Conduction of Heat

Admin / March 13, 2026

Conduction of Heat

Understanding how thermal energy transfers through materials without the material itself moving

Heat Transfer through Solids

What is Conduction?

Particle Vibration

Heat conduction occurs when vibrating particles pass their kinetic energy to neighboring particles.

Energy Transfer

Thermal energy moves from the hotter end to the colder end of an object.

Temperature Gradient

The greater the temperature difference, the faster the rate of conduction.

Key Concept

Conduction is the main method of heat transfer in solids. In metals, free electrons also help transfer heat very efficiently.

Particle Model of Conduction

How Heat Travels Through Materials

Cold End

Particles vibrate slowly

Heat Source →

Particles vibrate rapidly

Energy transfers from hot to cold as vibrating particles collide with their neighbors

Good vs Poor Conductors

Good Conductors

Materials that transfer heat quickly:

Silver - Best conductor
Copper - Used in pans
Aluminum - Cooking foil
Iron - Radiators

High Thermal Conductivity

Poor Conductors (Insulators)

Materials that transfer heat slowly:

Wood - Handles
Plastic - Coatings
Glass - Windows
Air - Trapped in insulation

Low Thermal Conductivity

Why are metals good conductors?

Metals have free electrons that can move through the metal and transfer kinetic energy quickly from the hot end to the cold end. This makes them much better conductors than non-metals.

Thermal Conductivity Values

Material	Thermal Conductivity (W/mK)	Type	Common Use
Silver	429	Excellent Conductor	Electronics
Copper	401	Excellent Conductor	Cooking pans, wires
Aluminum	237	Good Conductor	Foil, pans
Iron	80	Moderate Conductor	Radiators
Glass	0.8	Poor Conductor	Windows
Wood	0.15	Insulator	Handles, furniture
Air	0.024	Excellent Insulator	Double glazing

Higher values mean better conduction of heat

Interactive Conduction Experiment

See how different materials conduct heat at different rates:

20°C

Heat Intensity

50%

Observations:

Copper

Heats fastest

Iron

Heats quickly

Glass

Heats slowly

Wood

Heats very slowly

Factors Affecting Conduction

Temperature Difference

Greater temperature difference = faster heat transfer

Cross-sectional Area

Thicker materials conduct more heat

Length

Shorter distance = faster conduction

Material Type

Different materials have different conductivity

Time

Longer time = more heat transferred

Rate of conduction ∝ (Area × Temperature Difference) ÷ (Length × Material Resistance)

Real-World Applications

Copper or aluminum bases conduct heat quickly and evenly to food.

Metal conducts heat from hob to food
Wood/plastic handles are insulators

Materials like fiberglass trap air to reduce heat loss through walls and roofs.

Loft insulation
Cavity wall insulation
Double glazing

Vacuum flasks use a vacuum to prevent conduction and keep drinks hot or cold.

Double-walled construction
Vacuum prevents conduction

Metal fins on electronics conduct heat away from components to prevent overheating.

Made of copper or aluminum
Large surface area helps cooling

Insulation in Daily Life

Clothing

Trapped air between fibers insulates our bodies

Upholstery

Foam and fabric reduce heat loss

Double Glazing

Air gap between glass panes

Coolers

Expanded polystyrene keeps food cold

Pizza Boxes

Corrugated cardboard traps air

Safety Gear

Heat-resistant gloves for handling hot objects

Solved Examples

GCSE Foundation

Example 1: Identifying Conductors

Question: Explain why a metal spoon in a hot drink becomes hot to touch, but a plastic spoon does not.

GCSE Higher

Example 2: Comparing Conductivity

Question: A copper rod and a glass rod of the same dimensions are heated at one end. After 2 minutes, the copper rod is hot along its entire length, but the glass rod is only hot at the heated end. Explain why.

Grade 10 Challenge

Example 3: Practical Application

Question: A house has single-glazed windows. Suggest two ways to reduce heat loss through the windows and explain how they work.

