BS Physics (Foundation) Series

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Module # 35
Thermal Conductivity & Specific Heat
Thermal Conductivity
The thermal conductivity of a substance is a measure of its ability
to conduct heat energy.
Experimentally, thermal conductivity can be measured as follows.
Consider a solid slab of thickness L and face area A. Its two
faces are maintained at temperatures T1 and T2. The amount of
heat Q flowing through the slab in time t depends on:
1 temperature difference, T = T2 – T1 where T2  T1,
2 face area A,
3 time for which heat flows, t and
4 thickness L.
It has been observed that

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Q  A,
Q  T,
Q  t and
Q  1/L
A x T x t A x T x t
Q  ---------------- OR Q = K ----------------- [1]
L L
Where, K is a constant of proportionality called thermal
conductivity. Its value depends on the material of the slab and is a
measure of the thermal conductivity of the material.
If
A = 1m2
L = 1m
T = 1°C
and
t = 1 Sec
then, by putting these values in Eq. [1]
we get,

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Q = K
Thus, the thermal conductivity can be defined as
"The amount of heat conducted for one second through a meter
cube of the substance whose two opposite faces are maintained
at a temperature difference of 1°C."
K is large for metals and small for non-metallic solids, liquids and
gases.
Thermal Efficiency
It is defined as the ratio of the heat actually utilized to the total
heat produced. Consider the case of the electric kettle used for
boiling water. Out of the total heat produced
(i) some goes to heat the apparatus itself i.e. kettle (ii) some is
lost in the air due to radiation. The remaining (iii) is utilized for
heating the water. Out of these, the heat utilized for useful
purpose is that in (iii).
Hence, thermal efficiency of this electric apparatus is the ratio of
the heat utilized for heating the water to the total heat produced.
Remember that
1 K calorie = 4187 joules
1 Ib. = 0.4536 Kg

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1 B.T.U = 0.252. Kcal
1°F = 5/9°C
1 gallon = 10 Ibs.
Thermal Engineering
The field of engineering science which deals with the applications
of thermodynamics and its laws to work producing and work
absorbing devices, in order to understand their performance, is
known as thermal Engineering.
Thermometric Properties of Matter
A thermometric property of matter is that property of matter which
changes uniformly with change of temperature. Examples of
thermometric properties are:
(1) Expansion or Change of Volume
The volume of a gas, liquid and solid changes with temperature.
Nearly, all materials expand on heating and contract on cooling.
For example, iron is longer when it is hot than when it is cold.
(2) Change of Color
The color of matter changes with change of temperature. At very
high temperatures, solids become red. At still higher

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temperatures, iron and some other solids turn orange and then
white.
(3) Change of Electrical Resistance
Electric resistance of a conductor is directly proportional to its
temperature. It means that higher the temperature of the wire, the
greater is its resistance. This is known as thermometric property
of conductor. Thus, the resistance of a metallic wire increases on
heating and decreases on cooling.
(4) Change of Physical State
Change of temperature also affects the physical state of a
material. For example, water at low temperature is ice (a solid), at
a higher temperature, it is liquid, and still at higher temperature; it
is steam (a gas).
(5) Heat Radiation
Material objects emit heat or thermal radiation when heated. The
intensity of these radiations increases with rise in temperature.
Mechanical Theory of Heat
The first clear experimental observations showing that caloric
cannot be conserved were made at the end of the eighteenth
century by Count Rumford, a German army engineer. He
supervised the boring of huge cannon barrels in the Munich

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Arsenal. Because of the heat generated by the boring tool, water
was used for cooling. It had to be replaced continually because it
boiled away during the boring. According to the caloric theory, as
the metal from the bore was cut into small chips, its ability to
retain caloric was decreased. Therefore, it released caloric to the
water, heating it and causing it to boil. Rumford noticed, however,
that even when the drill was too dull to cut the metal, the water
still boiled away as long as the drill was turned. Rumford also
realized that this process would go on indefinitely and produce
limitless amount of heat. This was not consistent with the idea
that heat is a substance and that only a finite amount of it could
be contained within an object. Rumford, therefore, rejected the
caloric theory and correctly guessed that heat was only a form of
energy which when disappears, definite proportion of heat is
produced.
Therefore, he concluded that heat is not the flow of caloric but it is
a form of energy which is produced by friction or by mechanical
work. The idea was supported by Joule and he proved by
experiment that, 4.2 Joule of work produces 1 calorie heat.
Therefore, 4.2 J is called mechanical Equivalent of heat.
Mechanical Equivalent of Heat
Mechanical equivalent of heat is equal to the amount of work

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required to produce one unit of heat. Its value is 778 ft-lb/BTU and
427 Kg-m/Kcal.
It may be defined as the number of works unit which, when
completely converted into heat, furnish 1 unit of heat. It has been
found that J is equal to 4.2 joules/calorie. (1 joule = 107
ergs).
Total Heat or Enthalpy of Steam
It is the amount of heat absorbed by water from freezing point to
saturation temperature plus the heat absorbed during
evaporation.
Total heat or enthalpy of steam = sensible heat + Latent heat
It is denoted by (H) and its value for dry saturated steam may be
read directly from steam tables.
Specific Heat
The quantity of heat required to raise the temperature of a body of
mass 1kg by 1k is called specific heat. It can be expressed
mathematically as
Q
C = -----------
m T

