Module No. 31

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Module # 31
Heat & Temperature
Heat
Heat may be defined as the energy transferred without transfer of
mass across the boundary of a system because of a temperature
difference between system and surroundings. Heat always travels
from the body at higher temperature towards the body at lower
temperature.
The heat is, usually, generated by the combustion of fuel which
may be solid, liquid or gas.
OR
The energy that transfers or flows from one point to another point
in a body or from one body to another body, due to temperature
difference is called heat.
For example, if a thick plate is placed on fire, it will be found that
with the passage of time, the plate becomes warmer and warmer
and after sometime it will become too hot to touch. We may say
that something has gone from the fire into the plate which has
made it hot. This something is called heat.

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The molecules of matter always remain in motion and have kinetic
energy. This kinetic energy of molecules which constitute a body
appears as its heat energy.
Heat as Energy in Transit
Joule performed a series of experiments on the production of heat
by performing work in different ways. In his famous experiment
(1847), which ultimately gave a death blow to the caloric theory,
he could convert the mechanical energy of a falling weight into
heat. Water was churned in a calorimeter by means of a brass
paddle wheel which revolved by a string tied to the falling weight
and the final temperature of water was found to have increased.
Further, he found the same result when electric current was
passed through a wire immersed in a liquid and when gases were
compressed. Thus, any mechanical or electrical work done
produces heat. This firmly established that heat is merely another
form of energy and not a substance like caloric.
All the experiments of Rumford, Devy and Joule lead to a very
simple statement that heat is energy in transit.
Microscopic Description of Heat as Transfer of Energy
In order to explain microscopically the flow of heat as transfer of
energy, we consider a pot, containing water, placed on stove.
Since the thermal kinetic energy of the molecules is proportional

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to temperature, thus, the molecules of the stove burner have
much more kinetic energy on the average than those of the pot
and cold water in it. When the fast moving molecules of the stove
burner collide with the slow moving molecules of the pot, some of
their kinetic energy is transferred to the pot molecules, just as a
fast moving billiard ball transfers some of its kinetic energy to a
ball with which it collides. The molecules of the pot gain kinetic
energy. Now, the fast moving pot molecules, in turn, transfer
some of their kinetic energy by collision to slow moving water
molecules. The temperature of the pot and water consequently
rises. Thus, we conclude that heat flow is a transfer of energy.
Internal Energy
The sum of the total translational kinetic energy, vibrational
energy and rotational energy is called the internal energy or
thermal energy of the substance. Therefore, the energy contained
in a body is not the heat energy but it is the internal energy of the
body. The heat supplied to a body will increase its translational
K.E, vibrational energy and the rotational energy. The
translational energy only is used up to increase the velocity of
molecules and hence the temperature.
The temperature of a gas is a measure of the vibrational energy
of its molecules; this molecular Kinetic energy is known as

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internal energy of the gas. Hence temperature of a body is a
function of its internal energy, i.e. higher the internal energy of a
body, higher will be its temperature.
Sometime, we use the term "heat content" of an object for
expressing internal energy. Heat, on the other hand, is not the
energy that an object contains in it, but, it refers to the amount of
energy transferred from a hot to a cold body. Once, the heat
energy is transferred to an object, it becomes the part of the
internal energy of that object. Thus, heat is the energy in
transition (i.e., on the move) from one body or system to another
because of a temperature difference between the systems. In
other words, heat is the interaction between systems which
occurs by virtue of their temperature difference.
Internal Energy of a Gas 'U'
When a certain amount of heat energy is supplied to a gas, some
of it is converted into mechanical energy and the remaining is
stored in the gas itself. The part of energy which is utilized for
doing external work is known as the external energy of the gas.
The part of energy which is stored in the gas and is used for
raising its temperature is called the Internal energy of the gas.
The heat energy stored in the gas, and used for raising
temperature of the gas is known as internal energy of the gas