Quick Facts

Best Conductor Silver

Best Insulator Vacuum

Metals conduct via Free electrons

Non-metals conduct via Particle vibration

Conservation and dissipation of energy

Admin / March 13, 2026

Conservation & Dissipation of Energy

Understanding how energy is transferred, stored, and wasted in physical systems

Energy cannot be created or destroyed

The Law of Conservation of Energy

"Energy cannot be created or destroyed, only transferred from one store to another or dissipated to the surroundings."

⚡

Input Energy

Total energy going into a system

✓

Useful Energy

Energy transferred to where it's wanted

✗

Dissipated Energy

Energy wasted to surroundings

Key Principle

Total energy input = Useful energy output + Wasted energy output

No energy is ever lost - it just becomes less useful!

Energy Stores & Transfers

Kinetic Energy

Energy of moving objects

Example: A moving car, running athlete

Thermal Energy

Energy of hot objects

Example: Hot coffee, warm radiator

Gravitational Potential

Energy due to height

Example: Water behind a dam, lifted weight

Chemical Energy

Energy stored in chemical bonds

Example: Food, batteries, fuel

Elastic Potential

Energy in stretched/compressed objects

Example: Stretched spring, drawn bow

Nuclear Energy

Energy stored in atomic nuclei

Example: Nuclear power, sun

Dissipation of Energy

When energy is transferred, some is always dissipated (wasted) to the surroundings, usually as thermal energy.

Energy Flow in a Light Bulb

10 J/s

Light Energy (Useful)

90 J/s

Heat Energy (Wasted)

100 J/s

Total Input

Only 10% of electrical energy is converted to light - the rest is dissipated as heat!

Common Ways Energy is Dissipated:

Friction - Kinetic energy → Thermal energy
Sound - Energy transferred as noise
Air Resistance - Objects heating the air
Electrical Resistance - Wires heating up

Efficiency

Efficiency tells us how much of the input energy is transferred usefully.

As a Decimal

Efficiency =
Useful Output ÷ Total Input

As a Percentage

Efficiency =
(Useful ÷ Total) × 100%

Example: LED Bulb (90% Efficient)

90% Useful

Example: Filament Bulb (10% Efficient)

10% Useful

Efficiency of Common Devices:

LED Bulb

90%

Electric Motor

85%

Car Engine

25%

Filament Bulb

10%

Solar Panel

20%

Sankey Diagrams

Sankey diagrams show energy flow - the width of the arrows represents the amount of energy.

LED Light Bulb

100 J Input

90 J Light

10 J Heat

Efficiency: 90%

Car Engine

100 J Fuel

25 J Motion

75 J Heat + Sound

Efficiency: 25%

The thicker the arrow, the more energy is transferred that way!

Interactive Efficiency Calculator

Calculate Efficiency

Useful Energy Output (J)

75 J

Total Energy Input (J)

100 J

Efficiency

75%

Wasted Energy: 25 J

Real-World Applications

Electric Vehicles

Electric cars are much more efficient than petrol cars.

85%

Electric Motor

25%

Petrol Engine

Electric cars waste less energy as heat

Home Insulation

Reduces energy dissipation from houses.

30%

Heat Saved

£300

Yearly Saving

Loft insulation, double glazing, cavity walls

LED Lighting

LED bulbs are 90% efficient vs 10% for filament bulbs.

90%

LED

10%

Filament

Uses 90% less electricity for same light

Regenerative Braking

Captures kinetic energy that would otherwise be wasted as heat.

70%

Energy Recovered

30%

Range Increase

Used in electric and hybrid vehicles

Solved Examples

GCSE Foundation

Example 1: Calculating Efficiency

Question: A motor transfers 500J of electrical energy. It produces 400J of kinetic energy. Calculate its efficiency.

