9th Class Physics · Punjab Board · Complete learning guide

Chapter 7Thermal Properties of Matter

Every topic, every MCQ and every exercise question, explained step by step in simple language. Written for the Punjab Board new-syllabus Physics book, English medium.

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What you will find inside

Part 1

Learn the chapter

10 topics with diagrams

Part 2

MCQs fully solved

24 MCQs with reasoning

Part 3

Short questions

15 exam-ready answers

Comprehensive questions

10 detailed long answers

Formulas, key terms, test

On their own page:Chapter 7 MCQs Chapter 7 Short Questions Chapter 7 Long Questions Chapter 7 Numericals

How to use this guide

Read Part 1 slowly. Do the worked examples yourself on paper, then compare.
Try each MCQ before opening its answer, then read why the wrong options are wrong.
Learn the short answers in your own words, then do the numericals without looking.
Finish with the self-test in Part 7. A wrong answer tells you which topic to read again.

Part 1of 7

Learn the Chapter

Read this first. Everything in the exercises comes from these topics.

1Kinetic molecular theory of matter
2Plasma: the fourth state of matter
3Temperature, heat and internal energy
4Thermometers and thermometric properties
5The liquid-in-glass thermometer
6Fixed points and the three temperature scales
7Converting between the scales
8Marking a scale on an ungraduated thermometer
9Sensitivity, range and linearity
10Clinical and thermocouple thermometers

Topic 1

Kinetic molecular theory of matter

Definition

Kinetic molecular theory

Matter is made of very small particles (molecules) that are always moving. Their motion may be vibrational, rotational or linear (translational).

Definition

Intermolecular force

The force of attraction between molecules. It depends on the distance between them and becomes weaker as the distance increases.

Arrangement of molecules in a solid, a liquid and a gas.

	Solid	Liquid	Gas
Intermolecular force	very strong	weaker	very weak
Spacing	very close, fixed positions	close, can slide over each other	far apart
Motion	vibrate about mean positions	move about at random, sliding past each other	move freely at random in all directions
Shape	definite	takes the shape of the container	no definite shape
Volume	definite	definite	no definite volume (fills the container)

Remember

Solids keep their shape because strong forces lock the molecules in place. Gases fill any container because their molecules are far apart and hardly attract each other.

Topic 2

Plasma: the fourth state of matter

Definition

Plasma

A gas in which most atoms are ionised, so it contains positive ions and free electrons in about equal numbers. Because of the free charges, plasma conducts electricity.

Heating a gas to a very high temperature (or passing a strong electric current through it) knocks electrons out of its atoms. Its properties are then so different from those of an ordinary gas that it is called the fourth state of matter.

Where plasma is found	Why
The Sun and other stars	Their very high temperature ionises the atoms
Lightning (its early "streamers")	Ionised air forms a conducting path
Neon signs, discharge tubes, plasma TVs	Electric current passing through the gas ionises it

Exam tip

The kinetic molecular theory also applies to plasma: its ions and electrons are in constant random motion, like the molecules of a gas.

Topic 3

Temperature, heat and internal energy

Definition

Temperature

The degree of hotness or coldness of a body. It is the physical quantity that decides the direction in which thermal energy flows. In terms of molecules, it is a measure of the average kinetic energy of the molecules.

Definition

Heat

The energy that is transferred from one body to another because of the difference in their temperatures. Heat is energy in transit.

Definition

Internal energy

The sum of the kinetic and potential energies of all the molecules of a body.

Heat flows from the hotter body to the colder one until their temperatures are equal (thermal equilibrium).

When a substance is heated, its molecules move more vigorously; their average kinetic energy rises and so does its temperature.

Heat	Internal energy	Temperature
Energy moving from hot to cold	Energy stored in the molecules	Degree of hotness
Exists only while it flows	A body always has it	Decides which way heat flows
Unit: joule (J)	Unit: joule (J)	Units: K (SI), °C, °F

Check your book

A hot body does not "contain heat". It contains internal energy; the word heat is used only for energy that is actually moving from a hotter to a colder body.

Remember

Touching a cold surface, energy flows from your hand to the surface; "cold" does not flow into your hand.

Topic 4

Thermometers and thermometric properties

Touch can tell roughly whether something is hot or cold, but it cannot measure temperature. For that we need a thermometer.

Definition

Thermometer

An instrument that measures temperature, using a property of a substance that changes steadily with temperature.

Definition

Thermometric property

A property of a substance that changes appreciably and regularly with temperature, so it can be used to measure temperature.

Thermometric property	Thermometer that uses it
Expansion of a liquid	Liquid-in-glass (mercury or alcohol) thermometer
Pressure of a fixed mass of gas	Constant-volume gas thermometer
Resistance of a wire	Platinum resistance thermometer
Current between two junctions of different metals	Thermocouple thermometer

A good thermometric liquid

is visible (not colourless)
is a good conductor of heat, so it responds quickly
expands uniformly (linearly)
has a large expansivity
has a low freezing point and a high boiling point
does not wet the glass
does not evaporate easily

Topic 5

The liquid-in-glass thermometer

Mercury-in-glass thermometer: a thin-walled bulb of mercury, a narrow uniform capillary tube and a linear scale. Here it reads 38 °C.

