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# NCERT Textbook - Thermal Properties of Matter Class 11 Notes | EduRev

## Class 11 : NCERT Textbook - Thermal Properties of Matter Class 11 Notes | EduRev

``` Page 1

CHAPTER ELEVEN
THERMAL PROPERTIES OF MATTER
11.1  INTRODUCTION
We all have common-sense notions of heat and temperature.
Temperature is a measure of ‘hotness’ of a body. A kettle
with boiling water is hotter than a box containing ice. In
physics, we need to define the notion of heat, temperature,
etc., more carefully. In this chapter, you will learn what heat
is and how it is measured, and study the various proceses by
which heat flows from one body to another. Along the way,
you will find out why blacksmiths heat the iron ring before
fitting on the rim of a wooden wheel of a bullock cart and
why the wind at the beach often reverses direction after the
sun goes down. You will also learn what happens when water
boils or freezes, and its temperature does not change during
these processes even though a great deal of heat is flowing
into or out of it.
11.2  TEMPERATURE AND HEAT
We can begin studying thermal properties of matter with
definitions of temperature and heat. Temperature is a relative
measure, or indication of hotness or coldness. A hot utensil
is said to have a high temperature, and ice cube to have a
low temperature. An object that has a higher temperature
than another object is said to be hotter. Note that hot and
cold are relative terms, like tall and short. We can perceive
temperature by touch. However, this temperature sense is
somewhat unreliable and its range is too limited to be useful
for scientific purposes.
We know from experience that a glass of ice-cold water left
on a table on a hot summer day eventually warms up whereas
a cup of hot tea on the same table cools down. It means that
when the temperature of body, ice-cold water or hot tea in
this case, and its surrounding medium are different, heat
transfer takes place between the system and the surrounding
medium, until the body and the surrounding medium are at
the same temperature. We also know that in the case of glass
tumbler of ice cold water, heat flows from the environment to
11.1 Introduction
11.2 Temperature and heat
11.3 Measurement of
temperature
11.4 Ideal-gas equation and
absolute temperature
11.5 Thermal expansion
11.6 Specific heat capacity
11.7 Calorimetry
11.8 Change of state
11.9 Heat transfer
11.10 Newton’s law of cooling
Summary
Points to ponder
Exercises
not to be republished
Page 2

CHAPTER ELEVEN
THERMAL PROPERTIES OF MATTER
11.1  INTRODUCTION
We all have common-sense notions of heat and temperature.
Temperature is a measure of ‘hotness’ of a body. A kettle
with boiling water is hotter than a box containing ice. In
physics, we need to define the notion of heat, temperature,
etc., more carefully. In this chapter, you will learn what heat
is and how it is measured, and study the various proceses by
which heat flows from one body to another. Along the way,
you will find out why blacksmiths heat the iron ring before
fitting on the rim of a wooden wheel of a bullock cart and
why the wind at the beach often reverses direction after the
sun goes down. You will also learn what happens when water
boils or freezes, and its temperature does not change during
these processes even though a great deal of heat is flowing
into or out of it.
11.2  TEMPERATURE AND HEAT
We can begin studying thermal properties of matter with
definitions of temperature and heat. Temperature is a relative
measure, or indication of hotness or coldness. A hot utensil
is said to have a high temperature, and ice cube to have a
low temperature. An object that has a higher temperature
than another object is said to be hotter. Note that hot and
cold are relative terms, like tall and short. We can perceive
temperature by touch. However, this temperature sense is
somewhat unreliable and its range is too limited to be useful
for scientific purposes.
We know from experience that a glass of ice-cold water left
on a table on a hot summer day eventually warms up whereas
a cup of hot tea on the same table cools down. It means that
when the temperature of body, ice-cold water or hot tea in
this case, and its surrounding medium are different, heat
transfer takes place between the system and the surrounding
medium, until the body and the surrounding medium are at
the same temperature. We also know that in the case of glass
tumbler of ice cold water, heat flows from the environment to
11.1 Introduction
11.2 Temperature and heat
11.3 Measurement of
temperature
11.4 Ideal-gas equation and
absolute temperature
11.5 Thermal expansion
11.6 Specific heat capacity
11.7 Calorimetry
11.8 Change of state
11.9 Heat transfer
11.10 Newton’s law of cooling
Summary
Points to ponder
Exercises
not to be republished
the glass tumbler, whereas in the case of hot
tea, it flows from the cup of hot tea to the
environment. So, we can say that heat is the
form of energy transferred between two (or
more) systems or a system and its
surroundings by virtue of temperature
difference. The SI unit of heat energy
transferred is expressed in joule (J) while SI unit
of temperature is kelvin (K), and
°
C is a
commonly used unit of temperature. When an
object is heated, many changes may take place.
