Energy Principles, Consumption Trends, and Fuel Energetics

First Law of Thermodynamics: In a system of constant mass, energy is neither created nor destroyed during physical or chemical changes; it only changes form (exceptions include the Sun emitting energy and nuclear fission reactions).
Second Law of Thermodynamics: Energy converts from a more concentrated, useful form to a less concentrated, less useful form, predominantly lost as heat and friction.
Efficiency Formula: $\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\%$
Conversion Efficiencies:
- Photovoltaic Solar Panels: Commercial cells operate in the $20\%$ to $27\%$ range; black color allows broad absorption of electromagnetic radiation.
- Plant Photosynthesis: Typically $\sim 1\%$ (reaches $4\%$ to $8\%$ under optimal conditions); reflects green light, reducing absorption capacity.
- Thermal Power Plants: Traditional nuclear and natural gas plants exhibit an efficiency of $35\%$ to $40\%$ .
- Renewable Integration Paradox: Grid-level intermittency of wind and solar requires cycling traditional plants up and down, which lowers operational efficiency and can lead to increased carbon emissions.

Definitions and Units:
- Power: Rate of energy expenditure: $\text{Power} = \frac{\text{Energy}}{\text{Time}}$ . Unit: watt ( $1\,\text{W} = 1\,\text{J/s}$ ).
- Energy: Capacity to do work: $\text{Energy} = \text{Power} \times \text{Time}$ . Measured in joules ( $\text{J}$ ), watt-hours ( $\text{Wh}$ ), or kilowatt-hours ( $\text{kWh}$ ).
Dimensional Analysis Examples:
- Lamp Energy Consumption ( $60\,\text{W}$ bulb for $1\,\text{hour}$ ): $60\,\text{J/s} \times \frac{60\,\text{s}}{1\,\text{min}} \times \frac{60\,\text{min}}{1\,\text{hr}} \times 1\,\text{hr} = 216{,}000\,\text{J}$
- Appliance Operating Cost ( $0.2\,\text{kW}$ refrigerator for $24\,\text{hours}$ at $\$0.10/\text{kWh}$ ): \frac{\0.10}{1\,\text{kWh}} \times 0.2\,\text{kW} \times 24\,\text{hr} = \ $0.48$

Historical Shifts: Fuel reliance transitioned from traditional biofuels (wood) before the 1900s to coal, followed by rapid expansions in petroleum and natural gas beginning in the 1950s. Over $90\%$ of global energy still derives from fossil fuels.
U.S. Coal Phase-Out: Driven primarily by public health standards targeting sulfur gas and mercury emissions rather than climate policies alone; coal has been largely replaced by natural gas expanded through hydraulic fracturing (fracking).
U.S. Energy Consumption by Source (2025 Data):
- Petroleum: $37\%$
- Natural Gas: $36\%$
- Renewable Energy: $\sim 9\%$
- Coal: $9\%$
- Nuclear: $9\%$ (100% utilized for electricity generation)
Sector Allocations:
- Transportation: $89\%$ reliant on petroleum fuels ( $55\%$ gasoline, alongside distillates and jet fuel).
- Industrial: $41\%$ natural gas, $33\%$ petroleum, $13\%$ electricity, plus renewables and coal; used for boiler fuel, electricity self-generation, mechanical equipment, and feedstocks for bulk chemicals, refining, mining, and plastics.
- Residential: $44\%$ electricity, $42\%$ natural gas, and $8\%$ fuel oil (notably in the Pacific Northeast).

Residential End-Use Distribution: Space heating and cooling account for over $50\%$ of total residential energy demand; water heating, lighting, and refrigeration comprise another $25\%$ , with the remainder used by appliances.
Degree Days (Baseline: $65^\circ\text{F}$ ):
- Heating Degree Days (HDD): Number of degrees the daily outside temperature falls below $65^\circ\text{F}$ .
- Cooling Degree Days (CDD): Number of degrees the daily outside temperature rises above $65^\circ\text{F}$ .
- Calculation Example: An $80^\circ\text{F}$ day ( $15\,\text{CDD}$ ) followed by a $75^\circ\text{F}$ day ( $10\,\text{CDD}$ ) totals $25\,\text{CDD}$ .
Institutional Thermal Management (UCI Campus):
- Includes a thermal energy storage tank holding $4{,}500{,}000\,\text{gallons}$ of water near the Bren Events Center to balance campus heating and cooling.
- Operates on-site natural gas power generation, grid purchases, parking lot/rooftop solar panels, and experimental solar-generated hydrogen integration.

Aviation Energy Requirement (Takeoff Calculation):
- Total takeoff energy combines kinetic and gravitational potential energy: $E = \frac{1}{2}mv^2 + mgh$
- A $150{,}000\,\text{kg}$ plane accelerating to $255\,\text{m/s}$ and ascending requires approximately $22{,}500\,\text{MJ}$ (1\,\text{MJ} = 1 \times 10^6\,\text{J}$).\n* **Fuel Comparisons:**\n * **Jet Fuel:** Gravimetric energy density of 48\,\text{MJ/kg} $; volumetric energy density of$ 38.6\,\text{MJ/L}.\n * Mass required for 22{,}500\,\text{MJ} $:$ \frac{22{,}500\,\text{MJ}}{48\,\text{MJ/kg}} = 469\,\text{kg}\n * Volume required for 22{,}500\,\text{MJ} $:$ \frac{22{,}500\,\text{MJ}}{38.6\,\text{MJ/L}} = 583\,\text{L}\n * **Hydrogen Gas:** Gravimetric energy density of 142\,\text{MJ/kg} $; volumetric energy density of$ 5.6\,\text{MJ/L}.\n * Mass required: \frac{22{,}500\,\text{MJ}}{142\,\text{MJ/kg}} = 158\,\text{kg}\n * Volume required: \frac{22{,}500\,\text{MJ}}{5.6\,\text{MJ/L}} = 4{,}018\,\text{L}\n* **Transportation Constraints:** Hydrogen provides high mass energy density but poor volumetric density, requiring impractically large containment vessels and heavy high-pressure steel tanks. Hydrocarbon fuels (gasoline, diesel, jet fuel) remain standard because they are dense in both mass and volume.\n* **Nuclear Fission of Uranium:** Yields an energy density of 77{,}000{,}000\,\text{MJ/kg} $and$ 1.5 \times 10^9\,\text{MJ/L}$$, orders of magnitude higher than chemical fuels.

Audience Question: What fuel did the campus central generation system originally run on?
- Response: Unconfirmed historically, though likely oil; the campus currently uses natural gas and is testing the injection of solar-generated hydrogen.
Audience Question: Is the final exam cumulative?
- Response: Not entirely; a study guide will specify excluded topics (such as adiabatic lapse rates and isobar maps).