# VCE Physics/Unit 1/AoS 1/Temperature, and how we measure it

< VCE Physics‎ | Unit 1‎ | AoS 1

## Editing Notes

Need to start adding suitable images etc.

## Introduction

You can feel if something is hot or cold. We refer to how hot or cold something is as its "temperature". However, our sense of whether something is hot or cold varies depending on our state. Imagine you have a bowl of water in which you wash your hands, it may feel cool to you. A friend might wash their hands in the same bowl of water and say it feels warm. Your perception of the temperature of the water, whether it feels cold or hot, depends on how hot or cold your hands are.

Safety First: If you carry out any experiments related to temperature make sure you are aware of any potential risks, for example you need to be aware of how different water temperatures relate to saftey - for example the Burns and Scalds - Children is a web page maintained by the Victorian Government which has information on the effect of different water temperatures on the body.

Can you design, and carry out, a simple experiment to confirm this?

For example, take three bowls of water, one warm, one cold and one at a temperature in between (ensure they are all safe temperatures). Hold your hands in the warm bowl for a while, and then put them in the in-between bowl... does it feel warm or cold? Then Hold your hands in the warm bowl for a while, and then put them in the in-between bowl... does it feel warm or cold? Your design of some experiment similar to this will have to take into account safe temperatures for the water... how much different the temperatures need to be for you to feel the effect - a difference of just one or two degrees is likely to be insufficient - you might start with an initial experiment to determine approximately how much difference you can feel. Also, you need to monitor the termperatures, putting your hands in the bowl may cause a significant change in the temperature of the water, over time the temperatures will change due to interaction with the room. The best strategy might be to have the middle bowl at room temperature?... even in a "simple" experiment like this, there is a lot to consider.

Other factors also affect our sense of the temperature of an object, for example, see the video:

There are further limitations to our ability to judge temperature. For example, we can be hurt be very hot or very cold temperatures - we do not want to thrust our hand into a fire to try and judge how hot it is!... similarly, we do not want to leave our hand exposed in the middle of Antartica to check how cold it is, it is advisable to stay covered up! Also, we cannot touch everything, or sometimes even get close, to make a judgement of the objects temperature - this might range from wanting to know the temperature of the lava in an inaccessible caldera (the big mountain bowl that can be formed as part of a volcano) to wanting to know the temperature of a star that is thousands of light years away.

So how do we try and overcome these limitations? We use measuring instruments called thermometers. The word thermometer originates from the Greek language with thermos = hot, meter = measure, so a thermometer is a device "to measure how hot something is".

As well as a thermos flask, there are many words containing "thermos" such as thermoplastics (plastics that can be molded using heat). Also, the name of many measuring instruments contain the word "meter" such as a voltmeter (an instrument for the electrical measurement of voltage).

Note that in UK English (and Australian) the measurement of length is the "metre" (the "r" comes before the "e") which distinguishes its use from "meter" (with the "r" after the "e") meaning a measuring device. However, in US English both are spelt "meter".

## Thermometers

Thermometers come in a variety of forms. There are two that might be familiar to you. A glass thermometer containing a liquid (usually an alcohol, most commonly ethanol) and an in ear thermometer (often used on babies but also on children and adults to determine their core body temperature).

It used to be far more common for a glass thermometer to contain mercury. However, mercury is a toxic substance and if you have any mercury thermometers at school, you would be advised to replace them with alcohol thermometers, digital thermometers or even an infrared thermometer - if you can, you might want some of each as they are each most useful in different situations.

Why are they useful in different situations?... well, how are we going to measure the temperature of something... let's consider a hot cup of tea and an alcohol thermometer. How would you use the thermometer to measure the temperature?... would you quickly dip it in the tea and then remove it, looking at the termperature shown on the gauge? You likely have a sense that this would not work. Why?

Let's go back to the example of putting our hands into a bowl of water. If the water feels slightly warm (or cold) and we leave our hands in there, after a while the water will feel "normal". Our hands will be the same temperature as the water, and so we do not "feel" the temperature of the water - with the way we sense temperature it is not quite that simple but from this experience you get the idea. We need to leave the thermometer in the tea long enough for it to reach the same temperature as the tea - we refer to this as reaching thermal equilibrium.

Before looking more closely at how thermometers work. We'll consider how we can even have a consistent definition of temperature, because the concept of thermal equilibrium is central to this definition.

## Definition of Temperature (Thermal Equilibrium and the Zeroth Law of Thermodynamics)

So lets say we have a bottle of water. It is said to be in thermal equilibrium with itself if there is no net (overall) flow of heat from one part of the bottle to another. For example, if you were heating the bottle at the bottom, so more heat was flowing from the bottom of the bottle to the top, than vice versa, then the bottle would not be in "thermal equilibrium". Equally we could say the bottle is in thermal equilibrium with itself if it has one uniform temperature.

Now imagine we have a bottle of water in a room which is warmer than the air in the room. For this discussion it is important that it is a bottle and not, for example, a bowl. When we are discussing thermal equilibrium we are discussing the exchange of heat between "systems" (the two systems here being the bottle and the air). If we had a bowl of water, some of the water could evaporate (water moleculres could leave the water and go into the air) or if the bowl was very cold, water might condense from the air into the bowl (water melecules in the air could clump together and form droplets in the bowl). This would be exchanging matter, not just heat.

So our bottle and air exchange heat. As the bottle is at a higher temperature more heat will flow from the bottle to the air than from the air to the bottle. So the temperature of the air will rise very slightly (the room is big) and the temperature of the bottle will fall. At some point they will be exchanging the same amount of heat. At this point they are in thermal equilibrium and we say they are the same temperature.

Now, the fact that this is not quite enough to define temperature is a subtle point. The Law that is associated with the extra, slightly more complicated requirement, is called the Zeroth Law of Thermodynamics (remember thermo = heat and dynamics = motion... so thermodynamics = the motion of heat). It is called the Zeroth Law because they had already named the First, Second etc. Laws and only then realised they were missing something... and had to go back and add a Zeroth Law... that is a clear indication that it is not obvious that we need it!

So lets say we have two bottles of water, Bottle A and Bottle B. They are some distance apart. Bottle A and Bottle B both reach thermal equilibrium with C, the air in the room. So each of the bottles is at the same temperature as the room. For temperature to have a consistent meaning, if we put the bottles together, we would expect them to be in thermal equilibrium with each other i.e. the heat going from bottle A to B would be the same as the heat going from bottle B to A. There is no net (overall) flow of heat from one bottle to the other.

So, the zeroth Law is:

If A is in thermal equilibrium with C, and B is in thermal equilibrium with C, then A and B are in thermal equilibrium.

Another way of saying this is:

If A is the same temperature as C, and B is the same temperature as C, then A and B are the same temperature.

To see how this is important in relation to using a thermometer. Imagine that C is a thermometer. If we use C to measure the temperature of the water in bottle A, and get a reading of "20" (on some scale). Then we use the thermometer to measure the water in bottle B and we also get a reading of "20" then, to be a useful measure, we would want that to mean that A and B are in the same "state", that they have the same temperature, if we brought them together they would be in thermal equilibrium (no net flow of heat). So the termperature of an object defines something about the state of that object.

For the teacher, or interested students: The definition of thermal equilibrium, along with the Zeroth Law, defines temperature mathematically as an equivalence relation - thermal equilibrium is reflexive and symmetric, the Zeroth Law adds the property of temperature being transitive, to complete the requirements of an equivalence relation.

Unfortunately the statement in the Study Design fails to suitably describe the Zeroth Law (see the end of this page for a cpoy of the dot point) - I would suggest the Study Design drop the Zeroth Law and just focus on thermal equilibrium, or correct the dot point.