Its temperature may rise, it may expand or
change state. We will study the effect of heat on
different bodies in later sections.
11.3  MEASUREMENT OF TEMPERATURE
A measure of temperature is obtained using a
thermometer. Many physical properties of
materials change sufficiently with temperature
to be used as the basis for constructing
thermometers. The commonly used property is
variation of the volume of a liquid with
temperature. For example, a common
thermometer (the liquid-in-glass type) with
which you are familiar. Mercury and alcohol are
the liquids used in most liquid-in-glass
thermometers.
Thermometers are calibrated so that a
numerical value may be assigned to a given
temperature. For the definition of any standard
scale, two fixed reference points are needed.
Since all substances change dimensions with
temperature, an absolute reference for
expansion is not available. However, the
necessary fixed points may be correlated to
physical phenomena that always occur at the
same temperature. The ice point and the steam
point of water are two convenient fixed points
and are known as the freezing and boiling points.
These two points are the temperatures at which
pure water freezes and boils under standard
pressure. The two familiar temperature scales
are the Fahrenheit temperature scale and the
Celsius temperature scale. The ice and
steam point have values 32 °F and 212 °F
respectively, on the Fahrenheit scale and 0 °C
and 100 °C on the Celsius scale. On the
Fahrenheit scale, there are 180 equal intervals
between two reference points, and on the celsius
scale, there are 100.
Fig. 11.1 A plot of Fahrenheit temperature (t
F
) versus
Celsius temperature (t
c
).
A relationship for converting between the two
scales may be obtained from a graph of
Fahrenheit temperature (t
F
) versus celsius
temperature (t
C
) in a straight line (Fig. 11.1),
whose equation is
t t
F C
–32
180 100
=
(11.1)
11.4  IDEAL-GAS EQUATION AND ABSOLUTE
TEMPERATURE
Liquid-in-glass thermometers show different
readings for temperatures other than the fixed
points because of differing expansion properties.
A thermometer that uses a gas, however, gives
the same readings regardless of which gas is
used. Experiments show that all gases at low
densities exhibit same expansion behaviour. The
variables that describe the behaviour of a given
quantity (mass) of gas are pressure, volume, and
temperature (P, V, and T )(where T = t + 273.15;
t is the temperature in °C). When temperature
is held constant, the pressure and volume of a
quantity of gas are related as  PV = constant.
This relationship is known as Boyle’s law, after
Robert Boyle (1627-1691) the English Chemist
who discovered it. When the pressure is held
constant, the volume of a quantity of the gas is
related to the temperature as V/T = constant.
This relationship is known as Charles’ law, after
the French scientist Jacques Charles (1747-
1823). Low density gases obey these laws, which
may be combined into a single relationship.
THERMAL PROPERTIES OF MATTER 275
not to be republished
Page 3

CHAPTER ELEVEN
THERMAL PROPERTIES OF MATTER
11.1  INTRODUCTION
We all have common-sense notions of heat and temperature.
Temperature is a measure of ‘hotness’ of a body. A kettle
with boiling water is hotter than a box containing ice. In
physics, we need to define the notion of heat, temperature,
etc., more carefully. In this chapter, you will learn what heat
is and how it is measured, and study the various proceses by
which heat flows from one body to another. Along the way,
you will find out why blacksmiths heat the iron ring before
fitting on the rim of a wooden wheel of a bullock cart and
why the wind at the beach often reverses direction after the
sun goes down. You will also learn what happens when water
boils or freezes, and its temperature does not change during
these processes even though a great deal of heat is flowing
into or out of it.
11.2  TEMPERATURE AND HEAT
We can begin studying thermal properties of matter with
definitions of temperature and heat. Temperature is a relative
measure, or indication of hotness or coldness. A hot utensil
is said to have a high temperature, and ice cube to have a
low temperature. An object that has a higher temperature
than another object is said to be hotter. Note that hot and
cold are relative terms, like tall and short. We can perceive
temperature by touch. However, this temperature sense is
somewhat unreliable and its range is too limited to be useful
for scientific purposes.
We know from experience that a glass of ice-cold water left
on a table on a hot summer day eventually warms up whereas
a cup of hot tea on the same table cools down. It means that
when the temperature of body, ice-cold water or hot tea in
this case, and its surrounding medium are different, heat
transfer takes place between the system and the surrounding
medium, until the body and the surrounding medium are at
the same temperature. We also know that in the case of glass
tumbler of ice cold water, heat flows from the environment to
11.1 Introduction
11.2 Temperature and heat
11.3 Measurement of
temperature
11.4 Ideal-gas equation and
absolute temperature
11.5 Thermal expansion
11.6 Specific heat capacity
11.7 Calorimetry
11.8 Change of state
11.9 Heat transfer
11.10 Newton’s law of cooling
Summary
Points to ponder
Exercises
not to be republished
the glass tumbler, whereas in the case of hot
tea, it flows from the cup of hot tea to the
environment. So, we can say that heat is the
form of energy transferred between two (or
more) systems or a system and its
surroundings by virtue of temperature
difference. The SI unit of heat energy
transferred is expressed in joule (J) while SI unit
of temperature is kelvin (K), and
°
C is a
commonly used unit of temperature. When an
object is heated, many changes may take place.
