# OCR AS/A Level Physics A

# Thermal physics

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## Introduction

### Overview

Delivery guides are designed to represent a body of knowledge about teaching a particular topic and contain:

- Curriculum Content: A clear outline of the content covered by the delivery guide
- Thinking Conceptually: Expert guidance on the key concepts involved, common difficulties students may have, approaches to teaching that can help students understand these concepts and how this topic links conceptually to other areas of the subject
- Thinking Contextually: A range of suggested teaching activities using a variety of themes so that different activities can be selected which best suit particular classes, learning styles or teaching approaches.

## Curriculum Content

### Overview

**Content (from A Level)**

**5.1 Thermal physics **

The aim of module 5 (Newtonian world and astrophysics) is to show the impact Newtonian mechanics has on physics. The microscopic motion of atoms can be modelled using Newton’s laws and hence provide us with an understanding of macroscopic quantities such as pressure and temperature.

This section sets out to provide knowledge and understanding of temperature, matter, specific heat capacity and specific latent heat with contexts involving heat transfer and change of phase (HSW1, 2, 5, 7). Experimental work can be carried out to safely investigate specific heat capacity of materials (HSW4). It also provides an opportunity to discuss how Newton’s laws can be used to model the behaviour of gases (HSW1) and significant opportunities for the analysis and interpretation of data (HSW5).

**5.1.1 Temperature**

(a) thermal equilibrium

(b) absolute scale of temperature (i.e. the thermodynamic scale) that does not depend on a property of any particular substance

(c) temperature measurements both in degrees Celsius (°C) and in kelvin (K)

(d) *T* (K) ≈ *θ* (°C) + 273.

**5.1.2 Solid, liquid and gas **

(a) solids, liquids and gases in terms of the spacing, ordering and motion of atoms or molecules

(b) simple kinetic model for solids, liquids and gases

(c) Brownian motion in terms of the kinetic model of matter and a simple demonstration using smoke particles suspended in air

(d) internal energy as the sum of the random distribution of kinetic and potential energies associated with the molecules of a system

(e) absolute zero (0 K) as the lowest limit for temperature; the temperature at which a substance has minimum internal energy

(f) increase in the internal energy of a body as its temperature rises

(g) changes in the internal energy of a substance during change of phase; constant temperature during change of phase.

**5.1.3 Thermal properties of materials **

(a) specific heat capacity of a substance; the equation *E* = *mc*Δ*θ*

(b) (i) an electrical experiment to determine the specific heat capacity of a metal or a liquid

(ii) techniques and procedures used for an electrical method to determine the specific heat capacity of a metal block and a liquid

(c) specific latent heat of fusion and specific latent heat of vaporisation; *E* = *mL*

(d) (i) an electrical experiment to determine the specific latent heat of fusion and vaporisation

(ii) techniques and procedures used for an electrical method to determine the specific latent heat of a solid and a liquid.

**5.1.4 Ideal gases**

(a) amount of substance in moles; Avogadro constant N_{A} equals 6.02 x 10^{2}^{3} mol^{–1 }

(b) model of kinetic theory of gases;

(c) pressure in terms of this model

(d) (i) the equation of state of an ideal gas *pV* = *nRT*, where *n* is the number of moles

(ii) techniques and procedures used to investigate PV = constant

(Boyle’s law) and \(\displaystyle \frac {P}{T}\) = constant

(iii) an estimation of absolute zero using variation of gas temperature with pressure

(e) the equation \(\displaystyle pV=\frac{1}{3}Nm\overline {c{^2}}\) where *N* is the number of particles (atoms or molecules) and \(\displaystyle \overline {c{^2}}\) is the mean square speed

(f) root mean square (r.m.s.) speed; mean square speed

(g) the Boltzmann constant; \(\displaystyle k = \frac {R}{N_{A}}\)

(h) \(\displaystyle pV=NkT\); \(\displaystyle \frac{1}{2}m\overline {c{^2}}=\frac{3}{2}kT\)

(i) internal energy of an ideal gas.

## Thinking Conceptually

### Overview

**Approaches to teaching the content **

This topic can be approached from various starting points. Students will have a variety of prior experiences of the content depending on the GCSE science courses they studied. Teachers may choose differing paths between the topics or within the topics themselves.

The spacing, ordering and motion of atoms and molecules as solids, liquids and gases will refer back to work in key stage 3 or earlier but will need sound reinforcement to ensure an understanding which underpins the remainder of the topic at A level and beyond. The understanding of energy transfers and change of phase will deepen the understanding from the earlier key stages.