Construction and working

A thin-walled glass bulb at one end holds the liquid (mercury or alcohol).
A narrow capillary tube of uniform bore runs from the bulb, with the air removed above the liquid.
A thick glass stem protects the tube and acts as a lens, making the thread look wider.
On heating, the liquid expands and moves up the tube as a thread; the end of the thread is read on the scale.

Mercury	Alcohol
Opaque and shiny: easy to see	Colourless: must be coloured with a dye
Good conductor: quick response	Poorer conductor
Does not wet glass	Wets glass
Freezes at −39 °C, boils at 357 °C: long range	Freezes at about −112 °C, boils at 78 °C: good for very low temperatures
Smaller expansivity	Expands about six times as much as mercury: more sensitive

Remember

Water is not used: it expands unevenly (it even contracts between 0 °C and 4 °C), it is colourless and it wets glass.

Topic 6

Fixed points and the three temperature scales

Definition

Fixed points

Two standard temperatures used to mark a thermometer scale. Lower fixed point (ice point): the melting point of pure ice. Upper fixed point (steam point): the temperature of steam over pure water boiling at standard atmospheric pressure.

The same two fixed points on the Fahrenheit, Celsius and Kelvin scales.

Scale	Ice point	Steam point	Divisions between them
Celsius (centigrade)	0 °C	100 °C	100
Fahrenheit	32 °F	212 °F	180
Kelvin (absolute)	273 K	373 K	100

Definition

Absolute zero

The lowest possible temperature, 0 K = −273.15 °C (taken as −273 °C in calculations). It is the zero of the Kelvin scale, so the Kelvin scale has no negative values.

Celsius and Fahrenheit are used in daily life; the Kelvin scale is the SI scale used in science. One kelvin is the same size as one Celsius degree; one Celsius degree equals 1.8 Fahrenheit degrees.

Topic 7

Converting between the scales

A temperature is the same fraction of the way from the ice point to the steam point on every scale:

(T_C − 0) ÷ 100 = (T_F − 32) ÷ 180 = (T_K − 273) ÷ 100

T_F = 1.8 T_C + 32

Celsius to Fahrenheit (1.8 = 9/5)

T_C = (T_F − 32) ÷ 1.8

Fahrenheit to Celsius (= 5/9 × (T_F − 32))

T_K = T_C + 273

Celsius to Kelvin; T_C = T_K − 273

Worked exampleHow much is 30 °C on the Fahrenheit and Kelvin scales? (Solved Example 7.1)

T_F = 1.8 × 30 + 32 = 54 + 32 = 86 °F.
T_K = 30 + 273 = 303 K.

Answer86 °F and 303 K

Worked exampleConvert 98.6 °F, normal body temperature, to Celsius.

T_C = (98.6 − 32) ÷ 1.8 = 66.6 ÷ 1.8.

Answer37 °C (310 K)

Exam tip

−40 °C = −40 °F. If an answer for °F is less than −40 when °C was positive, you have used the formula the wrong way round.

Topic 8

Marking a scale on an ungraduated thermometer

Ice point and steam point marked on a plain thermometer; the thread stands a length l above the ice point.

Put the bulb in melting ice; mark where the thread stops: the ice point (0 °C).
Put it in steam over boiling water; mark the steam point (100 °C).
Measure the distance L between the two marks; divide it into 100 equal parts.
If the thread later stands a length l above the ice mark, the temperature is:

T_C = (l ÷ L) × 100

l = length above the ice point, L = length from ice point to steam point

Worked exampleThe fixed points are 192 mm apart and the thread is 67.2 mm above the ice point. (Numerical 7.5)

T = (67.2 ÷ 192) × 100.

Answer35 °C

Topic 9

Sensitivity, range and linearity

Definition

Sensitivity

The ability of a thermometer to detect a small change in temperature. A thermometer marked every 0.1 °C is more sensitive than one marked every 1 °C.

Definition

Range

The span of temperature, from lowest to highest, that the thermometer can measure. A clinical thermometer: about 35–42 °C; a laboratory thermometer: −10 °C to 110 °C.

Definition

Linearity

Equal changes in temperature give equal changes in the reading over the whole range, so the scale marks are evenly spaced.

Quality	How the design improves it
Sensitivity	Thin-walled bulb (heat reaches the liquid quickly); a small amount of liquid; a narrow capillary (a small expansion moves the thread a long way); alcohol, which expands more
Range	Choice of liquid: mercury −39 °C to 357 °C; alcohol down to about −112 °C
Linearity	A tube of uniform bore and a liquid that expands uniformly

Remember

A narrow capillary makes a thermometer more sensitive; a thin bulb makes it respond more quickly.

Topic 10

Clinical and thermocouple thermometers

Clinical thermometer

Clinical thermometer: short range 35–42 °C, marked every 0.1 °C, with a constriction near the bulb.

Used to measure the temperature of the human body (normal 37 °C, 98.6 °F).
Short range, about 35–42 °C, so the scale can be marked in 0.1 °C steps (very sensitive).
A constriction (kink) near the bulb breaks the thread when the thermometer is taken out, so the reading stays until it is shaken down.

Thermocouple thermometer

Thermocouple: two different metals joined at two junctions; a temperature difference between the junctions drives a current through the meter.