Its temperature may rise, it may expand or
change state. We will study the effect of heat on
different bodies in later sections.
11.3  MEASUREMENT OF TEMPERATURE
A measure of temperature is obtained using a
thermometer. Many physical properties of
materials change sufficiently with temperature
to be used as the basis for constructing
thermometers. The commonly used property is
variation of the volume of a liquid with
temperature. For example, a common
thermometer (the liquid-in-glass type) with
which you are familiar. Mercury and alcohol are
the liquids used in most liquid-in-glass
thermometers.
Thermometers are calibrated so that a
numerical value may be assigned to a given
temperature. For the definition of any standard
scale, two fixed reference points are needed.
Since all substances change dimensions with
temperature, an absolute reference for
expansion is not available. However, the
necessary fixed points may be correlated to
physical phenomena that always occur at the
same temperature. The ice point and the steam
point of water are two convenient fixed points
and are known as the freezing and boiling points.
These two points are the temperatures at which
pure water freezes and boils under standard
pressure. The two familiar temperature scales
are the Fahrenheit temperature scale and the
Celsius temperature scale. The ice and
steam point have values 32 °F and 212 °F
respectively, on the Fahrenheit scale and 0 °C
and 100 °C on the Celsius scale. On the
Fahrenheit scale, there are 180 equal intervals
between two reference points, and on the celsius
scale, there are 100.
Fig. 11.1 A plot of Fahrenheit temperature (t
F
) versus
Celsius temperature (t
c
).
A relationship for converting between the two
scales may be obtained from a graph of
Fahrenheit temperature (t
F
) versus celsius
temperature (t
C
) in a straight line (Fig. 11.1),
whose equation is
t t
F C
–32
180 100
=
(11.1)
11.4  IDEAL-GAS EQUATION AND ABSOLUTE
TEMPERATURE
Liquid-in-glass thermometers show different
readings for temperatures other than the fixed
points because of differing expansion properties.
A thermometer that uses a gas, however, gives
the same readings regardless of which gas is
used. Experiments show that all gases at low
densities exhibit same expansion behaviour. The
variables that describe the behaviour of a given
quantity (mass) of gas are pressure, volume, and
temperature (P, V, and T )(where T = t + 273.15;
t is the temperature in °C). When temperature
is held constant, the pressure and volume of a
quantity of gas are related as  PV = constant.
This relationship is known as Boyle’s law, after
Robert Boyle (1627-1691) the English Chemist
who discovered it. When the pressure is held
constant, the volume of a quantity of the gas is
related to the temperature as V/T = constant.
This relationship is known as Charles’ law, after
the French scientist Jacques Charles (1747-
1823). Low density gases obey these laws, which
may be combined into a single relationship.
THERMAL PROPERTIES OF MATTER 275
not to be republished
276 PHYSICS
Notice that since PV = constant  and V/T =
constant for a given quantity of gas, then PV/T
should also be a constant. This relationship is
known as ideal gas law. It can be written in a
more general form that applies not just to a given
quantity of a single gas but to any quantity of
any dilute gas and is known as ideal-gas
equation:
PV
R
T
µ =
or PV = µRT (11.2)
where, µ is the number of moles in the sample
of gas and R is called universal gas constant:
R = 8.31 J mol
–1
K
–1
In Eq. 11.2, we have learnt that the pressure
and volume are directly proportional to
temperature : PV ? T. This relationship allows a
gas to be used to measure temperature in a
constant volume gas thermometer. Holding the
volume of a gas constant, it gives P ?T. Thus,
with a constant-volume gas thermometer,
temperature is read in terms of pressure. A plot
of pressure versus temperature gives a straight
line in this case, as shown in Fig. 11.2.
However, measurements on real gases deviate
from the values predicted by the ideal gas law
at low temperature. But the relationship is linear
over a large temperature range, and it looks as
though the pressure might reach zero with
decreasing temperature if the gas continued to
be a gas. The absolute minimum temperature
for an ideal gas, therefore, inferred by
extrapolating the straight line to the axis, as in
Fig. 11.3.  This temperature is found to be
– 273.15 °C and is designated as absolute zero.
Absolute zero is the foundation of the Kelvin
temperature scale or absolute scale temperature
named after the British scientist Lord Kelvin.
