Physics Study Notes: Energy and Use of Energy

Hello! Welcome to your study notes for "Energy and Use of Energy". This chapter is super practical because it's all about the physics happening in your home, in your city, and how it affects your wallet and our planet. We'll explore how appliances work, what makes a building energy-efficient, and where our electricity comes from. By the end, you'll be a smarter energy consumer and understand the science behind it. Let's get started!


Section A: Electricity at Home

Ever wonder how much it costs to run your air-conditioner or why some light bulbs are better than others? This section answers those questions. We use electricity for almost everything, so let's see how it works.

1. Energy in Our Appliances

Almost every device at home is an energy converter. It takes electrical energy and changes it into other forms.

  • An electric fan converts electrical energy into kinetic energy (the moving blades) and sound energy.
  • A kettle converts electrical energy into thermal energy (heat).
  • A light bulb converts electrical energy into light energy and thermal energy.

But are they good at their job? That's where efficiency comes in.

End-use Energy Efficiency

This is a measure of how much of the input energy is converted into the useful form we actually want. No machine is 100% efficient; some energy is always 'wasted', usually as heat.

Analogy: Imagine pouring water into a leaky bucket to water a plant. The total water you pour is the 'Energy Input'. The water that actually reaches the plant is the 'Useful Energy Output'. The water that leaks out is 'Wasted Energy'. Efficiency is the ratio of water for the plant to the total water you poured.

The formula is:

\( \text{Efficiency } (\eta) = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\% \)

A higher efficiency means less energy is wasted, which saves money and is better for the environment!

Key Takeaway

Appliances convert electrical energy into other forms. End-use efficiency tells us how well an appliance does its job without wasting energy.


2. Let There Be Light: Lighting Explained

We use different types of lights at home. Let's look at how they work and which are the best.

Types of Lighting
  • Incandescent Lamps: An old-fashioned bulb. Electricity heats a tiny wire (filament) until it glows white-hot. Think of it like a toaster that gets so hot it makes light. This is very inefficient, as over 90% of the energy is wasted as heat!
  • Gas Discharge Lamps: This includes fluorescent tubes. Electricity excites gas atoms inside the tube, causing them to release ultraviolet (UV) light. A white coating inside the tube absorbs this UV light and glows, producing visible light. More efficient than incandescent bulbs.
  • Light Emitting Diodes (LEDs): These are the champions of efficiency! They use semiconductor material to convert electrical energy directly into light at an atomic level. They produce very little heat, last a long time, and are the most energy-efficient option.
Measuring Light

To compare bulbs properly, we need some specific terms. Don't worry, they're simpler than they sound!

  • Luminous Flux (\( \Phi \), Unit: lumen, lm): This is the total amount of visible light a source emits in all directions per second. Think of it as the total 'power' of the visible light coming out of the bulb. A higher lumen rating means a brighter bulb.
  • Illuminance (\( E \), Unit: lux, lx): This is the luminous flux that falls per unit area of a surface: \( E = \frac{\Phi}{A} \) (where 1 lx = 1 lm/m²). It's a measure of how brightly lit a surface appears. If Luminous Flux is the total rain from a cloud, Illuminance is how much rain falls into a bucket per unit area on the ground.
Important Laws for Illuminance from a Point Source

1. The Inverse Square Law: For a point source radiating luminous flux \( \Phi \) uniformly in all directions, the light spreads over a sphere of area \( A = 4\pi r^2 \). The illuminance on a surface perpendicular to the light is inversely proportional to the square of its distance \( r \):

\( E = \frac{\Phi}{4\pi r^2} \)

If you double your distance from a light source, the illuminance drops to 1/4 of its initial value!

2. Lambert's Cosine Law: Illuminance depends on the angle of incidence \( \theta \) between the incident light ray and the normal (perpendicular) to the surface:

\( E = \frac{\Phi \cos\theta}{4\pi r^2} \)

When light shines directly perpendicular to the surface (\( \theta = 0^\circ \)), \( \cos(0^\circ) = 1 \) giving maximum illuminance. As the angle of incidence increases, the illuminance decreases.

Efficacy of Electric Lights

This is the most important number for choosing a bulb! It's the ratio of luminous flux (how much light you get) to the electrical power input (how much energy you use).

\( \text{Efficacy} = \frac{\text{Luminous Flux (lm)}}{\text{Electrical Power (W)}} \)

The unit is lumens per watt (lm/W). A higher efficacy is better!

  • Incandescent Bulb: ~15 lm/W (Poor)
  • Fluorescent Bulb: ~60 lm/W (Good)
  • LED Bulb: ~100+ lm/W (Excellent)
Key Takeaway

To choose the best light bulb, don't just look at the watts. Look at the lumens (brightness) and the efficacy (lm/W). LEDs are the most efficient choice.


3. Cooking Without Fire

Modern kitchens use electricity to cook in clever ways.