Two wires of different metals (for example copper and iron) are joined at two junctions.
One junction is kept cold (in ice); the other is placed in the hot body.
The temperature difference produces a small current, read on a galvanometer calibrated in °C.
The junction is tiny, so it responds very quickly; it can measure from about −200 °C to over 1000 °C, for example in furnaces and engines.

Exam tip

A thermometer reads its own temperature. It gives the right reading only after it has reached thermal equilibrium with the body.

End of Part 1Next: Part 2 · MCQs fully solved ↓

Part 2of 7

MCQs Fully Solved

Try each one first: tap an option to check it, then read the reasoning and why the others are wrong.

Only the mcqs on one page →

A note about the questions

The wording follows published solved exercises and every answer was re-checked by hand, so the wording or the order of options may differ slightly from your print.

Answered 0 of 24 · Correct 0

Set A: Textbook exercise 11 MCQs

The multiple-choice questions at the end of Chapter 7 in your book, in the book's option order.

Q7.1Kinetic Molecular Theory

How do the molecules in a solid behave?

Q7.2Kinetic Molecular Theory

What type of motion is of the molecules in a gas?

Q7.3Temperature and Heat

Temperature of a substance is:

Q7.4Temperature and Heat

Heat is the:

Q7.5Temperature Scales

In Kelvin scale, the temperature corresponding to the melting point of ice is:

Q7.6Temperature Scales

The temperature which has the same value on the Celsius and Fahrenheit scales is:

Q7.7Thermometers

Which one is a better choice for a liquid-in-glass thermometer? A liquid that:

Q7.8Thermometers

One disadvantage of using alcohol in a liquid-in-glass thermometer is that:

Q7.9Thermometers

Water is not used as a thermometric liquid mainly because it:

Q7.10Sensitivity, Range and Linearity

A thermometer has a narrow capillary tube so that it:

Q7.11Thermometers

Which thermometer is most suitable for recording a rapidly varying temperature?

Set B: More MCQs from this chapter 13 MCQs

Extra questions on the same ideas, of the kind set in board papers and class tests.

QB1Kinetic Molecular Theory

Plasma is called the fourth state of matter. It consists of:

QB2Kinetic Molecular Theory

The Sun and other stars are made of matter in which state?

QB3Temperature and Heat

The sum of the kinetic and potential energies of all the molecules of a body is called its:

QB4Temperature and Heat

Heat always flows from:

QB5Temperature Scales

The value of absolute zero on the Celsius scale is:

QB6Temperature Scales

On the Fahrenheit scale, the space between the ice point and the steam point is divided into:

QB7Temperature Scales

A temperature of 300 K on the Celsius scale is:

QB8Temperature Scales

A temperature of 50 °C on the Fahrenheit scale is:

QB9Temperature Scales

A change of temperature of 1 K is equal to a change of:

QB10Thermometers

The usual range of a clinical thermometer is:

QB11Thermometers

The narrow constriction (kink) near the bulb of a clinical thermometer:

QB12Thermometers

Mercury freezes at −39 °C. For measuring temperatures in very cold regions (below −39 °C) we use a thermometer filled with:

QB13Thermometers

A thermocouple thermometer works because:

End of Part 2Next: Part 3 · Short questions ↓

Part 3of 7

Short Questions

Exam-ready answers. Learn the meaning, then write them in your own words.

Only the short questions on one page →

Short Q 7.1

Why do solids have a fixed volume and shape according to the particle theory of matter?

Answer

In a solid the intermolecular forces are very strong. They hold the molecules at fixed positions, where the molecules can only vibrate about their mean positions. Since the molecules cannot move from place to place, a solid keeps a definite shape and a definite volume.

Short Q 7.2

What are the reasons that gases have neither a fixed volume nor a fixed shape?

Answer

Gas molecules are far apart and the forces between them are very weak. They move freely and randomly in all directions and spread out to fill whatever container they are in. So a gas has no fixed shape and no fixed volume.

Short Q 7.3

Compare the spacing of molecules in the solid, liquid and gaseous states.

Answer

Solid	Liquid	Gas
Very close together, at fixed positions	Close together, but free to slide over each other	Far apart
Strongest forces	Weaker forces	Very weak forces

Short Q 7.4

What is the effect of raising the temperature of a liquid?

Answer

Its molecules move faster and more vigorously, so their average kinetic energy increases. The liquid usually expands, and if heated enough the fastest molecules escape and it evaporates or boils.

Short Q 7.5

What is meant by temperature of a body?

Answer

Definition

Temperature

The degree of hotness or coldness of a body. It decides the direction of heat flow and is a measure of the average kinetic energy of its molecules. SI unit: kelvin (K).

Short Q 7.6

Define heat as 'energy in transit'.

Answer

Definition

Heat

The energy that is transferred from one body to another because of a temperature difference between them.

It is called energy in transit because it exists as heat only while it is flowing; once it reaches the colder body it becomes part of that body's internal energy.

Short Q 7.7

What is meant by thermometric property of a substance? Enlist some thermometric properties.

Answer

Definition

Thermometric property

A property of a substance that changes appreciably and regularly with temperature, so it can be used to measure temperature.

Volume (expansion) of a liquid: liquid-in-glass thermometer.
Pressure of a fixed mass of gas: gas thermometer.
Electrical resistance of a wire: platinum resistance thermometer.
Thermo-electric current: thermocouple.

Short Q 7.8

State the main scales used for the measurement of temperature.

Answer

Scale	Ice point	Steam point
Celsius (centigrade)	0 °C	100 °C
Fahrenheit	32 °F	212 °F
Kelvin (absolute)	273 K	373 K

Short Q 7.9

What is meant by sensitivity of a thermometer?

Answer

Definition

Sensitivity

The ability of a thermometer to detect small changes in temperature. A thermometer with marks 0.1 °C apart is more sensitive than one with marks 1 °C apart.

Short Q 7.10

What do you mean by the linearity of a thermometer?

Answer

Definition

Linearity

A direct proportional relationship between the change in temperature and the change in the scale reading over the whole range: equal rises in temperature move the thread by equal lengths.

Short Q 7.11

What makes the scale reading of a thermometer accurate?

Answer

The scale must be linear: equal changes in temperature must give equal increments on the scale, so the markings are evenly spaced over the whole range. This needs a capillary of uniform bore and a liquid that expands uniformly, like mercury.

Short Q 7.12

What does determine the direction of heat flow?

Answer

Temperature. Heat always flows from the body at higher temperature to the body at lower temperature, whatever their sizes, and stops when their temperatures become equal.

Short Q 7.13

Distinguish between heat and internal energy.

Answer

Heat	Internal energy
Energy transferred from a hot body to a cold body because of a temperature difference	Sum of the kinetic and potential energies of all the molecules of a body
Exists only while flowing (energy in transit)	Stored in the body all the time
Depends on a temperature difference	Depends on the temperature, mass and state of the body

Short Q 7.14

When you touch a cold surface, does cold travel from the surface to your hand or does energy travel from your hand to the cold surface?

Answer

Energy travels from your hand to the cold surface, because your hand is at the higher temperature. There is no such thing as "cold" flowing; the hand feels cold because it is losing energy.

Short Q 7.15

Can you feel your fever by touching your own forehead? Explain.

Answer

No, not reliably. The hand and the forehead are at nearly the same raised temperature, so the hand feels little difference. Touch only gives a rough idea of hot and cold and cannot measure temperature; a clinical thermometer is needed.

End of Part 3Next: Part 4 · Constructed response ↓

Part 4of 7

Constructed Response Questions

These test whether you really understand. Give a reason every time.

CRQ 7.1

Is kinetic molecular theory of matter applicable to the plasma state of matter? Describe briefly.

Answer

Yes. Plasma is an ionised gas made of positive ions and free electrons. Like the molecules of a gas, these particles are in constant random motion, and their average kinetic energy rises with temperature. So the kinetic molecular theory applies to plasma too.

CRQ 7.2

Why is mercury usually preferred to alcohol as a thermometric liquid?

Answer

It is opaque and shiny, so the thread is easy to see.
It is a good conductor, so it responds quickly to temperature changes.
It does not wet (stick to) the glass.
It expands uniformly, giving a linear scale.
It stays liquid from −39 °C to 357 °C, a long range; alcohol boils at only 78 °C.

Alcohol is used only for very low temperatures, below −39 °C, where mercury would freeze.

CRQ 7.3

Why is water not suitable for use in thermometers? Without calculations, guess the equivalent temperature of 373 K on the Celsius and Fahrenheit scales.

Answer

Water expands unevenly; between 0 °C and 4 °C it even contracts on heating.
It is colourless and hard to see.
It wets the glass.
It is a poor conductor, and its range (0–100 °C) is short.

373 K is the steam point, the boiling point of water: 100 °C = 212 °F.

CRQ 7.4

Mention two ways in which the design of a liquid-in-glass thermometer may be altered to increase its sensitivity.

Answer

Make the capillary tube narrower: the same small expansion of the liquid then moves the thread a longer distance.
Use a liquid that expands more, such as alcohol, or a larger bulb: more expansion for each degree. (A thin-walled bulb also makes the thermometer respond faster.)

CRQ 7.5

One litre of water is heated by a stove and its temperature rises by 2 °C. If two litres of water are heated on the same stove for the same time, what will be the rise in temperature?

Answer

The same stove for the same time gives the same amount of energy. Two litres have twice the mass, so the same energy is shared by twice as many molecules. The rise is half as much: 1 °C.

ΔT ∝ 1 ÷ mass for the same energy

CRQ 7.6

Why are there no negative numbers on the Kelvin scale?

Answer

The Kelvin scale starts at absolute zero (0 K = −273.15 °C), the lowest temperature possible, where the molecules have the least possible energy. Nothing can be colder, so there is nothing below 0 K to label with a negative number.

CRQ 7.7

Comment on the statement: "A thermometer measures its own temperature."

Answer

The statement is correct. When a thermometer is put in contact with a body, heat flows until the two reach thermal equilibrium, the same temperature. The reading shows the temperature of the thermometer's own liquid, which by then equals that of the body. That is why we wait a minute before reading it.

CRQ 7.8

There are various objects made of cotton, wood, plastic, metals, etc. On a winter night, compare their temperatures with the air temperature by touching them with your hand.