On this scale, – 273.15 °C is taken as the zero
point, that is 0 K (Fig. 11.4).
The size of the unit for Kelvin temperature is
the same celsius degree, so temperature on these
scales are related by
T = t
C
+ 273.15 (11.3)
11.5  THERMAL EXPANSION
You may have observed that sometimes sealed
bottles with metallic lids are so tightly screwed
that one has to put the lid in hot water for
sometime to open the lid. This would allow the
metallic cover to expand, thereby loosening it to
unscrew easily. In case of liquids, you may have
observed that mercury in a thermometer rises,
when the thermometer is put in a slightly warm
water. If we take out the thermometer from the
Fig. 11.2 Pressure versus temperature of a low
density gas kept at constant volume.
Fig. 11.3 A plot of pressure versus temperature and
extrapolation of lines for low density gases
indicates the same absolute zero
temperature.
Fig. 11.4 Comparision of the Kelvin, Celsius and
Fahrenheit temperature scales.
not to be republished
Page 4

CHAPTER ELEVEN
THERMAL PROPERTIES OF MATTER
11.1  INTRODUCTION
We all have common-sense notions of heat and temperature.
Temperature is a measure of ‘hotness’ of a body. A kettle
with boiling water is hotter than a box containing ice. In
physics, we need to define the notion of heat, temperature,
etc., more carefully. In this chapter, you will learn what heat
is and how it is measured, and study the various proceses by
which heat flows from one body to another. Along the way,
you will find out why blacksmiths heat the iron ring before
fitting on the rim of a wooden wheel of a bullock cart and
why the wind at the beach often reverses direction after the
sun goes down. You will also learn what happens when water
boils or freezes, and its temperature does not change during
these processes even though a great deal of heat is flowing
into or out of it.
11.2  TEMPERATURE AND HEAT
We can begin studying thermal properties of matter with
definitions of temperature and heat. Temperature is a relative
measure, or indication of hotness or coldness. A hot utensil
is said to have a high temperature, and ice cube to have a
low temperature. An object that has a higher temperature
than another object is said to be hotter. Note that hot and
cold are relative terms, like tall and short. We can perceive
temperature by touch. However, this temperature sense is
somewhat unreliable and its range is too limited to be useful
for scientific purposes.
We know from experience that a glass of ice-cold water left
on a table on a hot summer day eventually warms up whereas
a cup of hot tea on the same table cools down. It means that
when the temperature of body, ice-cold water or hot tea in
this case, and its surrounding medium are different, heat
transfer takes place between the system and the surrounding
medium, until the body and the surrounding medium are at
the same temperature. We also know that in the case of glass
tumbler of ice cold water, heat flows from the environment to
11.1 Introduction
11.2 Temperature and heat
11.3 Measurement of
temperature
11.4 Ideal-gas equation and
absolute temperature
11.5 Thermal expansion
11.6 Specific heat capacity
11.7 Calorimetry
11.8 Change of state
11.9 Heat transfer
11.10 Newton’s law of cooling
Summary
Points to ponder
Exercises
not to be republished
the glass tumbler, whereas in the case of hot
tea, it flows from the cup of hot tea to the
environment. So, we can say that heat is the
form of energy transferred between two (or
more) systems or a system and its
surroundings by virtue of temperature
difference. The SI unit of heat energy
transferred is expressed in joule (J) while SI unit
of temperature is kelvin (K), and
°
C is a
commonly used unit of temperature. When an
object is heated, many changes may take place.
Its temperature may rise, it may expand or
change state. We will study the effect of heat on
different bodies in later sections.
11.3  MEASUREMENT OF TEMPERATURE
A measure of temperature is obtained using a
thermometer. Many physical properties of
materials change sufficiently with temperature
to be used as the basis for constructing
thermometers. The commonly used property is
variation of the volume of a liquid with
temperature. For example, a common
thermometer (the liquid-in-glass type) with
which you are familiar. Mercury and alcohol are
the liquids used in most liquid-in-glass
thermometers.
Thermometers are calibrated so that a
numerical value may be assigned to a given
temperature. For the definition of any standard
scale, two fixed reference points are needed.
Since all substances change dimensions with
temperature, an absolute reference for
expansion is not available. However, the
necessary fixed points may be correlated to
physical phenomena that always occur at the
same temperature. The ice point and the steam
point of water are two convenient fixed points
and are known as the freezing and boiling points.
These two points are the temperatures at which
pure water freezes and boils under standard
pressure. The two familiar temperature scales
are the Fahrenheit temperature scale and the
Celsius temperature scale. The ice and
steam point have values 32 °F and 212 °F
respectively, on the Fahrenheit scale and 0 °C
and 100 °C on the Celsius scale. On the
Fahrenheit scale, there are 180 equal intervals
between two reference points, and on the celsius
scale, there are 100.
