Power and Efficiency

know that there is a fundamental limit to the efficiency of some systems such as heat exchangers and refrigerators  which depends on the limiting temperatures in which they are working;

know that when designing various machines and heating systems, consideration of the most economical methods of transferring energy will be required;

compare the energy input and work done in a variety of real-life situations and understand that the work done is equal to the energy transferred;
 

Power

Power is the rate at which energy is transferred, in other words, how quickly it is transferred.

Power (W) = Energy transferred or work done (J) / time (s)

The heater in this kettle gives the water 3,000J of heat energy very second. Its power is 3kW	This is a 60W light bulb. It transfers 60J of electrical energy every second.	This motor does 500J of work every second. It is a 500W motor.

When we pay our electricity bill we are paying for energy. How much energy a device transfers depends on its power and how long it is used for. e.g. a 3kW kettle used for 5 minutes will transfer 3,000 x (5 x 60) = 900,000J of energy. All we have done here is multiply power by time to find the energy transferred.

When working out or bills the electricity companies don't use joules. They use units called kilowatt hours (kWh) which are more convenient. 1 kWh is the energy used by a 1kW device in 1 hour. A kWh, or unit, can cost anything between 7p and 12p.

Cost = Power (kW) x time (h) x cost per unit (p)

Here are a few examples. (assume that 1 unit costs 9p)

A 3kW kettle is used for 30 minutes cost = 3 x 0.5 x 9 = 13.5p	A 60W bulb is used for 10 hours cost = 0.06 x 10 x 9 = 5.4p	A 5 kW vacuum cleaner is used for 1 hour cost = 5 x 1 x 9 = 45p	A 400W television is used for 8 hours cost = 0.4 x 8 x 9 = 28.8p

Efficiency

	If we give a filament lamp 100J of electrical energy every second then it is likely that only about 7J of this will be usefully transferred into light. The other 97J is wasted as heat. It goes into the room that the bulb is in, warming it slightly. We can say that this bulb is 7% efficient.
	This bulb has a power of of 24W but it is just as bright as the 100W bulb above. How can this be? It is much more efficient, around 30%, so a bigger fraction of the electrical energy we give it every second is usefully transferred into light.

In general, efficiency = useful energy transferred / total energy supplied. This will give you a fraction. To get a percentage just multiply by 100%.