Objectives:

• To appreciate that energy can be transferred usefully, stored or dissipated, but cannot be created or destroyed.
• To be able to describe with examples where there are energy transfers in a closed system, that there is no net change to the total energy.
• To be able to describe, with examples, how in all system changes energy is dissipated, so that it is stored in less useful ways. This energy is often described as being ‘wasted’.
• To be able to explain ways of reducing unwanted energy transfers, for example through lubrication and the use of thermal insulation.
• To understand that The higher the thermal conductivity of a material the higher the rate of energy transfer by conduction across the material.
• To learn how the rate of cooling of a building is affected by the thickness and thermal conductivity of its walls.

This entire topic has focused on what energy is, the capacity to do work, the different types of energy that we come across and converting from one type of energy to another.

Energy is a fundamental quantity which Scientists use. The main rule is that energy cannot be created or destroyed – Energy is always conserved!

You may question where energy has therefore come from since we can consume food to fuel ourselves with the energy. There are theories behind this but they go beyond GCSE, if you are interested in finding out, click here.

The idea that energy is conserved is a very important concept that in Physics is always obeyed. If you lift something up in to the air, you use your chemical potential energy store to push the object away from gravity:

$\text{chemical potential energy} \rightarrow \text{gravitational potential energy}$

If you were to then let go of this object, gravity accelerates it down, which means it would lose this gravitational potential energy store, so where does it go? Well, it speeds up and therefore the gravitational potential energy store goes in to the kinetic energy store if the object:

$\text{gravitational potential energy} \rightarrow \text{kinetic energy}$

Eventually of course this object will strike the ground and lose all of its kinetic energy store, m so where then does the energy go next? It would end up as heat and sound – heat due to the friction when in contact with the ground, and sound… well because we would hear it:

$\text{kinetic energy} \rightarrow \text{thermal energy} + \text{sound energy}$

The total energy is always constant and can never change, it will simply transform from one type to another.

This is always true for a given system, what this means is, you have to imagine a scenario where there are no outside influencers. Take a cup of tea for example, you know the temperature will decrease over time because it cools down, this heat goes into the surrounding room. We then assume that the system is the room and cup of tea, if we start including outside of the room and think of the heat losses there too, an energy system can suddenly get very complex. Physicists… believe it or not… try to make like easy for themselves!

Rollercoaster engineers use the principle of conservation of energy to determine the maximum speeds that rollercoasters may end up moving at.

The engineers will know how tall they want to build a rollercoaster and will also know the mass of the carts used on the rollercoaster. With this information, the would be able to determine the maximum gravitational potential energy:

$E_{p} = mgh$

The engineers can then assume that in the case that all friction is lost and that no sound is emitted, that all of this gravitational potential energy will be transferred into the kinetic energy of the cart (as it goes down the track).

$G.P.E \rightarrow K.E$

This would be the maximum kinetic energy that the cart could obtain because the engineers would assume that no other forces would act on the rollercoaster, the kinetic energy could be calculated using:

$E_{k} = \frac{1}{2} mv^{2}$

Since the engineers are modelling this scenario as though all of the gradational potential energy transfers to kinetic energy, the following can be written:

$G.P.E = K.E$

$mgh = \frac{1}{2} mv^{2}$

This can then be rearranged to find v – the maximum speed the rollercoaster may reach:

$v^{2} = \frac{2mgh}{m}$

The masses then cancel – this tells us that the mass does not determine the maximum speed in which the rollercoaster can obtain – the speed comes from the height and gravitational acceleration alone!

$v^{2} = 2gh$

$v = \sqrt{2gh}$

So there we have it, engineers have quite a simple but very useful final equation to determine the maximum speed that a rollercoaster will end up moving at.

In reality, the rollercoaster cart would move through the air and so there would be air resistance slowing it down, air resistance is friction with air and therefore is wasted thermal energy. Additionally, the wheels rotating on the tracks will result in energy transferred to sound. In other words, kinetic energy is not the only energy that the gravitational potential energy turns into.

Reduce unwanted wasted energy

To refer back to the rollercoaster scenario, how could engineers prevent energy being wasted in the form of heat and sound? They could use forms of lubrication where the wheels of the carts meet the tracks. Of course they would have to be exceptionally careful with this! lubrication enables a smoother transitions between the two surfaces, this could reduce sound energy and friction with the wheels on the tracks.

In a more unlikely scenario the engineers could reduce air resistance; they could build the rollercoaster in a tube, extract all the air and make a vacuum inside, get all of guests to where special suits that would allow them to exist in a vacuum. This is likely too costly and a little over the top – it is much more likely they would just attach an engine to the cart to make it move faster!

Reducing unwanted wasted energy in our home

Home owners and builders are constantly searching for way to reduce unwanted energy transfers. They may not always think about it from an energy perspective but ultimately they want to reduce costs in their homes. We all pay for our heating some way or another, if you have the windows open and the radiators on, a lot of the heat will expel outside of the house and will therefore be wasted – you would literally be paying to heat up outside!

The obvious thing to do would be to close the window. Well what if the window was made from a thin sheet of glass? A thin sheet of glass has a high thermal conductivity, this means it will conduct electricity at a high rate. So the heat conducts through the glass to outside – wasting energy!

Home owners therefore ideally want double glazing. This means there is another whole piece of glass that the heat needs to conduct through! Double glazing is better than just two pieces of glass though, it actually had a layer of gas in between he two panes. This layer has a low thermal conductivity (mainly because it is a gas and the particles a spread far apart), this means that f the first pane conducts heat through, the gas doesn’t conduct very much and therefore the whole window doesn’t conduct much – the total connectivity of the window has lowered. This is a form of insulation!

How does the type of material and thickness of a piece of material affect the thermal conductivity?

On a previous page focussing on insulation (click here), the difference between insulators and conductors was discussed. Some materials allow heat to be transferred through it quicker than others do. Metals tend to be very good conductors and therefore have a very high thermal conductivity rate, whereas wood and specially designed plastic for example are poor conductors (or good insulators) and therefore have a very low thermal conductivity rate.

$\text{good conductor} \rightarrow \text{high conductivity rate}$

$\text{poor conductor} \rightarrow \text{small conductivity rate}$

If a type of material is used to insulate something, the more of a type of material there is, so an increased thickness, results in a greater distance for the heat to be transferred through at that rate.
In otherwords, if you use an insulator around a mug of hot tea, this will have a low conductivity rate and therefore it will take a long time for the heat to transfer through and so it will stay hotter for longer. The more material, the further the heat needs to travel to escape and therefore the more it insulates.
If you use a good conductor around a mug of hot tea, this will have a high conductivity rate and therefore it will take a short time for the heat to transfer through it, so it cools quickly.

Different metals have different conductivity rates, this can be seen from the following video: