlying most thermal power plants
  • Combined cycle: Gas turbine exhaust feeds a steam cycle, achieving 60%+ efficiency
  • Otto and Diesel cycles: The thermodynamic foundations of internal combustion engines
  • Refining: Distillation, cracking, and reforming transform crude oil into useful products
  • Committed emissions: Existing infrastructure locks in decades of future carbon output

5.9 Exercises

  1. Combustion stoichiometry: Calculate the mass of CO2 produced per kg of fuel for: (a) methane, (b) propane (\(C_3H_8\)), (c) octane. Which has the lowest CO2 per unit mass? Per unit energy?

  2. Rankine cycle analysis: A coal plant operates with steam at 550°C and condenses at 40°C. (a) What is the Carnot efficiency for these temperatures? (b) If the actual plant achieves 42% efficiency, what fraction of the Carnot limit does it achieve? (c) How much waste heat must be rejected per MWh of electricity produced?

  3. Combined cycle breakdown: A combined cycle plant is 62% efficient overall. The gas turbine is 40% efficient. What is the efficiency of the steam bottoming cycle in converting the gas turbine exhaust heat to electricity?

  4. Vehicle electrification: Compare the well-to-wheel efficiency of: (a) a gasoline car (25% engine efficiency, gasoline from 90%-efficient refining), (b) an electric car (90% motor efficiency, 8% charging losses) powered by a 60%-efficient gas plant. Which produces less CO2 per km?

  5. Carbon budget: A developing country plans to build 50 GW of coal capacity with a 35-year expected life. At 70% capacity factor and 900 kg CO2/MWh, what would be the cumulative emissions from this fleet? How does this compare to the country’s “fair share” of remaining carbon budget?

  6. Methane leakage threshold: At what methane leakage rate does the 20-year climate impact of natural gas equal that of coal? (Assume methane has 80× the warming potential of CO2 over 20 years, natural gas is 95% methane by mass, and compare per unit of electricity generated from 60%-efficient CCGT vs 38%-efficient coal plant.)

TipFramework Application

This chapter illustrates Reduction to Practice in fossil energy systems. The Principles (thermodynamics, combustion chemistry) enable Technologies (Rankine cycles, gas turbines, refining), which become Products (power plants, vehicles, fuels), shaped by Policies (emissions standards, fuel taxes), yielding Outcomes (electricity supply, air quality, carbon emissions).

The chapter also reveals why transition is difficult: each stage of the framework involves massive infrastructure investment and decades of optimization. Displacing this system requires alternatives that are not merely better in principle, but competitive across all five stages.