Calculations, such as those in activity two, using specific heat capacity demonstrate the relationship between internal energy and temperature, whilst those involving specific latent heat support the understanding of changes in internal energy at the change of phase, with the transfer of energy to or from the material with no associated temperature change. Practical activity (PAG) 11.2 allows learners to determine specific heat capacity both by an electric means and/or a means based on the method of mixtures.

The most common teaching sequences for ideal gases (section 5.1.4) start either with the macroscopic measurements which can be made and related in simple mathematical form leading on to the kinetic theory, or the converse, dealing with the more abstract notion of kinetic theory and then observing how this underpins those macroscopic measurements of pressure, temperature and volume.

Combining the macroscopic and microscopic gas equations provides an example of how macroscopic measurements and modelling can provide estimates of microscopic quantities such as particle speeds.

It is important to emphasise to students both the random nature of the motion of individual particles in a gas and how, due to the large number of particles involved, making assumptions about this completely random motion can lead to models that account for predictable macroscopic behaviour. As is noted in the additional guidance, the assumptions made to support the kinetic theory are:

- large number of molecules in random, rapid motion
- particles (atoms or molecules) occupy negligible volume compared to the volume of gas
- all collisions are perfectly elastic and the duration of the collisions is negligible compared to the time between collisions
- negligible forces between particles except during collisions.

Considering the relevance of the effect each of these assumptions on simple systems, such as a balloon, if the collisions between particles were not perfectly elastic it could be argued that there would be an increase in temperature and if the particles have less kinetic energy after each collision there would be a reduction in pressure, which is not the case.

The basic macroscopic relationships can be demonstrated:

*PV* = constant (at constant temperature) using Boyle’s Law apparatus

*V α T* (at constant pressure) Charle’s Law, that volume reduces as temperature decreases can be demonstrated dramatically by collapsing a can or using the reduction in pressure in a conical flask to draw a hard-boiled egg into the flask, whilst more sober quantitative activities are detailed in CLEAPSS guide R231 “Gas laws: Experiments and Apparatus”.

*P α T* (at constant volume) using a constant volume gas thermometer can achieve a surprisingly accurate value for absolute zero, working with simple equipment in the school laboratory, as detailed in the CLEAPSS guide above and in Practical Activity (PAG) 8.1, available on OCR Interchange.

This activity also lends itself to the understanding of absolute zero as a concept and the nature of its measurement independent of the properties of any specific material.

The microscopic behaviour can be observed as Brownian motion, which was first documented in 1827, but not understood to be demonstrating the kinetic theory of atoms and molecules in constant movement. The work of Einstein and others in the early 1900s linked the observations of Brownian motion to the motion of atoms and molecules, the existence of which was still not fully established beyond doubt. Students may find it reassuring and interesting that Albert Einstein expressed his discomfort with the idea that completely random processes were behind the workings of the universe, with the comment recorded that “God does not play dice”, which can lead to some very interesting discussions, or act as a prompt to the memory of the study of this topic.

It is important to reinforce the point that the particles in a gas are behaving completely randomly even though, due to the large number of particles involved, the outcome of this random behaviour is a set of predictable rules. This may be referenced to radioactive decay, the other topic where the exact moment of decay for an individual nucleus is entirely unpredictable, yet a half-life can be calculated to accurately model the decay of several billion nuclei.

The derivation of the formula \(\displaystyle pV=\frac{1}{3}Nm\overline {c{^2}}\) is not required, but being able to derive, or at least knowledge of how it is derived, from first principles may aid understanding.

It is expected that learners will be able to link \(\displaystyle pV=\frac{1}{3}Nm\overline {c{^2}}\) and *pV =NkT* to derive = \(\displaystyle \frac{1}{2}m\overline {c{^2}}=\frac{3}{2}kT\)

The Boltzmann constant is used when considering molecules rather than moles in the context of the gas equations above, with the number of moles multiplied by molar gas constant (*nR*) being equal to the number of molecules multiplied by the Boltzmann constant (*Nk*).

Using the formula derived above, \(\displaystyle \frac{1}{2}m\overline {c{^2}}=\frac{3}{2}kT\), this theory can be extended to give the kinetic energy of a single molecule \(\displaystyle E = \frac {3}{2}kT\). Thus the random translational kinetic energy of an ideal gas is equivalent to its internal energy and directly proportional to its absolute temperature in kelvin.

**Common misconceptions or difficulties students may have **

Learners’ misconceptions in this topic begin with their understanding of temperature and its units which will pre-date their study of physics, and possibly any science, at school. Measurements in degrees Celsius (°C), and the idea of centigrade, are perceived as being fundamental rather than inferred from a measurement which is dependent on a property of a material.

