Consequences of Thermal Energy TransferCambridge IGCSE Physics: Revision notes

Energy can exist in multiple stores, each representing a different form. Understanding these stores is essential for applying conservation of energy.

The seven energy stores are:

During any process, energy may be stored in one or more of these stores simultaneously. When thermal energy is transferred to an object, the internal energy store increases, which typically results in a temperature rise.

Key point: Internal energy is the total kinetic and potential energy of all particles in a substance. It is fundamentally different from temperature, which is a measure of the average kinetic energy of particles.

Energy is never created or destroyed, but it is constantly transferred between stores through various mechanisms of energy transfer.

The four main mechanisms of energy transfer are:

1. By forces (mechanical work): A force acting over a distance transfers energy. This includes lifting an object (gravitational potential), accelerating an object (kinetic), or stretching a spring (elastic).

2. By electrical currents: Moving electrical charges carry energy. This occurs in circuits, electric motors, and heating elements.

3. By heating: Thermal energy flows from a hotter object to a cooler one due to a temperature difference. This includes conduction, convection, and radiation.

4. By waves: Energy can be transferred through electromagnetic radiation (light, infrared, microwaves), sound waves, or other wave forms without the need for a material medium (in the case of electromagnetic waves).

Energy transfer in thermal processes:

When an object is heated, thermal energy is transferred into the internal energy store. This causes:

• Particles to move faster (increased kinetic energy)
• Temperature to increase
• Possible change of state (if energy is sufficient)

When an object cools, thermal energy is transferred out of the internal energy store to the surroundings.

The principle of conservation of energy is fundamental to physics: energy cannot be created or destroyed; it can only be transferred between stores or transformed from one form to another. The total energy in a closed system remains constant.

Applying conservation of energy:

For any process or event:

Total energy in all stores before = Total energy in all stores after

Or: Energy input to system = Useful energy output + Wasted energy (usually as heat)

In simple examples:

1. Identify all energy stores that change during the process.
2. Write down the initial energy in each store.
3. Write down the final energy in each store.
4. Apply the principle: initial total energy = final total energy.
5. Use this equation to find unknown values.

Example: A ball falling from rest

• Initial state: Ball at height h; at rest

  • Gravitational potential energy = mgh
  • Kinetic energy = 0
  • Total initial energy = mgh

• Final state: Ball just before hitting ground

  • Gravitational potential energy = 0
  • Kinetic energy = ½mv²
  • Total final energy = ½mv²

• By conservation: mgh = ½mv² (ignoring air resistance)

Energy equations to use:

• Kinetic energy: Ek = ½mv²
• Change in gravitational potential energy: ΔEp = mgΔh

Sankey diagrams are visual representations of energy transfers in complex systems. They show:

• The width of each arrow is proportional to the amount of energy in that pathway.
• How energy flows from input, through the system, to useful and wasted outputs.
• Energy transfers at multiple stages within a process.

Key features of Sankey diagrams:

• Input energy: The primary source of energy (arrow entering the system).
• Useful energy output: The desired form of energy the system produces (arrow leaving to the right).
• Wasted energy: Energy lost, typically as heat (arrow leaving downward or in other directions).
• Total energy is conserved: The width of the input arrow equals the combined width of all output arrows.

Reading a Sankey diagram:

1. Identify the energy input and its value.
2. Trace the flow of energy through each stage.
3. Identify where energy is wasted at each stage.
4. Calculate the useful energy output by subtracting wasted energy from input.
5. Check that total energy in = total energy out.

Complex examples with multiple stages:

Many real processes involve several stages, each with its own efficiency:

• A power station: chemical energy → heat → mechanical → electrical energy, with losses at each stage.
• An electric motor: electrical energy → mechanical energy, with heat loss.
• A light bulb: electrical energy → light + heat, where heat is usually wasted.

For multi-stage processes:

• Calculate energy at each stage using conservation of energy.
• Track the cumulative losses.
• The overall efficiency = (total useful output ÷ total input) × 100%.

Two key equations underpin energy calculations in thermal physics and mechanics:

Kinetic energy equation: Ek = ½mv²

• Ek = kinetic energy (joules, J)
• m = mass (kilograms, kg)
• v = velocity (metres per second, m/s)

Use this equation when:

• Calculating energy due to motion
• Finding velocity from kinetic energy
• Comparing energy of objects with different speeds or masses

Gravitational potential energy equation: ΔEp = mgΔh

• ΔEp = change in gravitational potential energy (joules, J)
• m = mass (kilograms, kg)
• g = gravitational field strength (9.8 or 10 m/s²)
• Δh = change in height (metres, m)

Use this equation when:

• Calculating energy gained/lost due to change in height
• Finding the height an object rises to
• Converting between potential and kinetic energy

Problem-solving strategy:

1. Identify the energy stores that change in the scenario.
2. Decide which equations to use based on the energy stores involved.
3. Calculate initial energy using the appropriate equation.
4. Calculate final energy in each store.
5. Apply conservation of energy to find unknowns: E(initial) = E(final).
6. Rearrange equations if necessary to solve for unknown variables.
7. Check units are consistent and answers are reasonable.

Common pitfalls:

• Forgetting to square the velocity in Ek = ½mv² (a common algebraic error).
• Using change in height (Δh) rather than absolute height in ΔEp = mgΔh.
• Forgetting that both kinetic and potential energies may change simultaneously in free fall or projectile motion.