Capacity to do work or produce heat. Often measured as mechanical work, heat, or electrical energy.

Power relates to energy by time: power = energy/time (W = J/s).

• SI base: joule (J)
• Electrical: Wh and kWh
• Nutrition: Calorie = kilocalorie (kcal)

Electric bills charge in kWh; appliances list power (W) and you multiply by time to get kWh.

Food labels use Calories (kcal). Heating/cooling often uses BTU.

• Phone charge: ~10 Wh
• Shower (10 min, 7 kW heater): ~1.17 kWh
• Meal: ~600–800 kcal

Particle physics uses eV for photon and particle energies.

At atomic scales, Hartree and Rydberg energies appear in quantum mechanics.

• 1 eV = 1.602×10⁻¹⁹ J
• Visible photon: ~2–3 eV
• Planck energy is extremely large (theoretical)

Electric energy is billed in kWh; estimate consumption by power × time.

• LED bulb 10 W × 5 h ≈ 0.05 kWh
• Oven 2 kW × 1 h = 2 kWh
• Monthly bill sums all devices

Calories on labels are kilocalories (kcal) and often paired with kJ.

• 1 kcal = 4.184 kJ
• Daily intake ~2,000–2,500 kcal
• kcal and Cal (food) are the same

BTU, therms, and fuel equivalents (BOE/TOE) appear in HVAC and energy markets.

• 1 therm = 100,000 BTU
• Natural gas and oil use standardized equivalents
• kWh ↔ BTU conversions are common

Energy (kWh) × price per kWh

• Example: 2 kWh × $0.20 = $0.40
• 1,000 W × 3 h = 3 kWh

mAh × V ÷ 1000 ≈ Wh

• 10,000 mAh × 3.7 V ≈ 37 Wh
• Wh ÷ device W ≈ runtime (hours)

Estimate emissions from electricity use

• CO₂ = kWh × grid intensity
• Example: 5 kWh × 400 gCO₂/kWh = 2,000 g (2 kg)
• Low‑carbon grid (100 g/kWh) cuts this by 75%

Common confusions

• kW is power (rate); kWh is energy (amount)
• A 2 kW heater for 3 h uses 6 kWh
• Bills use kWh; appliance plates show W/kW

Renewables generate power (kW) that integrates over time into energy (kWh).

Output varies with weather; long‑term averages matter.

• Capacity factor: % of max output over time
• Rooftop solar: ~900–1,400 kWh/kW·yr (location dependent)
• Wind farms: capacity factor often 25–45%

Batteries store surplus and shift energy to when it’s needed.

• kWh capacity vs kW power matters
• Round‑trip efficiency < 100% (losses)
• Time‑of‑use tariffs encourage shifting

A 60 kWh Tesla battery stores the same energy a typical home uses in 2-3 days — imagine carrying 3 days of electricity in your car!

A therm is 100,000 BTU (29.3 kWh). Natural gas bills use therms because it's easier to say '50 therms' than '5 million BTU'!

Food labels use 'Calorie' (capital C) which is actually a kilocalorie! So that 200 Cal cookie is really 200,000 calories (lowercase c).

1 liter of gas has 9.4 kWh of energy, but engines waste 70% as heat! Only ~2.5 kWh actually moves your car. EVs waste only ~10-15%.

1 kWh can: power a 100W bulb for 10 hours, charge 100 smartphones, toast 140 slices of bread, or keep your fridge running for 24 hours!

EVs recover 15-25% of energy during braking by turning the motor into a generator. That's free energy from wasted kinetic energy!

Your body has enough mass-energy (E=mc²) to power all of Earth's cities for a week! But converting mass to energy requires nuclear reactions.

Pound-for-pound, rocket fuel has 10× the energy of chocolate. But you can't eat rocket fuel — chemical energy ≠ metabolic energy!

For millennia, humans understood energy only through its effects: warmth from fire, strength from food, and the power of water and wind. Energy was a practical reality without theoretical understanding.

• **Fire mastery** (~400,000 BCE) - Humans harness chemical energy for heat and light
• **Water wheels** (~300 BCE) - Greeks and Romans convert kinetic energy to mechanical work
• **Windmills** (~600 CE) - Persians capture wind energy for grinding grain
• **Nutrition understanding** (antiquity) - Food as 'fuel' for human activity, though mechanism unknown

These practical applications predated any scientific theory by thousands of years. Energy was known through experience, not equations.

The Industrial Revolution demanded better understanding of how heat converts to work. Engineers measured engine efficiency, leading to the birth of thermodynamics.

• **James Watt's steam engine improvements** (1769) - Quantified work output, introduced horsepower
• **Sadi Carnot's heat engine theory** (1824) - Proved theoretical limits on converting heat to work
• **Julius von Mayer** (1842) - Proposed mechanical equivalent of heat: heat and work are interchangeable
• **James Joule's experiments** (1843-1850) - Precisely measured: 1 calorie = 4.184 joules of mechanical work

Joule's experiments proved energy conservation: mechanical work, heat, and electricity are different forms of the same thing.

The 19th century synthesized disparate observations into a single concept: energy is conserved, transforming between forms but never created or destroyed.

• **Hermann von Helmholtz** (1847) - Formalized the law of conservation of energy
• **Rudolf Clausius** (1850s) - Introduced entropy, showing energy degrades in quality
• **James Clerk Maxwell** (1865) - Unified electricity and magnetism, showing light carries energy
• **Ludwig Boltzmann** (1877) - Connected energy to atomic motion via statistical mechanics

By 1900, energy was understood as the central currency of physics—transforming but conserved across all natural processes.

The 20th century revealed energy at extremes: Einstein's mass-energy equivalence and quantum mechanics at atomic scales.

