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{PE}+E{KE}+E{TH}+E{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{KE} \propto m and E{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.