GCSE Higher

Example 2: Finding Wasted Energy

Question: A television with 250W input power is 65% efficient. Calculate the power wasted.

Grade 10 Challenge

Example 3: Sankey Diagram

Question: A kettle uses 2000J of electrical energy. 1500J heats the water, the rest is wasted. Draw a Sankey diagram and calculate efficiency.

Energy Efficiency of Common Devices

Device	Input Energy	Useful Output	Wasted Output	Efficiency
LED Light Bulb	100 J	90 J (light)	10 J (heat)	90%
Electric Motor	100 J	85 J (movement)	15 J (heat)	85%
Solar Panel	100 J	20 J (electricity)	80 J (heat)	20%
Car Engine	100 J	25 J (movement)	75 J (heat, sound)	25%
Filament Bulb	100 J	10 J (light)	90 J (heat)	10%

Reducing Energy Dissipation

Lubrication

Reduces friction between moving parts, reducing heat dissipation.

Example: Oil in car engines

Insulation

Traps air to reduce thermal energy transfer.

Example: Loft insulation, double glazing

Streamlining

Reduces air resistance, saving energy.

Example: Aerodynamic cars

Low Resistance

Using materials with lower electrical resistance.

Example: Superconductors, thicker wires

Key Facts

Conservation Law Energy can't be destroyed

Dissipation Energy spreads out

Maximum Efficiency 100% (theoretically)

Wasted Energy Usually heat

power

Admin / February 16, 2026

Power

Understanding the rate of energy transfer - from light bulbs to power plants

P = E/t = W/t = VI

What is Power?

Definition

Power is the rate at which energy is transferred or work is done. It tells us how quickly energy is being used or generated.

Key Concept

A high power device transfers energy quickly, while a low power device transfers energy slowly.

Unit

Power is measured in watts (W). 1 watt = 1 joule per second (1 W = 1 J/s)

Real-World Understanding

A 100W light bulb converts 100 joules of electrical energy into light and heat every second. A 2000W kettle converts 2000 joules per second - that's why it heats water much faster!

Power Formulas

Basic Power Formula

P = E / t

Power (W)

Energy (J)

Time (s)

Work Formula

P = W / t

Power (W)

Work (J)

Time (s)

Electrical Power

P = V × I

Power (W)

Voltage (V)

Current (A)

Alternative Electrical

P = I²R

Power (W)

Current (A)

Resistance (Ω)

Formula Rearrangements

Find Energy

E = P × t

Find Time

t = E ÷ P

Find Current

I = P ÷ V

Find Voltage

V = P ÷ I

Interactive Power Calculator

Adjust the sliders to see how power, energy, and time are related:

Energy Transfer Simulator

Power (Watts)

100 W

Time (seconds)

60 s

Energy Used

6000 J

E = P × t

Energy Transfer Rate

100 J/s

Your device transfers 100 joules of energy every second

In 60 seconds, total energy = 6000 J

Household Appliance Power Ratings

Different appliances have different power ratings - see how they compare:

LED Light Bulb

10W

Uses 10 J/s
Cost: ~£0.03 per day
100 hours on 1 kWh

Laptop

50W

Uses 50 J/s
Cost: ~£0.15 per day
20 hours on 1 kWh

LED TV (50")

100W

Uses 100 J/s
Cost: ~£0.30 per day
10 hours on 1 kWh

Refrigerator

150W

Uses 150 J/s (avg)
Cost: ~£0.45 per day
Runs 30% of time

Kettle

2000W

Uses 2000 J/s
Cost: ~£0.10 per boil
30 minutes on 1 kWh

Electric Shower

9000W

Uses 9000 J/s
Cost: ~£0.45 per 10 mins
6.7 minutes on 1 kWh

Key Point: High power appliances (like kettles and showers) transfer energy very quickly, which is why they heat things rapidly but also cost more to run.

Real-World Power Examples

Solar Panel

Typical residential solar panel produces about 300W of power in full sunlight.