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such that
ΔU = mCv (T2-T1)
Heat and Internal Energy always Inseparable
Heat is not possessed by anybody. Whatever a body possesses
is the internal energy. Internal energy of a body is the sum of
kinetic and potential energies of all the molecules constituting the
body. When a body absorbs heat its internal energy increases
and when it radiates (emits) heat its internal energy decreases.
Thus heat is the energy in transit from one body to another or
from one point to another in the same body due to the
temperature difference.
According to S.I., the units of heat are the same as that of energy,
i.e. Joule.
The following units have been adopted by engineers for
measuring quantities of heat.
(1) Centigrade Heat Unit (CHU)
It is defined as the quantity of heat required to raise the
temperature of one pound of water through one degree
centigrade. This is also known as pound calorie.
(2) British Thermal Unit (BTU)

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It is defined as the quantity of heat required in raising the
temperature of one pound of water through one degree
Fahrenheit.
(3) M.K.S Heat Unit (Kcal)
In metric system of units, the unit of heat is Kilogram caloric (Kcal)
which is defined as the quantity of heat required to raise the
temperature of one Kg of water through one degree centigrade.
Heat and Work Relationship
Joule established the fact that same amount of mechanical work
produces same amount of heat. The greater the amount of work,
the larger the heat produced.
Examples
(1) Rub the palms of hands briskly. They get warm.
(2) When brakes are repeatedly applied on a bicycle, its wheels
get heated up. This proves that mechanical energy (work) and
thermal energy (heat) are interchangeable.
Heat Capacity
The heat capacity of a body of any Kind is defined as the heat
required to raise its temperature by 1 K. The SI unit of heat
capacity is the joule per Kelvin (J/K).

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Thus, the amount of heat required to produce unit temperature
change is known as heat capacity of an object. If heat energy
causes a change in temperature, we write
Heat Capacity = Q/T
Heat Engine
A machine, which converts heat into mechanical work, is known
as Heat Engine. The working substances, widely used in the heat
engines, are fluids in the gaseous or liquid state.
Transfer of Heat
There are three different processes by which heat energy can be
transferred from one place to another. These processes are
conduction, convection and radiation.
Transmission of Heat
The transmission of heat from one location to another depends a
great deal on the material of the flow path. The transmission of
heat, however, can be achieved only by conduction, convection or
radiation.

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Conduction of Heat
The process, in which transfer of heat energy takes place from
atom to atom without the movement of substance or mass from
one position to another, is known as conduction of heat.
When one end of a long copper rod coated with paraffin wax is
placed in a Bunsen flame, the wax will be observed to melt near
the flame and then, gradually, melt farther and farther along the
rod. It means that the heat flows along the rod from heated end
towards the cold one. The heat energy absorbed by the copper
atoms directly from the Bunsen flame causes an increase in the
amplitude of vibrations about their mean positions. These atoms
collide with less hot neighboring atoms and a part of the heat
energy absorbed is transferred to them.
This process continues. Heat is said to be conducted along the
rod from the hot end to the cold end.
Conduction takes place at different rates in different materials. For
example, a wooden stick can burn at one end while the other end
remains relatively cool. A metal rod transmits heat rapidly from
one end to the other. The ability of a material to conduct heat
depends on its atomic or molecular structure.
When a container of water is placed on a heat source, at first only
the water at the very bottom receives heat by conduction through

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the container. As the bottom layer of water begins to receive heat,
it tends to expand somewhat. This condition causes it to become
less dense than the cooler water above it. As a result of this
condition, warm water begins to rise to the surface, which causes
heavier cold water to flow down towards the source of heat. The
new bottom layer of water will receive heat and rise to the top.
The process is repeated over & over again until boiling occurs.
If one end of a solid metal bar is placed in an open flame, the
other end will soon become hot. The process by which heat is
transferred from the flame to the cold end of the bar is called
conduction.
For conduction to take place, the heat source must touch the
object being heated.
The conduction process applies primarily to heat transmission
through solid materials.
Convection of Heat
This mode of heat transfer due to actual movement of molecules
from one place to another through large distances is known as
convection, or, the process of heat energy transfer due to
migration of a substance or bulk movement of a gas or a liquid
from one position to another is called convection.