Answer

If they have been in the room for a long time, they are all at the same temperature as the air.

They feel different because they conduct heat away from the hand at different rates. Metal is a good conductor and takes energy from the hand quickly, so it feels coldest. Cotton, wood and plastic are poor conductors and feel warmer, though their temperature is the same.

CRQ 7.9

Which is greater: an increase in temperature of 1 °C or one of 1 °F?

Answer

1 °C is greater. Between the ice and steam points there are 100 Celsius degrees but 180 Fahrenheit degrees, so 1 °C = 180 ÷ 100 = 1.8 °F.

CRQ 7.10

Why would you not expect all the molecules in a gas to have the same speed?

Answer

Gas molecules move at random and keep colliding with each other and the walls. In each collision some molecules gain energy and others lose it, so at any moment they have different kinetic energies and different speeds. Temperature depends on their average kinetic energy.

CRQ 7.11

Does it make sense to talk about the temperature of a vacuum?

Answer

No. Temperature measures the average kinetic energy of molecules. A perfect vacuum has no molecules, so there is nothing whose motion could give it a temperature.

Good to know

A thermometer placed in space does show a reading, but that is the thermometer's own temperature, set by the radiation (from the Sun, for example) it absorbs and gives out.

CRQ 7.12

Comment on the statement: "A hot body does not contain heat."

Answer

The statement is correct. A body contains internal energy, the kinetic and potential energies of its molecules. Heat is the name for energy only while it is moving from a hotter body to a colder one. So a hot body has a lot of internal energy, not "a lot of heat".

CRQ 7.13

Discuss whether the Sun is matter.

Answer

Yes. The Sun has mass and occupies space, so it is matter. It is in the plasma state, the fourth state of matter: its very high temperature has ionised its gases into positive ions and free electrons.

End of Part 4Next: Part 5 · Comprehensive questions ↓

Part 5of 7

Comprehensive (Long) Questions

Long answers, explained in full with headings. Learn the structure: definition, explanation, diagram or table, example.

Only the long questions on one page →

Set A: Textbook comprehensive questions 5 questions

The long questions at the end of the chapter in your book.

Long Q 7.1

Describe the main points of the particle theory of matter which differentiate solids, liquids and gases.

Answer

Kinetic molecular theory

Matter is made of very small particles called molecules.
The molecules are always moving: vibrating, rotating or moving in straight lines.
Molecules attract each other with intermolecular forces, which weaken as the distance increases.
The faster the molecules move, the higher the temperature.

Diagram

Molecules in a solid, a liquid and a gas.

Solids

The forces are so strong that the molecules are held at fixed positions; they only vibrate about them. So solids have a definite shape and volume.

Liquids

The forces are weaker and cannot hold the molecules in place; they slide over each other at random. A liquid has a definite volume but no definite shape: it flows and takes the shape of its container.

Gases

The molecules are far apart, the forces are very weak, and they move freely in all directions. A gas has neither a definite shape nor a definite volume.

Plasma

At very high temperatures a gas becomes ionised (positive ions and free electrons). This is plasma, the fourth state of matter; it conducts electricity.

	Solid	Liquid	Gas
Forces	strong	weaker	very weak
Motion	vibration	sliding	free random
Shape / volume	fixed / fixed	not fixed / fixed	not fixed / not fixed

Long Q 7.2

What is temperature? How is it measured? Describe briefly the construction of a mercury-in-glass thermometer.

Answer

Temperature

Definition

Temperature

The degree of hotness or coldness of a body; the quantity that decides the direction of heat flow. In molecular terms, a measure of the average kinetic energy of the molecules.

Measurement

Temperature is measured with a thermometer, which uses a thermometric property: a property that changes regularly with temperature, such as the expansion of a liquid.

Diagram

Mercury-in-glass thermometer.

Construction

A thin-walled glass bulb at the bottom is filled with mercury.
A narrow capillary tube of uniform bore rises from it; the air above the mercury is removed and the top is sealed.
A thick glass stem around the tube protects it and magnifies the thread.
A scale is marked using the ice point and the steam point.

Working

When the bulb is heated, the mercury expands and rises up the capillary as a thread. The end of the thread shows the temperature on the scale. Mercury is opaque and silvery, so it is easy to read.

Conclusion

Mercury is used because it is easy to see, responds quickly, does not wet glass and stays liquid from −39 °C to 357 °C.

Long Q 7.3

Compare the three scales used for measuring temperature.

Answer

Fixed points

Every scale uses two fixed points: the ice point (melting pure ice) and the steam point (steam over pure water boiling at standard atmospheric pressure).

Diagram

Fahrenheit, Celsius and Kelvin scales side by side.

Celsius scale

Ice point 0 °C, steam point 100 °C; the gap is divided into 100 equal parts, each 1 °C. Used in daily life.

Fahrenheit scale

Ice point 32 °F, steam point 212 °F; the gap is divided into 180 equal parts, each 1 °F. Used in daily life, for example for body temperature (98.6 °F).

Kelvin scale

Ice point 273 K, steam point 373 K, 100 divisions, so 1 K is the same size as 1 °C. Its zero is absolute zero, −273.15 °C, the lowest possible temperature, so it has no negative values. It is the SI scale used in science.

