Energy dissipation and efficiency

In real system changes, some energy is dissipated. For example, when a bat strikes a ball, some of the bat’s kinetic energy is transferred usefully to the ball’s kinetic energy store. Some increases the thermal energy stores of the bat and ball, and some is transferred away by sound. That sound eventually dissipates into the surroundings too.

How mechanical processes cause unwanted heating

Moving surfaces often rub against one another. Friction opposes their relative motion, and work done against friction increases the thermal energy stores of the surfaces. Their temperature rises, and energy is then transferred by heating to cooler surroundings.

For example, friction between a bicycle’s moving chain and gears can make them warmer. Energy that could have helped move the bicycle instead increases the thermal energy stores of the components and surroundings. The rider must supply more energy to maintain the same motion.

Whether heating is useful depends on the purpose. Heating the surroundings is unwanted for a lifting motor, but it is the intended output of a room heater. Similarly, a television’s light and sound are useful outputs, whereas heating its casing is usually unwanted. Dissipation and waste are therefore not identical: an energy transfer can serve its purpose before its energy spreads out.

Reducing unwanted transfers

Lubrication reduces friction between moving surfaces. Oil on a bicycle chain allows the parts to move with less friction, so less energy is transferred wastefully to their thermal energy stores. Lubrication is appropriate when moving parts rub together; it does not prevent energy escaping through a building’s walls.

Thermal insulation reduces unwanted energy transfer by heating. For example, loft insulation and cavity wall insulation reduce the rate at which energy leaves a warm building. Materials containing trapped air are useful because air is a poor thermal conductor. Less energy then needs to be supplied to maintain the indoor temperature.

The method must match the unwanted transfer. Lubrication tackles friction in machinery, whereas insulation slows heating transfers between regions at different temperatures. Neither method destroys the wasted energy: it reduces the amount transferred in the unwanted way.

Why wall thickness and material matter

When a building is warmer than the air outside, energy is transferred through its walls towards the cooler surroundings. Conduction is the transfer of energy through a material without the material as a whole moving.

For otherwise comparable walls and the same inside–outside temperature difference:

• Thicker walls transfer energy through them more slowly, so the building cools more slowly.
• Lower thermal conductivity means energy passes through the wall material less readily, so the building cools more slowly.
• Thinner walls or higher thermal conductivity allow faster energy transfer, so the building cools more quickly.

Thickness and thermal conductivity are separate properties. A thicker layer of the same material gives better insulation, while choosing a material with lower thermal conductivity can improve insulation without changing the thickness. Insulation slows cooling; it does not stop energy transfer completely.

Measuring efficiency

Efficiency tells us what proportion of the energy supplied to a device is transferred usefully:

$$\text{efficiency} = \frac{\text{useful energy transferred by the device}}{\text{total energy supplied to the device}}$$

Both energies must be measured in the same units, such as joules. The units cancel, so efficiency has no unit. It can be expressed as a decimal between 0 and 1, or as a percentage by multiplying the decimal by 100.

For a device whose energy input is accounted for by useful and wasted outputs:

$$E_{\text{input}} = E_{\text{useful}} + E_{\text{wasted}}$$

Consider a motor that receives 200 J of electrical energy. It transfers 150 J usefully to the gravitational potential energy store of a lifted load and dissipates the remaining 50 J through unwanted heating and sound.

Electrical energy supplied: 200 J. Increase in load's gravitational potential energy: 150 J. Unwanted heating and sound: 50 J. Wasted energy = 200 − 150 = 50 J. Efficiency = 150 ÷ 200 × 100% = 75%. Arrow shaft widths are proportional to energy.

Its efficiency is $150/200 = 0.75$, or $75\%$. This means three-quarters of the supplied energy achieves the intended purpose. If only the wasted energy had been given, the useful energy would first be found by subtraction: $200\text{ J} - 50\text{ J} = 150\text{ J}$.

Increasing efficiency — Higher Tier

Efficiency increases when a greater proportion of the energy input is transferred usefully. A suitable modification reduces an unwanted transfer while preserving the device’s intended function.

For a lifting motor, lubricating moving parts or using bearings reduces friction and unwanted heating. For the same energy input, more energy can then be transferred usefully to the load.

Other modifications target different causes of waste:

• Streamlining a moving object reduces air resistance, so less energy is dissipated as it moves through the air. A cyclist’s posture and the shape of their helmet can help achieve this.
• Using suitable lower-resistance electrical components reduces unwanted heating as current passes through them.
• Tightening loose machine parts reduces unwanted vibration and sound.
• Insulating a device intended to keep something hot reduces energy transfer to the surroundings, leaving more of the input available for its intended heating purpose.

Simply supplying more energy does not necessarily improve efficiency: the useful output must become a larger fraction of the total input.

• Lubrication reduces friction and unwanted heating between moving parts.
• Thermal insulation reduces unwanted heating transfers.
• For comparable walls at the same temperature difference: greater thickness → slower cooling; lower thermal conductivity → slower cooling.

Efficiency

$$\text{efficiency} = \frac{E_{\text{useful}}}{E_{\text{input}}}$$ $$E_{\text{useful}} = E_{\text{input}} - E_{\text{wasted}}$$

Efficiency is unitless. Multiply the ratio by 100 to express it as a percentage.

Increasing efficiency — Higher Tier

Reduce unwanted transfers so a greater fraction of the input is useful: lubricate or use bearings to reduce friction; streamline to reduce air resistance; use suitable lower-resistance components to reduce electrical heating; tighten loose parts to reduce vibration; insulate heating devices.