  • Electric Hotplates: A simple resistor gets hot when current flows through it (like an incandescent bulb, but for heat). It heats the pot by conduction. This is not very efficient as a lot of heat escapes into the surrounding air.
  • Induction Cookers: This is like magic! It uses a high-frequency changing magnetic field to create eddy currents directly inside a ferromagnetic pot (like iron or magnetic steel). The electrical resistance of the pot turns these currents into heat. It is very fast and efficient because heat is generated directly in the cookware.
  • Microwave Ovens: Uses microwaves (a type of electromagnetic wave) to cause polar molecules (primarily water) in food to oscillate rapidly, generating thermal energy quickly and uniformly throughout the food.
Calculating the Cost of Running Appliances

This is a life skill! Electricity companies charge you for the amount of energy you use, measured in kilowatt-hours (kWh).

Step-by-step guide:

  1. Find the power rating of the appliance in watts (W). Example: a microwave might be 1000 W.
  2. Convert the power to kilowatts (kW) by dividing by 1000. 1000 W / 1000 = 1 kW.
  3. Determine the running time in hours (h). Let's say you use it for 15 minutes. 15 mins / 60 = 0.25 h.
  4. Calculate the energy consumed in kWh.
    \( \text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (h)} \)
    Energy = 1 kW × 0.25 h = 0.25 kWh.
  5. Calculate the cost. Multiply the energy used by the price per kWh. If electricity costs $1.2 per kWh, then Cost = 0.25 kWh × $1.2/kWh = $0.30.
Key Takeaway

Induction cookers and microwaves are generally more energy-efficient than simple hotplates. You can calculate the running cost of any appliance using the formula Cost = Power (kW) × Time (h) × Price per kWh.


4. Moving Heat Around: Air-Conditioners

An air-conditioner doesn't "create cold". It's a heat pump – it moves heat from inside your room to the outside, against its natural direction of flow (heat naturally flows from hot to cold).

Analogy: Think of a bouncer at a club. The bouncer (A/C) uses energy to kick the unwanted "heat guests" out of the cool "room club" and into the hot "outside world".

Measuring A/C Performance
  • Cooling Capacity (Unit: kW): This is the rate at which the A/C removes heat from a room. A higher cooling capacity means it can cool a larger room or cool a room faster. Note: This is NOT the same as its electrical power consumption!
  • Coefficient of Performance (COP): This is the performance ratio for an A/C. It's the ratio of cooling rate (heat removed per second) to the electrical power input.

\( \text{COP} = \frac{\text{Cooling Capacity (kW)}}{\text{Electrical Power Input (kW)}} \)

Don't be confused! The COP for an A/C is often greater than 1 (usually between 2 and 4). This doesn't break the law of conservation of energy. It just means it's easier to move heat than to create it. For every 1 kW of electricity you use, the A/C might move 3 kW of heat out of your room (COP = 3).

A higher COP is better and means a more efficient A/C!

Hong Kong Energy Efficiency Labelling Scheme (EELS)

You've seen these stickers on appliances! They grade products from 1 to 5.

  • Grade 1: Most energy efficient (best!)
  • Grade 5: Least energy efficient (worst!)

Choosing a Grade 1 appliance can save you a lot of money on your electricity bill over its lifetime.

Key Takeaway

An A/C is a heat pump. Its efficiency is measured by its COP – a higher value is better. Look for the EELS label and choose Grade 1 appliances to save energy.

Section B: Energy Efficiency in Buildings and Transportation

Saving energy isn't just about appliances; it's also about the design of our buildings and how we travel.

1. Better Buildings

In a hot place like Hong Kong, a huge amount of energy is used for air-conditioning. A well-designed building reduces this by minimising heat gain from the outside.

Heat enters through conduction via the walls, roof, and windows, as well as solar radiation through glazing.

Rate of Heat Transfer by Conduction

The rate at which heat flows through a material depends on several factors:

\( \frac{Q}{t} = \frac{\kappa A (T_{\text{hot}} - T_{\text{cold}})}{d} \)

Where:

  • \( \frac{Q}{t} \) is the rate of heat transfer (in Watts, W).
  • \( \kappa \) (kappa) is the thermal conductivity of the material. A good insulator like foam has a low κ. A good conductor like metal has a high κ.
  • \( A \) is the surface area (m²). (Bigger walls/windows let more heat through).
  • \( (T_{\text{hot}} - T_{\text{cold}}) \) is the temperature difference across the material.
  • \( d \) is the thickness of the material (m). (Thicker walls slow down heat transfer).
Thermal Transmittance (U-value)

To make things simpler, we combine conductivity (κ) and thickness (d) into one number: the U-value.

\( U = \frac{\kappa}{d} \)

The U-value measures how easily heat can pass through a building component per unit area and temperature difference (W m⁻² K⁻¹).
A LOW U-value is GOOD! It means the material is a good thermal insulator.

Solar Radiation and Overall Thermal Transfer Value (OTTV)

Heat also enters through windows via radiation. The Solar Heat Gain Coefficient (SHGC) or Shading Coefficient (SC) measures how much solar radiation passes through the glass.

