Mechanics Tutorial 14 - Energy Efficiency

 Contents

No device is ever 100 % efficient.  You always have to put more energy in than you get out.  This is due to:

• Friction in the moving parts;

• Thermodynamic losses.

All machines lose energy.  It is possible to recover a small amount by having, for example, a turbo-charger in the exhaust system of a car.  Most energy is lost as low-grade heat which is difficult to use.  Car engines are much more efficient than they used to be.  The efficiency has gone up from about 25 % to 40 %.  Even so, for every 100 litres of petrol that you buy, only 40 litres are used to move the car along the road.  The rest is used to heat up the environment.

Heat engines depend on a heat gradient from hot to cold, with heat flowing into the environment which is a heat-sink.

You will have seen an energy transfer diagram at GCSE.  The picture below shows a crude version:

The arrow that shows the useful energy is the one that goes from left to right.  The arrow pointing down shows the energy that is wasted.

Sankey diagrams can also show the quantitative nature of the losses by having a scale. In this diagram we can see that a scale has been used, and the diagram has been plotted on graph paper.

• This diagram shows that for a car, 1000 J is put in (from the chemical energy in the petrol).

• Only 300 J of energy are converted into kinetic energy that moves the car along the road.

• 700 J are wasted as how grade heat to warm up the surroundings.  While it is possible to recover heat, for example in the interior heater or a turbo-charger, the heat is eventually wasted.

The diagram above is still very simple compared with the kind of diagram shown below:

This particular diagram sums up the performance of a large aircraft engine.  It gives the power units in horsepower (hp) where 1 hp = 746 watts.  Nowadays you will see the term PS (pferdstärke) used where 1 PS = 750 W.

The basic equation for energy efficiency is:

Efficiency = Useful energy (J)

Input energy (J)

This will give a fraction that will always be less than 1.  We often convert the fraction into a percentage, so that:

% Efficiency = Useful energy (J) × 100 %

Input energy (J)

 Question 1 An electric winch takes 500 A from a 12 V source.  It is 25 % efficient.  What is its useful power?

If a machine had an efficiency of 100 %, it would be a perpetual motion machine.  People have been trying to make these for centuries, without success.

The picture above shows a possible perpetual motion machine.  The motor shafts are joined by glue. The idea of this device is that one of the motors acts as a generator, while the other motor drives the generator.  And what the generator produces drives the motor.

 Question 2 Explain why the perpetual motion machine will not work.

It is possible to get "perpetual motion machines" as toys from novelty shops.  However they need a battery to keep them going, which is hidden in the base.  Once the battery goes flat, they stop.

The study of heat flows is called thermodynamics, which is covered in the Optional topic Engineering Physics.