300W

Peak Power

1.5kWh

Daily Energy

Car Engine

A typical family car engine produces around 100,000W (100kW) of power.

100kW

Engine Power

134hp

Horsepower

Wind Turbine

Modern wind turbines can generate up to 3,000,000W (3MW) of power.

3MW

Peak Power

2000 homes

Can Power

Human Power

An average healthy human can sustain about 100W of mechanical power output.

100W

Sustained

400W

Peak (short)

Energy Efficiency & Cost

Appliance Energy Cost Calculator

Appliance Power (W)

Hours Used per Day

Electricity Rate (p/kWh)

Efficiency Ratings (A+++ to G)

A+++ D G

A+++

Most Efficient

Saves ~60% energy

Average

Standard efficiency

Least Efficient

Costs 3x more to run

Solved Examples

GCSE Foundation

Example 1: Energy Transfer

Question: A 2.5kW kettle is used for 3 minutes. How much energy does it transfer?

GCSE Higher

Example 2: Electrical Power

Question: A hairdryer operates at 230V and draws a current of 4.35A. Calculate its power and the energy used in 5 minutes.

Grade 10 Challenge

Example 3: Cost Calculation

Question: A 2kW electric heater runs for 4 hours daily. If electricity costs 28p per kWh, calculate the weekly running cost.

Power Calculator

Solve Power Problems

Energy (J)

Time (s)

Power (W)

Time (s)

Energy (J)

Power (W)

Voltage (V)

Current (A)

Result:

Power Rating Comparison

Device	Typical Power	Energy in 1 hour	Cost per hour*
LED Light Bulb	10W	0.01 kWh	0.28p
Laptop	50W	0.05 kWh	1.4p
LED TV (50")	100W	0.1 kWh	2.8p
Fridge Freezer	150W	0.15 kWh	4.2p
Desktop Computer	300W	0.3 kWh	8.4p
Microwave	800W	0.8 kWh	22.4p
Kettle	2000W	2.0 kWh	56p
Electric Shower	9000W	9.0 kWh	£2.52

*Based on 28p per kWh electricity rate

Quick Facts

1 kW 1000 watts

1 MW 1,000,000 watts

1 GW 1,000,000,000 watts

1 hp 746 watts

1 kWh 3.6 million J

Common Power Ratings

LED Bulb 5-15W

Phone Charger 5-20W

Laptop 30-100W

TV 50-250W

Kettle 2000-3000W

Book Free Demo Class

Common Mistake

Don't confuse power (watts) with energy (joules or kWh)! Power is how FAST you use energy, energy is HOW MUCH you use.

Analogy: Power is like speed (mph), Energy is like distance (miles).

Physics

Kinetic Energy

Admin / December 10, 2025

Kinetic Energy: Formula & Calculations

Understanding the energy of motion - its formula, derivation, and practical applications

What is Kinetic Energy?

Kinetic energy is the energy possessed by an object due to its motion. Any object that is moving has kinetic energy. The amount of kinetic energy depends on two factors:

Mass (m)

The heavier the object, the more kinetic energy it has when moving at the same speed.

Velocity (v)

The faster the object moves, the more kinetic energy it has. Note: KE depends on velocity squared!

The Kinetic Energy Formula

Kinetic Energy Formula

KE = ½ × m × v²

Where kinetic energy (KE) equals one-half times the mass (m) times the square of the velocity (v)

Kinetic Energy (in joules, J)

Mass (in kilograms, kg)

Velocity (in meters per second, m/s)

Constant factor (one-half)

Derivation of the Formula

The kinetic energy formula can be derived from the work-energy theorem, which states that the work done on an object equals its change in kinetic energy.