The Overall Thermal Transfer Value (OTTV) measures the average rate of heat gain into a building per unit envelope area (including conduction through opaque walls and roof, and conduction plus solar radiation through fenestration/windows).
A LOW OTTV is GOOD! It means the building envelope reduces air-conditioning load.

Factors that keep OTTV low include:

  • Low U-values for walls, roofs, and windows.
  • Low window-to-wall ratio.
  • External shading devices (e.g. overhangs, fins).
  • Low-emissivity (low-e) or reflective window coatings.
Key Takeaway

To make buildings energy efficient, we want to minimise heat transfer by using materials with a low U-value and designing the building to have a low OTTV.


2. Smarter Transportation

Vehicles are a major source of energy consumption and pollution.

Electric Vehicles (EVs) vs. Fossil-Fuel Vehicles
  • Fossil-Fuel Vehicle: An internal combustion engine burns petrol or diesel. This process is very inefficient. Only about 20–30% of the fuel's chemical energy is converted to mechanical work; the rest is lost as waste heat.
  • Electric Vehicle (EV): Uses a rechargeable battery pack, an electronic power controller/inverter, and an electric motor. Electric motors convert electrical energy to mechanical work at over 90% efficiency.

Mechanical Power and Regenerative Braking:

  • The power required to maintain vehicle speed \( v \) against resistive forces \( F \) (such as air drag and rolling friction) is \( P = Fv \).
  • Regenerative Braking: When an EV slows down, the electric motor operates in reverse as a generator. It converts the vehicle's kinetic energy back into electrical energy to recharge the battery instead of dissipating it as friction heat in mechanical brakes.
Key Takeaway

Electric vehicles have a much higher end-use efficiency than fossil-fuel vehicles and recover energy during deceleration via regenerative braking.

Section C: Renewable and Non-renewable Energy Sources

Where does all our electricity come from? Let's look at the sources and their impact.

1. Types of Energy Sources

  • Non-renewable Sources: These are finite and will eventually run out. Once we use them, they're gone.
    Examples: Fossil fuels (coal, oil, natural gas), Nuclear fuel (uranium).
  • Renewable Sources: These are naturally replenished and won't run out.
    Examples: Solar, wind, hydroelectric (water), geothermal.

2. A Closer Look at Energy Sources

Nuclear Fission

Nuclear power plants use fission. A heavy nucleus (such as Uranium-235) absorbs a slow neutron and splits into lighter daughter nuclei and additional neutrons, releasing energy.

According to Einstein's mass-energy equation, the energy released \( E \) corresponds to the mass defect \( \Delta m \) (the total mass of reactants minus total mass of products):

\( E = \Delta m c^2 \)

A fission reactor controls this chain reaction using:

  • Moderator: (e.g. heavy water or graphite) Slows down fast neutrons to thermal speeds to maintain fission.
  • Control Rods: (e.g. boron or cadmium) Absorb neutrons to regulate the reaction rate or shut it down.
  • Coolant: Transfers the heat generated to steam generators to drive turbines.
Solar Power

The solar constant is the solar radiation flux incident normally per unit area at the top of the Earth's atmosphere, approximately 1360 W/m².

Solar cells (photovoltaic cells) convert sunlight directly into electrical energy via the photovoltaic effect, while solar thermal collectors absorb solar radiation to heat water.

Wind Power

The total kinetic energy of the air column passing per second through a swept area \( A \) with wind speed \( v \) gives the maximum available wind power:

\( P = \frac{1}{2} \rho A v^3 \)

Where \( \rho \) is air density, \( A = \pi r^2 \) is the area swept by the blades of length \( r \), and \( v \) is wind speed. The actual electrical power output is \( P_{\text{out}} = \eta P \), where \( \eta \) is the turbine efficiency.

Important Point: Power is proportional to the cube of wind speed (\( v^3 \)). If wind speed doubles, the available power increases by \( 2^3 = 8 \) times!

Hydroelectric Power

Hydroelectric power harnesses the gravitational potential energy of falling water. When water of mass \( \Delta m \) drops through height \( h \) in time \( \Delta t \), the mechanical power available is:

\( P = \frac{\Delta m}{\Delta t} g h = \rho Q g h \)

Where \( \rho \) is water density, \( Q = \frac{\Delta V}{\Delta t} \) is the volume flow rate (m³/s), \( g \) is acceleration due to gravity, and \( h \) is the effective hydraulic head.

3. Environmental Impact

Our energy choices have consequences:

  • Fossil Fuels: Burning releases greenhouse gases (CO₂) that accelerate global warming, as well as SO₂ and NOₓ causing acid rain and smog.
  • Nuclear Power: Emits almost zero greenhouse gases during operation, but requires strict long-term disposal and shielding for radioactive nuclear waste.
  • Renewables: Clean and low-emission, but intermittent and weather-dependent.

In Hong Kong, electricity is primarily generated from natural gas, imported nuclear power from Daya Bay, and coal.

Key Takeaway

Understanding energy generation—from fossil fuels and nuclear fission to solar, wind, and hydroelectric power—helps us make sustainable choices for the future.