Energy Systems, Conservation and Dissipation

Systems and their boundaries

A system is the object or group of objects being considered. Its boundary separates the system from everything called the surroundings. Choosing the boundary carefully determines which energy stores must be included.

For example, a swinging pendulum alone transfers energy to the air and its pivot, so energy crosses that narrow boundary. If the system is widened to include the pendulum, Earth, air and pivot, those transfers take place within the system instead.

A closed system does not exchange energy with its surroundings. Energy may still be transferred between stores inside it, but none enters or leaves across its boundary.

Conservation of energy

Energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed. In a closed system, this means:

$E_{\text{total before}}=E_{\text{total after}}$

Equivalently, the net change in the total energy of the closed system is zero:

$\Delta E_{\text{total}}=0$

Individual stores can change greatly even though the total does not. One store decreases by exactly as much as the other stores increase.

Consider a pendulum released from a raised position. Energy in the gravitational potential store of the pendulum–Earth system decreases as energy in the pendulum's kinetic store increases. Friction at the pivot and air resistance also transfer some energy into thermal stores. If the pendulum, Earth, pivot and surrounding air are all inside the boundary, every transfer is internal and the total energy remains unchanged.

Checking an energy account

To verify conservation, identify the initial stores, follow the transfers and account for every final store. For a process with one input transfer, the balance can be written as:

$\text{total energy transferred in}=\text{useful energy transferred}+\text{dissipated energy}$

Suppose an electric motor receives 100 J of energy. If 60 J is transferred usefully to the kinetic store of its moving parts, the remaining 40 J must be accounted for in other stores. Electrical resistance, friction and vibrations can ultimately increase the thermal energy stores of the motor and its surroundings. The output total is therefore $60\text{ J}+40\text{ J}=100\text{ J}$: there has been no net change in total energy.

Energy transferred to a motor: 100 J. Useful transfer to the kinetic store: 60 J. Dissipated into thermal stores: 40 J. Wasted energy = 100 − 60 = 40 J. Efficiency = 60 ÷ 100 × 100% = 60%. Arrow shaft widths are proportional to energy.

Why energy becomes less useful

In every real system change, some energy is dissipated. This means that it spreads into less useful stores, most commonly the thermal energy stores of objects and their surroundings.

When a car brakes, for example, its kinetic store decreases. Friction transfers energy mechanically into the thermal stores of the brakes, tyres, road and surrounding air. Vibrations may also produce sound, which is eventually absorbed and contributes to thermal stores. The car stops, but its original energy has not vanished: it has become more widely spread through the surroundings.

Spread-out thermal energy is difficult to transfer back into a useful store. Recovering it would require a temperature difference and suitable equipment, and even then not all of it could be recovered usefully. Dissipation therefore reduces the amount of energy available for the intended purpose, without reducing the total amount of energy.

“Wasted” does not mean destroyed

Whether a transfer is useful depends on the purpose of the system. The kinetic energy transferred to a motor's shaft may be useful if the motor is driving a fan. Heating of the motor casing is usually unwanted, so that transfer is called wasted.

“Wasted energy” is therefore shorthand for energy stored in less useful ways. It remains part of the conserved total. A complete description should name where it goes, such as the thermal energy stores of the device and surroundings, rather than saying simply that energy is lost.

Closed systems

• A system is an object or group of objects chosen for analysis.
• In a closed system, no energy crosses the system boundary.
• Energy can move between stores inside the system, but:

$E_{\text{total before}}=E_{\text{total after}}$

$\Delta E_{\text{total}}=0$

Energy balance

Account for every useful and unwanted transfer:

$\text{total input}=\text{useful transfer}+\text{dissipated transfer}$

The decrease in some stores must equal the combined increase in the others.

Dissipation

• Every real system change dissipates some energy.
• Friction, drag and electrical resistance commonly lead to increases in thermal energy stores.
• Dissipated energy spreads through the surroundings and becomes less useful.
• “Wasted” energy is not destroyed: it is still included in the conserved total.

Describe a transfer clearly

1. Name the store that decreases.
2. Name the store or stores that increase.
3. Identify useful and dissipated transfers.
4. Check that all energy is accounted for.