Fig. 11.1 A plot of Fahrenheit temperature (t
F
) versus
Celsius temperature (t
c
).
A relationship for converting between the two
scales may be obtained from a graph of
Fahrenheit temperature (t
F
) versus celsius
temperature (t
C
) in a straight line (Fig. 11.1),
whose equation is
t t
F C
–32
180 100
=
(11.1)
11.4  IDEAL-GAS EQUATION AND ABSOLUTE
TEMPERATURE
Liquid-in-glass thermometers show different
readings for temperatures other than the fixed
points because of differing expansion properties.
A thermometer that uses a gas, however, gives
the same readings regardless of which gas is
used. Experiments show that all gases at low
densities exhibit same expansion behaviour. The
variables that describe the behaviour of a given
quantity (mass) of gas are pressure, volume, and
temperature (P, V, and T )(where T = t + 273.15;
t is the temperature in °C). When temperature
is held constant, the pressure and volume of a
quantity of gas are related as  PV = constant.
This relationship is known as Boyle’s law, after
Robert Boyle (1627-1691) the English Chemist
who discovered it. When the pressure is held
constant, the volume of a quantity of the gas is
related to the temperature as V/T = constant.
This relationship is known as Charles’ law, after
the French scientist Jacques Charles (1747-
1823). Low density gases obey these laws, which
may be combined into a single relationship.
THERMAL PROPERTIES OF MATTER 275
not to be republished
276 PHYSICS
Notice that since PV = constant  and V/T =
constant for a given quantity of gas, then PV/T
should also be a constant. This relationship is
known as ideal gas law. It can be written in a
more general form that applies not just to a given
quantity of a single gas but to any quantity of
any dilute gas and is known as ideal-gas
equation:
PV
R
T
µ =
or PV = µRT (11.2)
where, µ is the number of moles in the sample
of gas and R is called universal gas constant:
R = 8.31 J mol
–1
K
–1
In Eq. 11.2, we have learnt that the pressure
and volume are directly proportional to
temperature : PV ? T. This relationship allows a
gas to be used to measure temperature in a
constant volume gas thermometer. Holding the
volume of a gas constant, it gives P ?T. Thus,
with a constant-volume gas thermometer,
temperature is read in terms of pressure. A plot
of pressure versus temperature gives a straight
line in this case, as shown in Fig. 11.2.
However, measurements on real gases deviate
from the values predicted by the ideal gas law
at low temperature. But the relationship is linear
over a large temperature range, and it looks as
though the pressure might reach zero with
decreasing temperature if the gas continued to
be a gas. The absolute minimum temperature
for an ideal gas, therefore, inferred by
extrapolating the straight line to the axis, as in
Fig. 11.3.  This temperature is found to be
– 273.15 °C and is designated as absolute zero.
Absolute zero is the foundation of the Kelvin
temperature scale or absolute scale temperature
named after the British scientist Lord Kelvin.
On this scale, – 273.15 °C is taken as the zero
point, that is 0 K (Fig. 11.4).
The size of the unit for Kelvin temperature is
the same celsius degree, so temperature on these
scales are related by
T = t
C
+ 273.15 (11.3)
11.5  THERMAL EXPANSION
You may have observed that sometimes sealed
bottles with metallic lids are so tightly screwed
that one has to put the lid in hot water for
sometime to open the lid. This would allow the
metallic cover to expand, thereby loosening it to
unscrew easily. In case of liquids, you may have
observed that mercury in a thermometer rises,
when the thermometer is put in a slightly warm
water. If we take out the thermometer from the
Fig. 11.2 Pressure versus temperature of a low
density gas kept at constant volume.
Fig. 11.3 A plot of pressure versus temperature and
extrapolation of lines for low density gases
indicates the same absolute zero
temperature.
Fig. 11.4 Comparision of the Kelvin, Celsius and
Fahrenheit temperature scales.
not to be republished
THERMAL PROPERTIES OF MATTER 277
warm water the level of mercury falls again.
Similarly, in the case of gases, a balloon partially
inflated in a cool room may expand to full size
when placed in warm water. On the other hand,
a fully inflated balloon when immersed in cold
water would start shrinking due to contraction
of the air inside.
It is our common experience that most
substances expand on heating and contract on
cooling. A change in the temperature of a body
causes change in its dimensions. The increase
in the dimensions of a body due to the increase
in its temperature is called thermal expansion.
The expansion in length is called linear
expansion. The expansion in area is called area
expansion. The expansion in volume is called
volume expansion (Fig. 11.5).
Fig. 11.5  Thermal Expansion.
If the substance is in the form of a long rod,
then for small change in temperature, ?T, the
fractional change in length, ?l/l, is directly
proportional to ?T.