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The convection mode of heat transfer is peculiar to fluids, i.e.
liquids and gases. For example; distribution of heat in the earth's
atmosphere takes place by winds which blow from hot regions to
the cold ones. Similarly, ventilators provided in the walls near the
ceiling of a room help to keep the temperature inside the room
moderate. The warm air inside the room rises and escapes
through the ventilators while fresh and cold air enters the room
through windows and doors.
Radiation (of Heat)
The mode of heat energy transfer from one place to another
without involving a material medium is called radiation.
The hot objects emit radiations which carry away energy. When
these radiations fall on an object, its energy is transferred to the
latter in the form of heat. It has been observed that, in general,
dark objects are good absorbers or bad reflectors of heat
radiation while white or light-colored objects are poor absorbers or
good reflectors. That is why; we commonly wear light colored
clothes in the summer to reduce heating effect on the body. In
winter, we prefer to wear dark-colored clothes so that maximum
heat is absorbed to keep our body warm.
Radiation is a process by which heat is transferred through the
motion of waves. A prime example of this is the heat that reaches

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the earth from the sun.
Since the space between earth and the sun is generally void of
molecules except near the earth surface, heat cannot be
transferred by conduction or convection. In effect, heat energy is
given off or radiated away from a heat source through infrared
rays. Energy of this type moves away from the source in a wave
like pattern at the speed of light. An interesting characteristic of
radiation is that the air between the heat source and the object,
which the waves must pass through, is not heated.
Temperature
The degree of hotness or coldness of a body is called
temperature. A hot body is said to be at higher temperature,
whereas the cold body to be at lower temperature.
Temperature is a measure of the relative hotness or coldness of a
body. It is defined as a number on some definite scale.
The temperature of a substance is a number which expresses its
degree of hotness on some chosen scale.
The average kinetic energy of the molecules of substance is a
(direct) measure of its temperature.
Temperature is regarded as a thermodynamic quantity, because,
its equality determines the thermal equilibrium between two

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systems.
In order to measure temperature, we make use of thermometric
properties of matter.
Temperature Coefficient
All pure metals and most conductor materials show positive
resistance temperature coefficient, that is, the resistance
increases with an increase in temperature. An exception is
carbon, which has negative resistance temperature coefficient,
that is, the resistance of carbon decreases when the temperature
increases. Insulating materials have resistance temperature
characteristics similar to that of carbon.
When temperature rises
1 Resistance of metallic conductors is increased by
comparatively large amount. Hence, metals are said to possess
positive temperature co-efficient of resistance.
2 Resistance of insulators and partial conductors is decreased.
Hence, they start losing their useful property of insulation. They
are said to possess negative temperature - coefficient of
resistance.

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3 Resistance offered by semiconductors is decreased and
their electrical behavior starts approaching negative temperature
co-efficient of resistance.
Temperature Scales
There are three scales for temperature measurement known as:
(1) Centigrade or Celsius Scale,
(2) Fahrenheit Scale, and
(3) Kelvin Scale
A thermometer may be calibrated in units of any one of these
scales. To assign numerical values to different temperatures, two
reference points are first fixed and interval between them is
divided into a number of equally spaced parts. The common
reference points for a temperature scale are ice point or freezing
point and boiling point or steam point of water. The ice point is the
temperature of ice and water in equilibrium under standard
atmospheric pressure. The steam point is the temperature at
which pure water boils at pressure of one atmosphere.
The most commonly used temperature scales are Celsius or
Centigrade and Fahrenheit.