Relations

T_F = 1.8 T_C + 32; T_K = T_C + 273

Scale	Ice point	Steam point	Divisions	Zero
Celsius	0	100	100	ice point
Fahrenheit	32	212	180	arbitrary
Kelvin	273	373	100	absolute zero

Worked example30 °C on the other scales

T_F = 1.8 × 30 + 32 = 86 °F.
T_K = 30 + 273 = 303 K.

Answer86 °F, 303 K

Long Q 7.4

What is meant by sensitivity, range and linearity of thermometers? Explain with examples.

Answer

Sensitivity

Definition

Sensitivity

The ability of a thermometer to detect small changes in temperature.

Example: a thermometer marked in 1 °C steps reads to 1 °C; one marked in 0.1 °C steps (a clinical thermometer) is more sensitive and more precise.

Range

Definition

Range

The span of temperature, from low to high, over which a thermometer can measure.

Example: a clinical thermometer has a short range, 35–42 °C; a laboratory thermometer measures from −10 °C to 110 °C. The liquid sets the limits: mercury freezes at −39 °C and boils at 357 °C.

Linearity

Definition

Linearity

Equal changes in temperature give equal changes in the reading over the whole range.

Example: on a mercury thermometer the marks are evenly spaced, because mercury expands uniformly in a tube of uniform bore. Water could not give a linear scale because it expands unevenly.

Quality	Question it answers
Sensitivity	How small a change can it show?
Range	How low and how high can it go?
Linearity	Are the marks evenly spaced?

Long Q 7.5

Explain how the parameters mentioned in question 7.4 are improved in the structure of a liquid-in-glass thermometer.

Answer

Diagram

The parts that decide sensitivity, range and linearity.

Improving sensitivity

Thin-walled bulb: heat passes quickly through the glass to the liquid.
Mercury, a metal, is a good conductor and responds quickly.
Small amount of liquid heats up quickly.
Narrow capillary: a small expansion moves the thread a long way.
Alcohol expands about six times as much as mercury, so it can be used for greater sensitivity.

Improving linearity

The capillary tube has a uniform bore, so equal expansions of the liquid give equal lengths of thread, and mercury expands uniformly. The scale marks are then evenly spaced.

Improving range

Mercury stays liquid from −39 °C to 357 °C, a long range. For very low temperatures alcohol is used, because it freezes at about −112 °C. A longer tube also gives a longer range.

Conclusion

Narrow bore and thin bulb for sensitivity; uniform bore for linearity; the choice of liquid for range.

Set B: More important long questions 5 questions

Long questions often set in board papers from this chapter, answered in the same full style.

Imp. LQ 1

Derive the relations between the Celsius, Fahrenheit and Kelvin scales.

Answer

Idea

A given temperature lies the same fraction of the way from the ice point to the steam point on every scale.

The same temperature on three scales.

Celsius and Fahrenheit

Fraction on Celsius: (T_C − 0) ÷ (100 − 0) = T_C ÷ 100.
Fraction on Fahrenheit: (T_F − 32) ÷ (212 − 32) = (T_F − 32) ÷ 180.
Equating: T_C ÷ 100 = (T_F − 32) ÷ 180.
So T_F = (180 ÷ 100) T_C + 32 = 1.8 T_C + 32, and T_C = (T_F − 32) ÷ 1.8.

Celsius and Kelvin

Fraction on Kelvin: (T_K − 273) ÷ 100.
Equating with T_C ÷ 100: T_K − 273 = T_C.
So T_K = T_C + 273.

T_F = 1.8 T_C + 32; T_K = T_C + 273

Worked example25 °C

T_F = 1.8 × 25 + 32 = 77 °F.
T_K = 25 + 273 = 298 K.

Answer77 °F, 298 K

Imp. LQ 2

Differentiate between heat, temperature and internal energy.

Answer

Internal energy

Definition

Internal energy

The sum of the kinetic and potential energies of all the molecules of a body. It depends on the mass, the temperature and the state of the body.

Temperature

Definition

Temperature

The degree of hotness or coldness; a measure of the average kinetic energy of the molecules. It decides the direction of heat flow.

Heat

Definition

Heat

Energy transferred from a hotter body to a colder body because of their temperature difference: energy in transit.

Diagram

Heat flows from hot to cold until the temperatures are equal.

Example

A bathtub of warm water has more internal energy than a cup of boiling tea (many more molecules), yet if the cup is put in the bath, heat flows from the tea to the water, because the tea is at the higher temperature.

Heat	Temperature	Internal energy
energy in transit	degree of hotness	energy stored
J	K, °C, °F	J
flows because of ΔT	average KE	total KE + PE

Imp. LQ 3

Describe the construction and use of a clinical thermometer.

Answer

Use

A clinical thermometer measures the temperature of the human body. Normal body temperature is 37 °C (98.6 °F).

Diagram

Clinical thermometer with its constriction.

Construction

A small thin-walled bulb of mercury and a very narrow capillary tube.
Short range, about 35–42 °C, marked in 0.1 °C steps, so it is very sensitive.
A constriction (narrow kink) in the capillary just above the bulb.
A thick glass stem shaped like a prism that magnifies the thread.