?
?
l
l
T = a
1
(11.4)
where a
1
is known as the coefficient of linear
expansion and is characteristic of the material
of the rod. In Table 11.1 are given typical average
values of the coefficient of linear expansion for
some materials in the temperature range 0 °C
to 100

°C. From this Table, compare the value
of a
l
for glass and copper. We find that copper
expands about five times more than glass for
the same rise in temperature. Normally, metals
expand more and have relatively high values
of a
l
.
Table 11.1 Values of coefficient of linear
expansion for some materials
Materials a a a a a
l
(10
–5
K
–1
)
Aluminium 2.5
Brass 1.8
Iron 1.2
Copper 1.7
Silver 1.9
Gold 1.4
Glass (pyrex) 0.32
Similarly, we consider the fractional change
in volume,
?V
V
, of a substance for temperature
change ?T and define the coefficient of volume
expansion, a
V
as
a
V
=
? ? ? ? ? ? ?
?
V
VT
1
(11.5)
Here a
V
is also a characteristic of the
substance but is not strictly a constant. It
depends in general on temperature (Fig 11.6). It
is seen that a
V
becomes constant only at a high
temperature.
Fig. 11.6 Coefficient of volume expansion of copper
as a function of temperature.
Table 11.2 gives the values of co-efficient of
volume expansion of some common substances
in the temperature range 0 –100 °C. You can
see that thermal expansion of these substances
(solids and liquids) is rather small, with
l
l
aT
l

l
2
A
aT
A

l
3
V
aT
V

(a) Linear expansion (b) Area expansion (c) Volume expansion
not to be republished
Page 5

CHAPTER ELEVEN
THERMAL PROPERTIES OF MATTER
11.1  INTRODUCTION
We all have common-sense notions of heat and temperature.
Temperature is a measure of ‘hotness’ of a body. A kettle
with boiling water is hotter than a box containing ice. In
physics, we need to define the notion of heat, temperature,
etc., more carefully. In this chapter, you will learn what heat
is and how it is measured, and study the various proceses by
which heat flows from one body to another. Along the way,
you will find out why blacksmiths heat the iron ring before
fitting on the rim of a wooden wheel of a bullock cart and
why the wind at the beach often reverses direction after the
sun goes down. You will also learn what happens when water
boils or freezes, and its temperature does not change during
these processes even though a great deal of heat is flowing
into or out of it.
11.2  TEMPERATURE AND HEAT
We can begin studying thermal properties of matter with
definitions of temperature and heat. Temperature is a relative
measure, or indication of hotness or coldness. A hot utensil
is said to have a high temperature, and ice cube to have a
low temperature. An object that has a higher temperature
than another object is said to be hotter. Note that hot and
cold are relative terms, like tall and short. We can perceive
temperature by touch. However, this temperature sense is
somewhat unreliable and its range is too limited to be useful
for scientific purposes.
We know from experience that a glass of ice-cold water left
on a table on a hot summer day eventually warms up whereas
a cup of hot tea on the same table cools down. It means that
when the temperature of body, ice-cold water or hot tea in
this case, and its surrounding medium are different, heat
transfer takes place between the system and the surrounding
medium, until the body and the surrounding medium are at
the same temperature. We also know that in the case of glass
tumbler of ice cold water, heat flows from the environment to
11.1 Introduction
11.2 Temperature and heat
11.3 Measurement of
temperature
11.4 Ideal-gas equation and
absolute temperature
11.5 Thermal expansion
11.6 Specific heat capacity
11.7 Calorimetry
11.8 Change of state
11.9 Heat transfer
11.10 Newton’s law of cooling
Summary
Points to ponder
Exercises
not to be republished
the glass tumbler, whereas in the case of hot
tea, it flows from the cup of hot tea to the
environment. So, we can say that heat is the
form of energy transferred between two (or
more) systems or a system and its
surroundings by virtue of temperature
difference. The SI unit of heat energy
transferred is expressed in joule (J) while SI unit
of temperature is kelvin (K), and
°
C is a
commonly used unit of temperature. When an
object is heated, many changes may take place.
Its temperature may rise, it may expand or
change state. We will study the effect of heat on
different bodies in later sections.
11.3  MEASUREMENT OF TEMPERATURE
A measure of temperature is obtained using a
thermometer. Many physical properties of
materials change sufficiently with temperature
to be used as the basis for constructing
thermometers. The commonly used property is
variation of the volume of a liquid with
temperature. For example, a common
thermometer (the liquid-in-glass type) with
which you are familiar. Mercury and alcohol are
the liquids used in most liquid-in-glass
thermometers.
Thermometers are calibrated so that a
numerical value may be assigned to a given
temperature. For the definition of any standard
scale, two fixed reference points are needed.