## How Thermometers Work

Many thermometers work by being put in thermal equilibrium with what they are measuring. There are also other, equivalent ways to measure temperature. For example we'll discuss how the infrared thermometer works in the climate section. Here we'll concentrate on thermometers that use thermal equilibrium, so this is thermometers like the glass thermometers that might contain mercury or alcohol, or the digital thermometers which have a probe which you put into the object similar to a glass thermometer or put in contact with the object, like an in-ear thermometer.

An alcohol thermometer works on the premise that the volume of the alcohol changes with termperature. When it is warmer, it takes up more space, when it is colder, it takes up less space. So a very small amount of alcohol is enclosed in a glass tube. When the temperature rises the volume of the alcohol increases and so the level of the alcohol rises up the tube as it fills more of the tube. We can then put markings on the tube to compare readings from one time to another or one object to another.

We can add numbers to the scale to make it easy to say where on the scale the alcohol has reached. We can then use these numbers as the "temperature" of an the object we are measuring i.e. the bowl of water in which we have immersed the thermometer.

But we would like to be able to compare the reading on one thermometer with the reading of another thermometer. We need an agreed scale so we can "calibrate" all thermometers - when one thermometer reads "10" it means the same thing as "10" on a different thermometer. We need an agreed temperature scale.

## Temperature Scales

To provide a consistent measure of something's temperature we can assign an agreed number to a particular temperature. In general for things that are hotter, we assign a higher number. Something that is colder, has a lower number. Historically, people have assigned numbers in different ways. The Celsius scale is one such scale.

### Celsius Scale

On the Celsius scale the temperature at which water freezes is labelled 0 (read as "zero degrees Celsius" or "zero degrees C", for short) and the temperature at which water boils is 100. To indicate that we are using the Celsius scale, we use the symbol "°C" which can be read as "degree Celsius". So the melting point of water is 0 °C ("zero degrees Celsius" or "zero degrees C", for short).

You are quite likely familiar with the Celsius scale. It is the scale we use for the weather in Australia - from a cold winter's day on which the temperature may be in single digits, just 1 or 2°C (or even below zero, in some places) to the height of summer where it may reach temperatures over 40°C.

However, the VCE Physics course (and hence this book) will usually use the units defined as part of the "International System of Units" (otherwise known as SI units, where SI is short for "Système International d'Unités"). Throughout this book, as we discuss physical quantities such as temperature, time, length and mass we will introduce the relevant SI units.

The SI is managed by the "Bureau International des Poids et Mesures" (BIPM) which, in English, means the International Bureau of Weights and Measures. The BIPM has its headquarters in France. This is why the BIPM and its associated work (like SI) have french names. See Appendix A : SI Units for more details on SI and the BIPM.

The SI unit for temperature is the "kelvin" (the name starts with a lowercase letter) and the symbol for the unit is "K" (an uppercase letter).

Using the correct names and symbols for units shows care, as well as an understanding of their history and use. So, correctly referring to the "kelvin" scale (starting the name with "k", and not "K") is important, even though it does not change what you are saying. Also, if you want to write zero kelvin and you write "0 k" when you should write "0 K" you could cause misunderstanding and confusion. When using units "k" is short for "kilo" indicating "thousands" of something - as in "km" (kilometres) meaning 1000 m. Again, you can see Appendix A : SI Units for more information about the conventions on the use of upper and lowercase letters in the names of, and symbols for, units - as well as other information, such as the use of letters such as "k" to mean some multiple of the unit.

### Kelvin Scale

The SI unit of temperature is the kelvin, symbol K. The melting point of water is 273.16K.

### Other Temperature Scales

There have been a number of temperature scales used in the past. However, currently, the Farenheit scale is the only scale in common use other than the kelvin and degree Celsius scales.

## Relevant dot points from the Study Design

• convert temperature between degrees Celsius and kelvin
• describe the Zeroth Law of Thermodynamics as two bodies in contact with each other coming to a thermal equilibrium
• describe temperature with reference to the average kinetic energy of the atoms and molecules within a system