Derivation Steps

Start with Work Done

Work done (W) on an object equals force (F) times displacement (s) in the direction of the force:

W = F × s

Apply Newton's Second Law

Force equals mass times acceleration (F = m × a). Substitute into the work equation:

W = (m × a) × s

Use Kinematics Equation

From kinematics, for constant acceleration starting from rest: v² = u² + 2as, where u=0, so v² = 2as, therefore a = v²/(2s):

W = m × (v²/(2s)) × s

Simplify the Equation

The displacement (s) cancels out:

W = m × v² / 2

Work Equals Change in Kinetic Energy

By the work-energy theorem, work done equals change in kinetic energy. Starting from rest, this gives us the kinetic energy formula:

KE = ½ × m × v²

Graphical Representation

The relationship between kinetic energy and velocity is quadratic, while the relationship with mass is linear.

Kinetic Energy vs. Velocity

KE increases with the square of velocity. Doubling velocity quadruples kinetic energy!

Kinetic Energy vs. Mass

KE increases linearly with mass. Doubling mass doubles kinetic energy (at constant velocity).

Interactive Kinetic Energy Demo

Adjust the mass and velocity sliders to see how they affect kinetic energy in real-time.

Mass (kg): 10

10 kg

Velocity (m/s): 10

10 m/s

Calculated Kinetic Energy

500 J

KE = ½ × 10 kg × (10 m/s)²

Example Problems

Example 1: Calculating Kinetic Energy

A car with a mass of 800 kg is traveling at a speed of 25 m/s. Calculate its kinetic energy.

Step 1: Write the formula

KE = ½ × m × v²

Step 2: Substitute known values

m = 800 kg, v = 25 m/s

KE = ½ × 800 × (25)²

Step 3: Calculate velocity squared

(25)² = 25 × 25 = 625

KE = ½ × 800 × 625

Step 4: Perform multiplication

½ × 800 = 400

400 × 625 = 250,000

Step 5: State the answer

KE = 250,000 J or 250 kJ

Example 2: Finding Mass from Kinetic Energy

A car has a kinetic energy store of 64,800 J. It is travelling at a speed of 12 m/s. Calculate its mass.

Step 1: Write the formula

KE = ½ × m × v²

Step 2: Rearrange to solve for mass (m)

m = (2 × KE) / v²

Step 3: Substitute known values

KE = 64,800 J, v = 12 m/s

m = (2 × 64,800) / (12)²

Step 4: Calculate denominator

(12)² = 12 × 12 = 144

m = (129,600) / 144

Step 5: Perform division

129,600 ÷ 144 = 900

Step 6: State the answer

Mass = 900 kg

Example 3: Finding Velocity from Kinetic Energy

A 0.5 kg ball has 100 J of kinetic energy. Calculate its velocity.

Step 1: Write the formula

KE = ½ × m × v²

Step 2: Rearrange to solve for velocity (v)

v² = (2 × KE) / m

v = √[(2 × KE) / m]

Step 3: Substitute known values

KE = 100 J, m = 0.5 kg

v = √[(2 × 100) / 0.5]

Step 4: Calculate numerator

2 × 100 = 200

v = √[200 / 0.5]

Step 5: Perform division

200 ÷ 0.5 = 400

v = √400

Step 6: Calculate square root

√400 = 20

Step 7: State the answer

Velocity = 20 m/s

Kinetic Energy Calculator

Use this calculator to solve for any variable in the kinetic energy equation.

Solve Kinetic Energy Problems

Mass (kg)

Velocity (m/s)

Kinetic Energy (J)

Velocity (m/s)

Kinetic Energy (J)

Mass (kg)

Result:

Real-World Applications

Free Demo: Kinetic Energy

Master kinetic energy calculations with our interactive demo class

Book Demo Class

Quick Tip: Velocity Squared

Remember that kinetic energy depends on velocity squared. This means if you double the speed, kinetic energy increases by a factor of 4. If you triple the speed, KE increases by a factor of 9!

Units Check

Always ensure your units are consistent: mass in kg, velocity in m/s, and energy in joules (J). 1 J = 1 kg·m²/s².

Alevel physics