Fundamentals of Sustainable Energy – Energy & Energy Conversion

Objectives & Learning Outcomes

• By the end of the lecture you should be able to:
  • Distinguish the various forms of energy (kinetic, potential, thermal, chemical, nuclear, etc.).
  • Describe energy transformation processes and identify where they occur in real systems.
  • Analyse the quantitative relationship between energy and work.
  • State and apply the Law of Conservation of Energy to closed systems.
  • Calculate:
  • Work (W)
  • Power (P)
  • Different efficiencies (η)
  • Apply the above to engineering examples such as cars, dams, lamps, and friction scenarios.

Core Terminology (be fluent with each word)

• Conservation, Work, Gravitational, Friction, Kinetic, Collision, Potential, Thermal, Power, Energy.
• Conservative vs Non-conservative force, System vs Environment.

Basic Energy Model

• Energy = the ability to do work (physical or mental activity).
• For a closed system the total energy $E$ is fixed:
  $E = E<em>{PE}+E</em>{KE}+E<em>{TH}+E</em>{CH}+E_{NUC}+\dots$
• SI unit of energy: Joule (J); 1 J = 1 N·m.

Forms of Energy & Key Equations

• Kinetic Energy (E_{KE}) – energy of motion

  • Translational vs rotational motion
  • Proportional to mass and square of velocity:
    $E<em>{KE} \propto m$ and $E</em>{KE} \propto v^2$
    $E_{KE} = \frac{1}{2}mv^2$
  • Example (given): 636 kg car, E_{KE}=53.2\,\text{kJ} \Rightarrow v=12.9\,\text{m·s}^{-1}

• Potential Energy (E_{PE}) – stored energy convertible to other forms

  • Gravitational: $E_{GPE}=mgh$ (m = mass, g = 9.8 m·s\^{-2}, h = height)
  • Elastic: $E_{EPE}=\tfrac{1}{2}kx^2$ (k = spring constant, x = displacement)
  • Example: 636 kg car 12 m above reference → $E_{GPE}=74.8\,\text{kJ}$

• Thermal Energy (E_{TH}) – associated with microscopic motion of molecules

  • Generated by friction: $E_{TH}=\mu mgx$ (µ = coefficient of friction, x = distance)

• Chemical, Nuclear – mentioned as part of total system energy but not derived in detail here.

Forces & Work

• Conservative Force – path-independent work; stores useful energy (gravity, elastic).
• Non-conservative Force – path-dependent work; dissipative (friction).
• Work (W) – mechanical transfer of energy when a force acts through a displacement: $W=\vec F\cdot\vec d$
  • Scalar quantity, unit Joule.
  • Example #1: 500 N push over 5 m → $W=2.5\,\text{kJ}$ (crate gains kinetic energy).
  • Example #2: Lift 800 kg piano 0.5 m → $W=3.92\,\text{kJ}$ (energy expended).

Power

• Rate of energy transfer/ conversion:
  $P = \frac{W}{t} = \frac{E}{t}$
• SI unit: Watt (W); 1 W = 1 J·s\^{-1}.
• Instantaneous power of a force where object speed is v:
  $P = \vec F\cdot\vec v$
• Example (hydropower): 1 m³ water (1000 kg) falling 30 m
  • $E_{GPE}=294\,\text{kJ}$
  • If released in 1 s, $P=294\,\text{kW}$

Energy Transformations & Conservation

• Energy cannot be created or destroyed, only converted between forms.
• In any closed (isolated) system total energy remains constant.
• Transformations often yield desired and undesired forms (e.g.
  motors produce motion + heat + sound).
• Example: Car descending hill converts GPE to KE; if only 70 % becomes KE
  E_{KE}=0.70\times74.8\,\text{kJ}=52.4\,\text{kJ}\;\Rightarrow v=12.8\,\text{m·s}^{-1}

Heat vs Work (Energy Transfer Modes)

• Work: mechanical energy transfer (push/pull).
• Heat: non-mechanical transfer driven by temperature difference.
• Both are ways energy crosses the system boundary.

Efficiency (η)

• $\eta = \frac{\text{Useful\;Energy\;Output}}{\text{Total\;Energy\;Input}}\times100\%$
• Losses come from:
  • Process limitations (design/ implementation).
  • Fundamental physical limits (thermodynamics, friction, etc.).
• Typical hydropower plant: η > 80 % (small) to > 90 % (large).
• Light-bulb example
  • Compact Fluorescent Lamp (CFL):
  • Input 60 J → 15 J light, 45 J heat
  • $\eta = \frac{15}{60}\times100\% = 25\%$
  • Incandescent lamp:
  • Input 100 J → 5 J light, 95 J heat
  • $\eta = \frac{5}{100}\times100\% = 5\%$

Ethical & Practical Significance

• Pursuing sustainable energy means maximizing efficiency and minimizing waste heat.
• Accurate energy accounting (work, power, efficiency) enables:
  • Better engineering design (e.g.
    high-efficiency turbines, efficient lighting).
  • Environmental impact reduction (less resource consumption per useful output).
• Understanding conservative vs non-conservative forces guides engineers in selecting materials & mechanisms that minimize frictional losses.

Summary Formula Sheet (quick reference)

• Translational KE: $E_{KE}=\frac{1}{2}mv^{2}$
• Gravitational PE: $E_{GPE}=mgh$
• Elastic PE: $E_{EPE}=\frac{1}{2}kx^{2}$
• Thermal (friction) energy: $E_{TH}=\mu mgx$
• Work (constant force): $W=\vec F\cdot\vec d$
• Power: $P=\frac{W}{t}=\frac{E}{t}=\vec F\cdot\vec v$
• Efficiency: $\eta=\frac{\text{Useful Output}}{\text{Total Input}}\times100\%$

Connections & Next-Step Learning

• Builds upon mechanics (force, motion) and thermodynamics (heat, work).
• Foundation for upcoming topics: renewable energy technology, exergy analysis, and system optimisation.