Since all substances change dimensions with
temperature, an absolute reference for
expansion is not available. However, the
necessary fixed points may be correlated to
physical phenomena that always occur at the
same temperature. The ice point and the steam
point of water are two convenient fixed points
and are known as the freezing and boiling points.
These two points are the temperatures at which
pure water freezes and boils under standard
pressure. The two familiar temperature scales
are the Fahrenheit temperature scale and the
Celsius temperature scale. The ice and
steam point have values 32 °F and 212 °F
respectively, on the Fahrenheit scale and 0 °C
and 100 °C on the Celsius scale. On the
Fahrenheit scale, there are 180 equal intervals
between two reference points, and on the celsius
scale, there are 100.
Fig. 11.1 A plot of Fahrenheit temperature (t
F
) versus
Celsius temperature (t
c
).
A relationship for converting between the two
scales may be obtained from a graph of
Fahrenheit temperature (t
F
) versus celsius
temperature (t
C
) in a straight line (Fig. 11.1),
whose equation is
t t
F C
–32
180 100
=
(11.1)
11.4  IDEAL-GAS EQUATION AND ABSOLUTE
TEMPERATURE
Liquid-in-glass thermometers show different
readings for temperatures other than the fixed
points because of differing expansion properties.
A thermometer that uses a gas, however, gives
the same readings regardless of which gas is
used. Experiments show that all gases at low
densities exhibit same expansion behaviour. The
variables that describe the behaviour of a given
quantity (mass) of gas are pressure, volume, and
temperature (P, V, and T )(where T = t + 273.15;
t is the temperature in °C). When temperature
is held constant, the pressure and volume of a
quantity of gas are related as  PV = constant.
This relationship is known as Boyle’s law, after
Robert Boyle (1627-1691) the English Chemist
who discovered it. When the pressure is held
constant, the volume of a quantity of the gas is
related to the temperature as V/T = constant.
This relationship is known as Charles’ law, after
the French scientist Jacques Charles (1747-
1823). Low density gases obey these laws, which
may be combined into a single relationship.
THERMAL PROPERTIES OF MATTER 275
not to be republished
276 PHYSICS
Notice that since PV = constant  and V/T =
constant for a given quantity of gas, then PV/T
should also be a constant. This relationship is
known as ideal gas law. It can be written in a
more general form that applies not just to a given
quantity of a single gas but to any quantity of
any dilute gas and is known as ideal-gas
equation:
PV
R
T
µ =
or PV = µRT (11.2)
where, µ is the number of moles in the sample
of gas and R is called universal gas constant:
R = 8.31 J mol
–1
K
–1
In Eq. 11.2, we have learnt that the pressure
and volume are directly proportional to
temperature : PV ? T. This relationship allows a
gas to be used to measure temperature in a
constant volume gas thermometer. Holding the
volume of a gas constant, it gives P ?T. Thus,
with a constant-volume gas thermometer,
temperature is read in terms of pressure. A plot
of pressure versus temperature gives a straight
line in this case, as shown in Fig. 11.2.
However, measurements on real gases deviate
from the values predicted by the ideal gas law
at low temperature. But the relationship is linear
over a large temperature range, and it looks as
though the pressure might reach zero with
decreasing temperature if the gas continued to
be a gas. The absolute minimum temperature
for an ideal gas, therefore, inferred by
extrapolating the straight line to the axis, as in
Fig. 11.3.  This temperature is found to be
– 273.15 °C and is designated as absolute zero.
Absolute zero is the foundation of the Kelvin
temperature scale or absolute scale temperature
named after the British scientist Lord Kelvin.
On this scale, – 273.15 °C is taken as the zero
point, that is 0 K (Fig. 11.4).
The size of the unit for Kelvin temperature is
the same celsius degree, so temperature on these
scales are related by
T = t
C
+ 273.15 (11.3)
11.5  THERMAL EXPANSION
You may have observed that sometimes sealed
bottles with metallic lids are so tightly screwed
that one has to put the lid in hot water for
sometime to open the lid. This would allow the
metallic cover to expand, thereby loosening it to
unscrew easily. In case of liquids, you may have
observed that mercury in a thermometer rises,
when the thermometer is put in a slightly warm
water. If we take out the thermometer from the
Fig. 11.2 Pressure versus temperature of a low
density gas kept at constant volume.
Fig. 11.3 A plot of pressure versus temperature and
extrapolation of lines for low density gases
indicates the same absolute zero
temperature.
Fig. 11.4 Comparision of the Kelvin, Celsius and
Fahrenheit temperature scales.
not to be republished
THERMAL PROPERTIES OF MATTER 277
warm water the level of mercury falls again.