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Where Q is the amount of heat which causes a change T in the
temperature of the substance having mass ‘m’.
Unit of Specific Heat
The unit of specific heat is Joule per kilogram per Kelvin.
OR
Joule per kilogram per degree centigrade.
Specific heat does not depend upon shape, volume or mass of
the body, but only on the material which makes the body.
Relation between Specific Heats
The specific heats CP & Cv of a perfect gas are assumed to
remain constant at all temperatures, but for real gases they
increase considerably at high temperatures.
For any particular gas the specific heat at constant pressure is
always greater than specific heat at constant volume and the ratio
of the two remains constant.
The constant is denoted by γ.
In other word,
γ = Cp/Cv
For air

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Cv = 0.17 kcal/kg-°k
Cp = 0.24 kcal/kg-°k
And in SI unit
For air
Cv = 2.7128 kJ/Kg-°k
CP = 1 KJ/kg-°k
Another relationship between specific heats and characteristic
gas constant is
CP-Cv = R/J
R is gas constant, whose value is taken as
0.287 KJ/Kg-°k
and J is mechanical heat equivalent.
Specific Heat of Water is higher while that of Earth is Low
Higher specific heat of water effects the climate i.e. climate of
areas situated around the lakes or sea shores is always mild.
During the daytime, the earth because of low specific heat gets
heated up quickly. Therefore, the air overland becomes warmer
and rises up. Thus, cold air from sea moves towards the land and

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lowers the temperature on land. This movement of air from sea to
land is called sea breeze.
Similarly, in the night, the land quickly cools down, but, the air
over water remains warmer. So, this breeze moves from land to
sea. These breezes keep temperature of the area milder.
Specific Heat Capacity
The specific heat capacity of a substance is defined as the heat
required to raise the temperature of unit mass of it through 1K.
The SI unit of specific heat capacity is the joule per Kilogram
Kelvin (J/Kg K) or KJ/Kg or MJ/Kg.
Specific Heat of a Gas
The specific heat of a substance may be broadly defined as the
amount of heat required to raise the temperature of its unit mass
through 1°C. All the liquids and solids have one specific heat only.
But a gas can have any number of specific heats (lying between
zero and infinity) depending upon the conditions, under which it is
heated. The following two types of specific heats of a gas are
important from the subject point of view.
1. Specific heat at constant volume and
2. Specific heat at constant pressure.

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Specific Heat of a Gas at Constant Pressure (CP)
Specific heat of a gas at constant pressure is defined as the
amount of heat required to raise the temperature of a unit mass of
a gas through 1°C. It is generally denoted by CP.
Thus, it is the amount of heat required to raise the temperature of
a unit mass of a gas through unit degree when the pressure is
kept constant.
If m kg of a gas is heated at constant pressure from initial
Temperature TI to final Temperature T2, then heat supplied is
Q = m CP (T2-T1)
Specific Heat of a Gas at Constant Volume (Cv)
Specific heat of a gas at constant volume is defined as the
amount of heat required to raise the temperature of a unit mass of
a gas through 1°C when it is heated at constant volume. It is
denoted by Cv.
Thus, it is the quantity of heat required to raise the temperature of
a unit mass of a gas through unit degree when the volume is kept
constant.
If m kg of a gas is heated at constant volume from initial
temperature T1 to final temperature T2, then heat supplied is

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Q = m Cv (T2-T1)
Latent Heat
The heat energy involved in a change of state is called Latent
heat.
Latent Heat of Melting
The quantity of heat required to transform one kilogram of solid
completely into liquid at its melting point is called latent heat of
melting or fusion.
Latent heat of ice is 3.36 x 105
J/Kg. It means that 3.36 x 105
J of
heat is required to transform one Kg of ice into water at 0°C.
When a solid is heated, its molecules vibrate vigorously because
their kinetic energy is increased. While on further heating, the
vibrations become so vigorous that they overcome the forces of
attraction between the molecules. So, these molecules start
moving apart and the solid starts melting. During this process, the
heat supplied to the solid is not indicated by rise in thermometer
temperature. Because this heat is used to overcome the forces of
attraction of molecules, therefore, temperature does not rise.
Latent Heat of Vaporization
It is the amount of heat absorbed to evaporate 1 kg of water at its
boiling point, without change of temperature. It is denoted by L,

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and its value depends upon the pressure. The latent heat of
vaporization of water or latent heat of steam is 537 kcal/kg at
atmospheric pressure.
It has been experimentally found that the value of L decreases as
the pressure increases.
Latent Heat of Vaporization or Boiling (Steam)
The amount of heat required to transform the mass of one kg of
liquid completely into gas at its boiling point is called the latent
heat of boiling or vaporization.
The latent heat of water is 2.26 x 106
J/Kg. It means that one Kg of
water requires 2.26 x 106
J to change into gas at 100o
C.
When a liquid is heated, its temperature rises and becomes equal
to the boiling point. At this temperature, the movement of
molecules becomes vigorous. This fast motion overcomes the
forces of attraction between molecules. So, some of these
molecules escape from the surface of liquid and converts the
liquid into gas. During this process, heat absorbed is used to
change the liquid into gas and, therefore, during this process,
temperature does not rise.
Specific Latent Heat of Vaporization
The specific latent heat of vaporization of a substance is the

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quantity of heat required to change unit mass of the substance
from the liquid to the vapor state without change of temperature.
The SI unit of specific latent heat of vaporization is the joule per
kilogram (J/kg).
Specific Latent Heat of Fusion
The specific latent heat of fusion of a substance is the quantity of
heat required to convert unit mass of the substance from the solid
to the liquid state without change of temperature.
The SI units of specific latent heat of fusion are J/Kg or KJ/Kg or
MJ/kg.