Working

The bulb is held under the tongue or in the armpit for about a minute.
The mercury expands and pushes past the constriction.
When the thermometer is removed, the mercury in the bulb contracts, but the thread breaks at the constriction and stays in place.
The maximum temperature can be read at leisure; then the thermometer is shaken to send the mercury back.

Precautions

Wash it in cold water, not hot (it would burst: the range ends at 42 °C).
Shake the mercury down before use.

Imp. LQ 4

What is a thermocouple thermometer? Describe its principle, construction and uses.

Answer

Principle

When two wires of different metals are joined at two junctions and the junctions are at different temperatures, a small electric current flows round the circuit. The bigger the temperature difference, the bigger the current (thermo-electric effect).

Diagram

Thermocouple with a hot and a cold junction.

Construction

Two wires of different metals, such as copper and iron, joined at both ends.
One junction kept at a fixed low temperature (melting ice); the other is the probe.
A galvanometer in the circuit, calibrated to read temperature.

Uses and advantages

Responds very quickly, because the junction is tiny: good for rapidly changing temperatures.
Wide range, from about −200 °C to over 1000 °C: furnaces, kilns, engines.
The reading can be recorded electrically and at a distance.

Imp. LQ 5

What are thermometric properties? Why is mercury used in thermometers? Compare mercury and alcohol as thermometric liquids.

Answer

Thermometric property

Definition

Thermometric property

A property that changes appreciably and regularly with temperature, such as the volume of a liquid, the pressure of a gas, the resistance of a wire or a thermo-electric current.

Qualities of a good thermometric liquid

visible
good conductor
uniform expansion
large expansivity
low freezing point and high boiling point
does not wet glass
does not evaporate easily

Mercury and alcohol compared

Property	Mercury	Alcohol
Visibility	opaque, shiny	colourless, needs dye
Conduction	good	poorer
Wets glass	no	yes
Freezing / boiling point	−39 °C / 357 °C	about −112 °C / 78 °C
Expansivity	smaller	about six times larger
Best for	ordinary and high temperatures	very low temperatures

Conclusion

Mercury is the usual choice; alcohol is used in very cold places.

End of Part 5Next: Part 6 · Numericals solved ↓

Part 6of 7

Numericals Solved Step by Step

Each numerical in the order you write it in the exam: Given Data, To Find, Formula, Calculation, Result.

Only the numericals on one page →

Numerical 7.1

Normal human body temperature is 98.6 °F. Convert it into the Celsius scale and the Kelvin scale.

Given Data

T_F = 98.6 °F

To Find

Formulas

T_C = (T_F − 32) ÷ 1.8

T_K = T_C + 273

Calculation

T_C = (98.6 − 32) ÷ 1.8 = 66.6 ÷ 1.8 = 37 °C.
T_K = 37 + 273 = 310 K.

Result

T_C = 37 °C; T_K = 310 K

Numerical 7.2

At what temperature would the Celsius and Fahrenheit thermometer readings be the same?

Given Data

T_C = T_F = T

To Find

Formula

T_F = 1.8 T_C + 32

Calculation

Put T_F = T_C = T: T = 1.8T + 32.
T − 1.8T = 32, so −0.8T = 32.
T = 32 ÷ (−0.8) = −40.

Result

T = −40 (−40 °C = −40 °F)

Numerical 7.3

Convert 5 °F to the Celsius and Kelvin scales.

Given Data

T_F = 5 °F

To Find

Formulas

T_C = (T_F − 32) ÷ 1.8

T_K = T_C + 273

Calculation

T_C = (5 − 32) ÷ 1.8 = −27 ÷ 1.8 = −15 °C.
T_K = −15 + 273 = 258 K.

Result

T_C = −15 °C; T_K = 258 K

Numerical 7.4

What is the equivalent temperature of 25 °C on the Fahrenheit and Kelvin scales?

Given Data

T_C = 25 °C

To Find

Formulas

T_F = 1.8 T_C + 32

T_K = T_C + 273

Calculation

T_F = 1.8 × 25 + 32 = 45 + 32 = 77 °F.
T_K = 25 + 273 = 298 K.

Result

T_F = 77 °F; T_K = 298 K

Numerical 7.5

The ice and steam points on an ungraduated thermometer are found to be 192 mm apart. What temperature will be on the Celsius scale if the length of the mercury thread is 67.2 mm above the ice point mark?

L = 192 mm from ice point to steam point; the thread is l = 67.2 mm above the ice point.

Given Data

distance between fixed points L = 192 mm
length above the ice point l = 67.2 mm

To Find

Temperature T_C

Formula

T_C = (l ÷ L) × 100

Calculation

T_C = (67.2 ÷ 192) × 100.
67.2 ÷ 192 = 0.35, so T_C = 35 °C.

Result

T_C = 35 °C

Note: Both lengths are in mm, so there is no need to change units: only their ratio matters.

Numerical 7.6

The length between the fixed points of a liquid-in-glass thermometer is 20 cm. If the mercury level is 4.5 cm above the lower mark, what is the temperature on the Fahrenheit scale?

L = 20 cm between the fixed points; the mercury is l = 4.5 cm above the lower mark.