There is also a tendency to blur the distinction between heat (measured in joule) and temperature, although changing the heat content of a body will change its temperature.

Even at A level there will be learners who do not see the need for melting ice to be in a beaker of water to obtain a reference zero degrees Celsius, assuming that ice itself exists only at zero rather than being able to exist at lower temperatures.

Learner activity one addresses some ideas of the creation of temperature scales and design factors affecting the operation of thermometers linking to energy transfer as well as concepts of precision and range of instruments.

Although learners are familiar with gases as a state of matter from earlier studies in science, they tend to have developed misconceptions such as gases having no significant mass. Most learners are unable to give a correct order of magnitude estimate of the mass of a given volume of air due to the effect of buoyancy on objects such as air filled balloons. The density of air is 1.3 kg m^{-3} so a balloon would contain a mass of air in the order of 2g. Try weighing an uninflated balloon and then inflated (or vice versa, although rapid deflation may cause the balloon to disintegrate).

Learners have encountered kinetic theory and possibly gas laws earlier in their education. Most are able to understand the particles in a box explanation of the cause of gas pressure; however, applying equations and mathematics to the model is difficult for most and may be best used as a demonstration of how assumptions can be made and a model derived as there is not a requirement for learners to demonstrate the derivation in the examination. Learner activity three is intended to give learners the opportunity to apply their knowledge in an unfamiliar scientific context with some element of synopticity.

### Interactive simulations

PhET Interactive Simulations, University of Colorado

An interesting interactive simulation allowing variation of pressure, volume and temperature capable of demonstrating Brownian motion, as well as the inter-relationship between pressure, volume and temperature.

Plus a straightforward computer model covering the basic relationships between temperature, pressure and volume.

### Gas laws: Equipment and apparatus

### Next Time questions

Paul Hewitt, Arbor Scientific, Free to download

These questions in the gases section address misconceptions and stimulate discussion:

“Weight of air”, “Balanced balls” and “Balanced Balloons” address the misconception that the “empty space” around us has no mass.

“Wood and Iron” and “Deep Glass” continue this theme with conceptual challenges.

“Air filled floating balloon” links gas pressure and volume with pressure in a liquid.

Similarly in the thermodynamics and thermal expansion section: “Helium Temperature” and “Twice as Hot” address absolute temperature.

### Energy

Teaching Advanced Physics, from the Institute of Physics

Episodes 600 to 603 on kinetic theory have background ideas along with activities and work-sheets for learners.

Episodes 607 and 608 have supporting information for Specific heat capacity and Specific latent heat.

## Thinking Contextually

### Overview

The range of contexts involving temperature, phases of materials (solid, liquid and gas), the thermal properties of materials and the behaviour of ideal gases is extensive.

At the simplest level the measurement of temperature in everyday situations based on properties of materials. Considering the use of a variety of thermometers in differing applications can lead to consideration of aspects of measurement such as range, precision, accuracy, linearity, response time and ease of use, linking to section 2.2.1 on measurement and uncertainties.

The properties of solids, liquids and gases have an immediate application in the use of materials around us, and complement the understanding of materials in section 3.4. In particular the application of the measurement of density and pressure can be applied to objects at different heights above earth’s surface or depths under the sea.

The thermal properties of materials provide significant opportunities for synoptic questions, linking specific heat capacity or specific latent heat to electrical energy, as in PAG 11.2. Other energy transfers can be considered and linked to increases or decreases in temperature, an example of which could be the temperature rise of a brake disc as a car is brought to a standstill.

Ideal gas behaviour can be related to balloons, with many text books using examples of fixed volume hot air balloons, balloons filled with a gas lighter than air and weather balloons whose volume changes with altitude. Other applications include the internal combustion engine, whose theory is not required by the specification, but for which the concept of work done on or by a gas is very pertinent, and addressed at a simple level in PAG 8.3 which asks learners to estimate the work done by a quantity of gas as its temperature is increased.

Whilst the Boltzmann constant is not apparent in such obvious concepts, but is the basis of many calculations relating to energy in chemical reactions and bridges the gap between the microscopic physics at atomic and molecular scale and the macroscopic physics of larger quantities of matter.

### Learner activity three: The refrigerator

### Different types of thermometer

ATP Ltd, Ashby-de-la-Zouch, Leicestershire

This page, and those linked from it, give an idea of the range of thermometer types available, liquid in glass, bi-metal strip, infra-red and thermocouple along with applications for each.

### Animated engines

Matt Keveney, Animated Engines

Simple animations showing the operation of a wide variety of engines from the earliest steam engines through to the four stroke petrol engine and jet propulsion.