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Centigrade Scale or Celsius Scale
In this scale, the melting point of ice (or freezing point of water) is
marked as 0° and the boiling point of water is marked as 100°.
The space (or distance) between these two marks is equally
divided into 100 parts (or divisions). Each division is called as
degree centigrade and is represented by °C. This scale is used by
engineer and scientists for all international work. This scale was
first used by Celsius in 1742.
This scale has its 0° at the melting point of ice and 100° at the
boiling point of water. The interval between these two points is
divided into 100 equal divisions or units. Each division is called a
degree Celsius.
Fahrenheit (1686-1736)
During the classical physics period (1700-1890 AD), Fahrenheit
developed thermometer and temperature scales in the field of
heat.
Fahrenheit Scale
The official scale of temperature used in English speaking
countries is the Fahrenheit scales. This scale is also used by
doctors. The freezing point of water under atmospheric pressure
is marked as 32 and the boiling point is designated as 212. The

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distance between these two points is divided into 180 equal units
called degrees Fahrenheit or °F.
Values on Fahrenheit scale can be readily converted into those
on the centigrade scale and vice-versa by noting that 180 degrees
of Fahrenheit scale are equal to 100 degrees on centigrade scale.
The relationship between centigrade scale and Fahrenheit scale
is given by:
°F =1.8°C + 32 and °C = (°F - 32) ÷ 1.8
In this scale, the melting point of ice is taken as 32° and the
boiling point of water as 212°. There are 180 equal divisions or
units between these two points.
Kelvin (1824-1907)
During the classical physics period (1700-1890 AD), in the field of
heat, Kelvin stated laws of thermodynamics which helped the
physicists to unify the concepts of heat with those of mechanics.
The Kelvin scale measures absolute centigrade temperature.
Second Law of Thermodynamics was given by Kelvin.
Kelvin Scale
In this scale, the melting point of ice is taken as 273 and the
boiling point of water as 373. There are 100 equal units between
these two points. Its unit is Kelvin denoted by K and it has the

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same magnitude as a degree Celsius. The lowest possible
temperature of this scale which corresponds to a minimum
molecular energy is O K or -273°C or - 460° F. Since zero
temperature on the Kelvin scale is taken as equal to absolute
lower limit, therefore, this scale is also called the absolute
temperature scale.
In this scale, the melting and boiling points of water are marked
as 273 and 373 respectively. The space between these two points
is equally divided into 100 parts. Each part is called as kelvin and
is represented by K. The zero of Kelvin scale starts from -273 °C
which is the lowest temperature even to be reached.
Note: In SI nomenclature, "degree" is not used with the Kelvin
scale; a temperature on the Kelvin scale, say -273, is read "273
kelvins" not "degree kelvins". We capitalize Kelvin when it refers
to the temperature scale, but the unit of temperature is the kelvin,
not capitalized but abbreviated K.
Temperature is regarded as a thermodynamic quantity, because,
its equality determines the thermal equilibrium between two
systems. The unit of temperature is kelvin. It is the fraction
1/273.16 of the thermodynamic temperature of the triple point of
water. It should be noted that the triple point of a substance
means the temperature at which solid, liquid and vapor phases

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are in equilibrium. The triple point of water is taken as 273.16 K.
This standard was adopted in 1967.
Interconversion of Temperature Scales
Since the difference between the melting point of ice and the
boiling point of water on the Kelvin and Celsius scales is the
same, that is, 100, therefore, we can convert Celsius Scale into
the Kelvin scale simply by adding 273 to the Celsius temperature,
i.e.
Tk = Tc + 273
OR
Tc = Tk - 273
To convert Celsius Scale into Fahrenheit Scale and vice versa,
we use the following relations:-
TF = 9/5 (Tc) + 32
Tc = 5/9 (TF - 32)
We can also convert one scale into any other by using the
following relation