• **Max Planck** (1900) - Quantized energy in radiation: E = hν (Planck's constant)
• **Einstein's E=mc²** (1905) - Mass and energy are equivalent; tiny mass = enormous energy
• **Niels Bohr** (1913) - Atomic energy levels explain spectral lines; eV becomes natural unit
• **Enrico Fermi** (1942) - First controlled nuclear chain reaction releases MeV-scale energy
• **Manhattan Project** (1945) - Trinity test demonstrates ~22 kilotons TNT equivalent (~90 TJ)

Nuclear energy validated E=mc²: fission converts 0.1% of mass to energy—millions of times denser than chemical fuels.

Post-war society standardized energy units for utilities, food, and physics while grappling with fossil fuels, renewables, and efficiency.

• **Kilowatt-hour standardization** - Global electric utilities adopt kWh for billing
• **Calorie labeling** (1960s-90s) - Food energy standardized; FDA mandates nutrition facts (1990)
• **Photovoltaic revolution** (1970s-2020s) - Solar panel efficiency climbs from <10% to >20%
• **Lithium-ion batteries** (1991-present) - Energy density rises from ~100 to 250+ Wh/kg
• **Smart grids & storage** (2010s) - Real-time energy management and grid-scale batteries

The 21st century recognizes energy's environmental cost. The focus shifts from merely generating energy to generating clean energy efficiently.

• **Carbon intensity** - Fossil fuels emit 400-1000 g CO₂/kWh; renewables emit <50 g CO₂/kWh lifecycle
• **Energy storage gaps** - Batteries store ~0.5 MJ/kg vs gasoline's 46 MJ/kg; range anxiety persists
• **Grid integration** - Variable renewables require storage and demand response
• **Efficiency imperatives** - LEDs (100 lm/W) vs incandescent (15 lm/W); heat pumps (COP > 3) vs resistive heating

The transition to net-zero requires electrifying everything and generating that electricity cleanly—a complete energy system overhaul.

Food labels list energy in Calories (kcal). Your body converts this to ATP for cellular work with ~25% efficiency.

• **Basal metabolic rate** - ~1,500-2,000 kcal/day (6-8 MJ) to stay alive
• **Marathon run** - Burns ~2,600 kcal (~11 MJ) over 3-4 hours
• **Chocolate bar** - ~250 kcal could power a 60W laptop for ~4.5 hours (if 100% efficient)
• **Dieting math** - 1 lb fat = ~3,500 kcal deficit; 500 kcal/day deficit = 1 lb/week

Electric bills charge per kWh. Understanding appliance consumption helps reduce costs and carbon footprint.

• **LED vs incandescent** - 10W LED = 60W incandescent light; saves 50W × 5 hrs/day = 0.25 kWh/day = $9/mo
• **Phantom loads** - Devices on standby waste ~5-10% of household energy (~1 kWh/day)
• **Heat pumps** - Move 3-4 kWh of heat using 1 kWh electricity (COP > 3); resistive heaters are 1:1
• **Electric car charging** - 60 kWh battery at $0.15/kWh = $9 for full charge (vs $40 gas equivalent)

Vehicles convert fuel energy to kinetic energy with significant losses. EVs are 3× more efficient than internal combustion engines.

• **Gasoline car** - 30% efficient; 1 gallon (132 MJ) → 40 MJ useful work, 92 MJ heat
• **Electric car** - 85% efficient; 20 kWh (72 MJ) → 61 MJ to wheels, 11 MJ losses
• **Regenerative braking** - Recovers 10-25% of kinetic energy back to battery
• **Aerodynamics** - Doubling speed quadruples drag power needed (P ∝ v³)

Heavy industry accounts for ~30% of global energy use. Process efficiency and waste heat recovery are critical.

• **Steel production** - ~20 GJ per ton (5,500 kWh); electric arc furnaces use scrap and less energy
• **Aluminum smelting** - ~45-55 GJ per ton; why recycling saves 95% energy
• **Data centers** - ~200 TWh/yr globally (2020); PUE (Power Usage Effectiveness) measures efficiency
• **Cement production** - ~3-4 GJ per ton; accounts for 8% of global CO₂ emissions

Solar, wind, and hydro convert ambient energy to electricity. Capacity factor and intermittency shape deployment.

• **Solar panel** - ~20% efficiency; 1 m² receives ~1 kW peak sun → 200W × 5 sun-hrs/day = 1 kWh/day
• **Wind turbine capacity factor** - 25-45%; 2 MW turbine × 35% CF = 6,100 MWh/year
• **Hydroelectric** - 85-90% efficient; 1 m³/s falling 100m ≈ 1 MW
• **Battery storage round-trip** - 85-95% efficient; losses as heat during charge/discharge

From particle accelerators to laser fusion, physics research operates at energy extremes.

• **Large Hadron Collider** - 362 MJ stored in beam; proton collisions at 13 TeV
• **Laser fusion** - NIF delivers ~2 MJ in nanoseconds; achieved breakeven in 2022 (~3 MJ out)
• **Medical isotopes** - Cyclotrons accelerate protons to 10-20 MeV for PET imaging
• **Cosmic rays** - Highest energy particle detected: ~3×10²⁰ eV (~50 J in one proton!)

kW is power (rate). kWh is energy (kW × hours). Bills use kWh.

Yes. Food ‘Calorie’ equals 1 kilocalorie (kcal) = 4.184 kJ.

Energy (kWh) × tariff (per kWh). Example: 2 kWh × $0.20 = $0.40.

Historical measurement at different temperatures led to variants (IT, thermochemical). For nutrition, use kcal.

eV is natural for atomic/particle scales. Convert to J for macroscopic contexts.

Actual energy output over time divided by the output if the plant ran at full power 100% of the time.