### Learner activity one: Designing a liquid in a glass thermometer

As a practical activity it can be credited towards the Practical Endorsement, particularly as it is intended to be investigative.

The student sheet is provided in Word as an outline which can be amended to suit your particular requirements and the availability of equipment. Should you not have the curriculum time or equipment an alternative sheet allows for a class or homework based consideration of the factors involved.

Aim

- To consider factors affecting the design of liquid in glass thermometers
- To understand terminology of measurement

Specification

- 2.2.1(a) systematic and random errors
- 2.2.1(b) precision and accuracy
- 2.2.1(c) absolute and percentage uncertainties
- 5.1.1(a) thermal equilibrium
- 5.1.1(c) temperature measurements in degrees Celsius
- 5.1.3(a) specific heat capacity of a substance; the equation
*E*=*mc*Δ*θ*

Practical skills

- 1.2.1(a) apply investigative approaches and methods
- 1.2.1(b) safely and correctly use a range of practical equipment
- 1.2.1(d) make and record observations and measurements
- 1.2.1(e) keep appropriate records of experimental activities
- 1.2.1(f) present information and data in a scientific way
- 1.2.1(j) use a wide range of experimental and practical instruments, equipment and techniques
- 1.2.2(a) use of appropriate analogue apparatus
- 1.2.2(b) use of appropriate digital instruments

Apparatus

- Test tubes
- Boiling tubes
- Small conical flasks
- Medium conical flasks
- Capillary tube
- Glass tube
- Bungs to allow each combination of tube and container
- Food colouring
- Water baths (minimum 2)
- Ice
- Beakers (sufficiently large to accommodate each conical flask)
- Metre rules
- Electronic balance
- Bunsen burners
- Tripods and gauzes

Health and safety

- Having the glass tubes already fitted into the bungs reduces the time needed to complete this activity and reduces the risk of learners cutting themselves on broken glass
- Learners should be specifically advised to insert the tubes by putting pressure on the bung and not the tube
- Care when using Bunsen burners and associated equipment.

Setting the scene

The learners are challenged to ascertain the best combination of reservoir and expansion tube to make a liquid in glass thermometer to consider

a) Greatest precision for a temperature of 50°C

b) Being able to give a value between 20°C and 80°C

Expectations

Learners are likely to establish that:

1) A larger reservoir results in a larger volume of expansion

2) A larger volume of expansion gives greater discrimination of measurement

3) A wider bore in the glass tube gives a smaller difference in the position of the distance of the end of the column of coloured liquid after expansion

4) A wider bore reduces precision but increases the potential range of the thermometer

Learners may not consider that:

5) A larger reservoir will require more energy to raise its temperature to be in thermal equilibrium with the liquid being measured

6) The resulting temperature of the combined system with the liquid being measured and a large reservoir on the thermometer will be lower than if a smaller reservoir were used

Calibration and use

Learners may calibrate their thermometers using ice/water mixture, boiling water and/or water baths at two defined temperatures (say 40°C and 60°C). They can then calculate their scale and mark their tubes accordingly.

One water bath can be at a temperature between 45°C and 55°C, with learners asked to use their thermometer to determine its temperature.

### Learner activity two: The method of mixtures - Calculations involving specific heat capacity and specific latent heat

The student sheet contains the information needed to run this activity. The answers to the questions posed are given below for your use.

Question 1: 1750 J kg^{-1} K^{-1}

Question 2: 3500 J kg^{-1} K^{-1}

Question 3: Teachers can credit any reasonable explanation.

Question 4:

Energy required to melt ice | Energy from steam |

Ice from -4.0°C to 0°C; 50 x 4 x 2100,
Ice to liquid; 50 x 3.3 x 10 ^{5} | Condensing; m x 2.3x10^{6},
Cooling as water from 100 to 0°C; m x 4200 x 100 |

1.69x107 J | m x 2.72 x 10^{6} J |

Mass of steam = 6.2 kg

### Estimating absolute zero from gas pressure and volume

### Investigating the relationship between pressure and volume in gas

### Estimating the work done by a gas as its temperature increases

### Determining the specific heat capacity of a material

## Acknowlegements

### Overview

OCR’s resources are provided to support the teaching of OCR specifications, but in no way constitute an endorsed teaching method that is required by the Board and the decision to use them lies with the individual teacher. Whilst every effort is made to ensure the accuracy of the content, OCR cannot be held responsible for any errors or omissions within these resources. We update our resources on a regular basis, so please check the OCR website to ensure you have the most up to date version.

© OCR 2016 - This resource may be freely copied and distributed, as long as the OCR logo and this message remain intact and OCR is acknowledged as the originator of this work.