Given Data

L = 20 cm
l = 4.5 cm

To Find

Temperature T_F

Formulas

T_C = (l ÷ L) × 100

T_F = 1.8 T_C + 32

Calculation

T_C = (4.5 ÷ 20) × 100 = 22.5 °C.
T_F = 1.8 × 22.5 + 32 = 40.5 + 32 = 72.5 °F.

Result

T_F = 72.5 °F

Note: Directly on the Fahrenheit scale: T_F = 32 + (4.5 ÷ 20) × 180 = 32 + 40.5 = 72.5 °F, the same answer.

End of Part 6Next: Part 7 · Revision & self-test ↓

Part 7of 7

Revision, Practice and Self-Test

Use this the night before the test.

One-page formula sheet

Celsius to Fahrenheit

T_F = 1.8 T_C + 32

Fahrenheit to Celsius

T_C = (T_F − 32) ÷ 1.8

Celsius to Kelvin

T_K = T_C + 273

Kelvin to Celsius

T_C = T_K − 273

General relation

T_C ÷ 100 = (T_F − 32) ÷ 180 = (T_K − 273) ÷ 100

Ungraduated thermometer

T_C = (l ÷ L) × 100

Same on C and F

−40 °C = −40 °F

Fixed points

0 °C = 32 °F = 273 K; 100 °C = 212 °F = 373 K

Absolute zero

0 K = −273.15 °C

Step sizes

1 K = 1 °C = 1.8 °F

Body temperature

37 °C = 98.6 °F = 310 K

Mercury range

−39 °C to 357 °C

Key definitions 13 terms

Kinetic molecular theory

Matter is made of very small particles (molecules) that are always moving. Their motion may be vibrational, rotational or linear (translational).

Intermolecular force

The force of attraction between molecules. It depends on the distance between them and becomes weaker as the distance increases.

Plasma

A gas in which most atoms are ionised, so it contains positive ions and free electrons in about equal numbers. Because of the free charges, plasma conducts electricity.

Temperature

Heat

The energy that is transferred from one body to another because of the difference in their temperatures. Heat is energy in transit.

Internal energy

The sum of the kinetic and potential energies of all the molecules of a body.

Thermometer

An instrument that measures temperature, using a property of a substance that changes steadily with temperature.

Thermometric property

A property of a substance that changes appreciably and regularly with temperature, so it can be used to measure temperature.

Fixed points

Absolute zero

The lowest possible temperature, 0 K = −273.15 °C (taken as −273 °C in calculations). It is the zero of the Kelvin scale, so the Kelvin scale has no negative values.

Sensitivity

The ability of a thermometer to detect a small change in temperature. A thermometer marked every 0.1 °C is more sensitive than one marked every 1 °C.

Range

The span of temperature, from lowest to highest, that the thermometer can measure. A clinical thermometer: about 35–42 °C; a laboratory thermometer: −10 °C to 110 °C.

Linearity

Equal changes in temperature give equal changes in the reading over the whole range, so the scale marks are evenly spaced.

Common mistakes to avoid

Adding 32 before multiplying by 1.8 when changing °C to °F.
Writing negative values on the Kelvin scale, or writing "°K" (the unit is just K).
Saying a hot body "contains heat": it contains internal energy.
Saying "cold flows into the hand": energy flows out of the hand.
Mixing up sensitivity (smallest change shown) and range (lowest to highest).
Thinking a narrow capillary makes a thermometer respond faster: that is the thin bulb; the narrow bore makes it more sensitive.
Calling the wetting of glass by alcohol an advantage.
Forgetting that Fahrenheit has 180 divisions, not 100.

Extra practice tap a question to see its answer

Convert 40 °C to °F.Show answer
1.8 × 40 + 32 = 104 °F
Convert 212 °F to °C.Show answer
(212 − 32) ÷ 1.8 = 100 °C
Convert 0 K to °C.Show answer
−273 °C
Convert 77 K to °C.Show answer
77 − 273 = −196 °C
Convert −10 °C to K and °F.Show answer
263 K and 14 °F
Convert 59 °F to K.Show answer
15 °C, so 288 K
The fixed points are 25 cm apart and the thread is 10 cm above the ice point. Find the temperature in °C.Show answer
(10 ÷ 25) × 100 = 40 °C
A thermometer's fixed points are 16 cm apart. Where will the thread be at 75 °C?Show answer
0.75 × 16 = 12 cm above the ice point
Which is larger, a rise of 10 °C or 15 °F?Show answer
10 °C = 18 °F, so 10 °C is larger
Why is alcohol used in thermometers in very cold places?Show answer
It freezes at about −112 °C; mercury freezes at −39 °C
What is the purpose of the constriction in a clinical thermometer?Show answer
It stops the mercury falling back, so the reading stays
Name the state of matter of the Sun.Show answer
Plasma
What decides the direction of heat flow?Show answer
Temperature: from higher to lower
Which thermometer suits a furnace at 900 °C?Show answer
A thermocouple (mercury boils at 357 °C)

Final self-test

Final self-test: all 24 MCQs, no answers

Give yourself 25 minutes. Pick one option for each question, then submit to see your score and which questions to revise. Any question you get wrong tells you which topic to read again.

End of Part 7Back to Part 1 ↑