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C -0 F - 32 K - 273
------- = ---------- = -----------
100 180 100
Absolute Zero Temperature
The temperature at which the volume of a gas becomes Zero is
called absolute zero temperature.
Absolute Temperature
As a matter of fact, the zero readings of centigrade and
Fahrenheit are chosen arbitrarily for the purpose of simplicity. It
helps us in our calculations, when changes of temperature in a
process are known. But, whenever the value of temperature is
used in equation relating to Fundamental laws, then the value of
temperature, whose reference point is true zero or absolute zero,
is used. The absolute zero temperature, for all sorts of
calculations, is taken as -273°C or -460°F. The temperatures
measured from this zero are called absolute temperature. The
absolute centigrade scale is called degrees Kelvin (K°) such that
°K = °C+273
Similarly, absolute Fahrenheit scale is called degree Rankine

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(R°), such that
°R = °F + 460
The relationship (approximate) between degree Kelvin and
degree Rankine is given below:
R°=1.8°K
Fixed Points (of Temperature)
For graduating the thermometer, two fixed points are first marked
on it. These are known as the lower fixed point and the upper
fixed point.
Upper Fixed Point (Steam or Boiling Point)
For this purpose, the bulb of the thermometer is placed in boiling
water (at an atmospheric pressure of 760 mm of mercury). The
mercury inside the thermometer expands and it rises to another
level. The level at which the mercury column stands (or the level
of mercury becomes constant) is marked. This point is known as
Upper Fixed Point (Boiling point).
The distance between two lower and upper fixed points is divided
into 100 equal parts. Each such part is known as "degree".
Upper Fixed Point (of Temperature)
The upper fixed point is the temperature of steam from water

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boiling under standard atmospheric pressure of 760mm Hg.
Lower Fixed Point (of Temperature)
The lower fixed point is the temperature of pure melting ice.
Lower Fixed Point (Ice or Freezing Point)
If the bulb of mercury thermometer is placed inside a vessel
containing dry ice, then, mercury inside the glass bulb contracts to
minimum volume and level of mercury in glass tube comes to its
lowest level. When the level of mercury becomes constant, then,
it is marked. This is known as freezing point or Lower Fixed Point.
Sensible Heat of Water
It is the amount of heat absorbed by 1 kg of water, when heated
at constant pressure, from O°C to the temperature of formation of
steam i.e. saturation temperature. The sensible heat is also
known as total heat of water.
The specific heat of water, over this range of temperature is
assumed to be unity.
Caloric Theory of Heat
The ideas or theories about the nature of heat changed with the
passage of time. In olden days, heat was considered as a fluid
substance, called caloric. According to this theory:

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(1) An object contains a certain amount of caloric.
(2) The caloric is a fluid substance which is weightless and
invisible.
(3) When the caloric enters a body, then, its temperature
increases and when it leaves a body, then, its temperature
decreases.
(4) The caloric can neither be created nor destroyed, therefore,
Heat lost = Heat gained.
(5) The caloric is released by cutting the matter such as boring
of a barrel of cannon. The caloric theory could not explain the
heat produced by friction and by mechanical work, therefore, it
was rejected.
Calorie
It is the amount of heat required to raise the temperature of 1
gram of water through 1°C.
It is defined as the amount of heat required to raise the
temperature of one gram of water from 14.5°C to 15.5°C,
i.e., by 1°C.

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Kilo Calorie (Kcal)
In MKS system of units, the unit of heat is Kilo calorie (Kcal)
which is defined as the quantity of heat required to raise the
temperature of one Kg of water through one degree centigrade.
Law of Heat Exchange
According to this law, no heat is lost or gained by an isolated
system constituted by the mixture of hot and cold substances.
OR
In any heat exchange system, the heat lost by the hot substance
is equal to the heat gained by cold substance,
i.e.
Heat Lost = Heat Gained.
Example
Bring two bodies of unequal temperatures close to one another.
The warmer body losses heat while the colder body gains heat till
the two have same temperature.

Module No. 31

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Module No. 31