Similarly, in the case of gases, a balloon partially
inflated in a cool room may expand to full size
when placed in warm water. On the other hand,
a fully inflated balloon when immersed in cold
water would start shrinking due to contraction
of the air inside.
It is our common experience that most
substances expand on heating and contract on
cooling. A change in the temperature of a body
causes change in its dimensions. The increase
in the dimensions of a body due to the increase
in its temperature is called thermal expansion.
The expansion in length is called linear
expansion. The expansion in area is called area
expansion. The expansion in volume is called
volume expansion (Fig. 11.5).
Fig. 11.5  Thermal Expansion.
If the substance is in the form of a long rod,
then for small change in temperature, ?T, the
fractional change in length, ?l/l, is directly
proportional to ?T.
?
?
l
l
T = a
1
(11.4)
where a
1
is known as the coefficient of linear
expansion and is characteristic of the material
of the rod. In Table 11.1 are given typical average
values of the coefficient of linear expansion for
some materials in the temperature range 0 °C
to 100

°C. From this Table, compare the value
of a
l
for glass and copper. We find that copper
expands about five times more than glass for
the same rise in temperature. Normally, metals
expand more and have relatively high values
of a
l
.
Table 11.1 Values of coefficient of linear
expansion for some materials
Materials a a a a a
l
(10
–5
K
–1
)
Aluminium 2.5
Brass 1.8
Iron 1.2
Copper 1.7
Silver 1.9
Gold 1.4
Glass (pyrex) 0.32
Similarly, we consider the fractional change
in volume,
?V
V
, of a substance for temperature
change ?T and define the coefficient of volume
expansion, a
V
as
a
V
=
? ? ? ? ? ? ?
?
V
VT
1
(11.5)
Here a
V
is also a characteristic of the
substance but is not strictly a constant. It
depends in general on temperature (Fig 11.6). It
is seen that a
V
becomes constant only at a high
temperature.
Fig. 11.6 Coefficient of volume expansion of copper
as a function of temperature.
Table 11.2 gives the values of co-efficient of
volume expansion of some common substances
in the temperature range 0 –100 °C. You can
see that thermal expansion of these substances
(solids and liquids) is rather small, with
l
l
aT
l

l
2
A
aT
A

l
3
V
aT
V

(a) Linear expansion (b) Area expansion (c) Volume expansion
not to be republished
278 PHYSICS
materials like pyrex glass and invar (a special
iron-nickel alloy) having particularly low values
of a
V
. From this Table we find that the value of
a
v
for alcohol (ethyl) is more than mercury and
expands more than mercury for the same rise
in temperature.
Table 11.2 Values of coefficient of volume
expansion for some substances
Materials a a a a a
v
(

K
–1
)
Aluminium 7  10
–5
Brass 6  10
–5
Iron 3.55  10
–5
Paraffin 58.8  10
–5
Glass (ordinary) 2.5  10
–5
Glass (pyrex) 1  10
–5
Hard rubber 2.4  10
–4
Invar 2  10
–6
Mercurry 18.2  10
–5
Water 20.7  10
–5
Alcohol (ethyl) 110  10
–5
Water exhibits an anomalous behavour; it
contracts on heating between 0 °C and 4 °C.
The volume of a given amount of water decreases
as it is cooled from room temperature, until its
temperature reaches 4 °C, [Fig. 11.7(a)]. Below
4 °C, the volume increases, and therefore the
density decreases [Fig. 11.7(b)].
This means that water has a maximum
density at 4

°C. This property has an important
environmental effect: Bodies of water, such as
lakes and ponds, freeze at the top first. As a
lake cools toward 4 °C, water near the surface
loses energy to the atmosphere, becomes denser,
and sinks; the warmer, less dense water near
the bottom rises. However, once the colder water
on top reaches temperature below 4 °C, it
becomes less dense and remains at the surface,
where it freezes. If water did not have this
property, lakes and ponds would freeze from the
bottom up, which would destroy much of their
animal and plant life.
Gases at ordinary temperature expand more
than solids and liquids. For liquids, the
coefficient of volume expansion is relatively
independent of the temperature. However, for
gases it is dependent on temperature. For an
ideal gas, the coefficient of volume expansion at
constant pressure can be found from the ideal
gas equation :
PV = µRT
At constant pressure
P?V = µR ?T
?? V
V
T
T
=
i.e.
a
v
T
=
1
for ideal gas (11.6)
At 0 °C, a
v
= 3.7  10
–3
K
–1
, which is much
larger than that for solids and liquids.
Equation (11.6) shows the temperature
dependence of a
v
; it decreases with increasing
temperature. For a gas at room temperature and
constant pressure a
v
–6
K
–1
, as
Temperature (°C) Temperature (°C)
(a) (b)
Fig. 11.7 Thermal expansion of water.
not to be republished
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