Power and efficiency

What you'll learn

• Why some mechanical processes become “wasteful” when they heat the surroundings.
• What power means, and how to calculate it using energy and time.
• Why 1 watt means 1 joule per second.
• How to calculate efficiency as a decimal or percentage.

Starting point: energy transfers and work done

In this topic, you are still using the big idea that energy is transferred between stores. Energy is measured in joules (J).

When a force moves an object, the force does work. In physics, work done means energy has been transferred by a force.

For this section, you often use the symbol $E$ for energy transferred or work done.

Why mechanical processes can be wasteful

A mechanical process is any process involving movement and forces, such as gears turning, brakes slowing a bike, or a motor lifting a load.

Mechanical processes often involve friction. Friction is a force that opposes motion between surfaces in contact. When surfaces rub, energy is transferred to the thermal energy stores of the objects and surroundings, so their temperature increases.

This does not mean energy has been destroyed. Energy is conserved, but it has been transferred in a way that is not useful for the job you wanted.

Power: how fast energy is transferred

Two machines might transfer the same amount of energy, but one might do it faster. That faster machine has a greater power.

A rate means “how much happens per second”. So power tells you how many joules of energy are transferred each second.

For Edexcel 1PH0, this is a recall equation:

$$P=\frac{E}{t}$$

where:

• $P$ is power in watts (W)
• $E$ is energy transferred or work done in joules (J)
• $t$ is time taken in seconds (s)

You may also see it written as:

$$power=\frac{work\; done}{time\; taken}$$

The watt

The unit of power is the watt, symbol W.

So a 60 W lamp transfers 60 J of energy every second. A 2000 W kettle transfers 2000 J of energy every second.

Rearranging the power equation

You should be able to use the power equation in different forms:

$$P=\frac{E}{t}$$

If you need energy:

$$E=Pt$$

If you need time:

$$t=\frac{E}{P}$$

Investigating power in a practical

A common practical is to estimate your power when climbing stairs, doing step-ups, or lifting an object.

If you climb stairs, your useful energy transfer is the gain in gravitational potential energy. From earlier energy work:

$$E_p=mgh$$

where:

• $m$ is mass in kilograms (kg)
• $g$ is gravitational field strength, about 10 N/kg on Earth
• $h$ is height gained in metres (m)

Then you use:

$$P=\frac{E}{t}$$

Efficiency: how much energy is useful?

No device transfers all its input energy usefully. Some energy is always dissipated to the surroundings, often by heating or sound.

For Edexcel 1PH0, this is also a recall equation:

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

Efficiency has no unit because it is a ratio. It can be written as a decimal or a percentage.

To convert a decimal efficiency to a percentage, multiply by 100.

A Sankey diagram shows energy transfers with arrows. The thicker the arrow, the larger the energy transfer.

Improving efficiency

A device is more efficient if less energy is dissipated and more of the input energy is transferred usefully.

For mechanical systems, efficiency can often be improved by reducing friction. For example, machines may use lubrication, smoother surfaces, or better bearings.

Be careful: improving efficiency does not always mean increasing power. A device can be powerful but inefficient if it transfers energy quickly but wastes a large fraction of it.