BS Physics (Foundation) Series

1. 1
Module # 34
Thermal Expansion & Classification of Steam
Types of Expansion
When a liquid contained in a vessel is heated, we observe two
types of expansions named as,
1 The apparent expansion, and
2 The real expansion
The Apparent Expansion
The expansion of liquid in a container observed without taking into
account the expansion of the container is called the apparent
expansion of the liquid.
Real Expansion
The subtraction of expansion of container from the total
expansion of container and liquid gives the real expansion of
liquid. In other words,
Real expansion = Apparent expansion + Expansion of container
The apparent expansion is always less than the real expansion.

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Experiment
Fill up a long necked round bottom flask with colored water. Cork
the flask and pass a thin tube through it into the liquid. The water
rises into the tube to the height A. Now heat the flask and observe
it carefully. At first the water level falls below A, to B. It is due to
the expansion of flask. Then on more heating, this level rises up
to C, which gives the expansion of liquid. Consider these two
expansions. First is the apparent expansion from A to C and the
second is the real expansion of water form B to C.
Fig: Real and apparent expansion
The rate of real expansion is always slightly higher than the
apparent rate of expansion.
Thus,
Rate of real expansion = Rate of expansion for the container +
Rate of apparent expansion
OR

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rr = rc + ra
Where the subscript c refers to the container, r stands for real and
a for apparent.
Thermal Expansion of Gases
Expansion of gases on heating is known as thermal expansion of
gases.
Consider an apparatus consisting of a flask tightly fitted with a
cork through which passes a long narrow tube. The lower end of
the tube is kept close to the bottom of the flask. The flask contains
a little colored water. When the upper part of the flask, containing
air, is held in both hands, the air warms up. Water now starts
rising in the tube which shows that the air has expanded.
Fig: Thermal Expansion of Gases

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Thermal Expansion of Solids
As the temperature of a solid is raised, the molecules vibrate
through larger distances. The increase in amplitude of vibration of
molecules causes an increase in the average distance between
them. Hence, solids expand on heating. Solids contract as the
temperature is lowered. This is true for most of the substances in
nature provided a phase transition does not occur.
A gap is left between two consecutive lengths of a railway line.
This provision is for allowing the lengths to expand as the
temperature rises on a summer day. Similarly, slots in concrete
roadway bridges are necessary to accommodate the expansion of
steel and concrete as the temperature rises on a summer day. In
the absence of this provision, railway tracks and bridges will
buckle and suffer damage or get destroyed.
Thermal Expansion of Liquids
The volumetric thermal expansion of a liquid is defined as the
fractional change in volume per degree change in temperature.

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Rate of Volume Thermal Expansion of Liquids
It is the change in unit volume of a liquid for unit rise of
temperature. It is actually the real rate of volume thermal
expansion of liquid.
Volumetric Thermal Expansion (of Solids)
When a solid is heated, it expands in all directions causing an
increase in its volume. Such an expansion is called volumetric
thermal expansion.
If the temperature of a solid of volume V is raised by an amount
T, then the increase in its volume V is given by:
V = VT
The constant  is known as the co-efficient of volumetric thermal
expansion. It can be defined as the fractional change in volume
per unit change in temperature. Its value depends upon the
nature of material and its unit is 1/Co
or 1/K.
Relation Between  and 
The general rule for solids that expand to the same extent in all
directions is that coefficient of volumetric thermal expansion is
three times the coefficient of linear thermal expansion, i.e.
 = 3 

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Hyperbolic Expansion
When a gas is heated in such a way that its pressure multiplied by
its volume remains constant, the expansion is called hyperbolic
expansion.
Mathematically,
Pressure x volume = Constant,
i.e.
PV = Constant
The work done and heat supplied in this case are the same as
those in the case of Isothermal Expansion.
Adiabatic Process or Isentropic Process
A process in which the working substance neither receives nor
gives out heat to its surroundings, during its expansion or
compression, is called an adiabatic process. This will happen
when the working substance remains thermally insulated so that
no heat enters or leaves it during the process.
It is thus obvious that in an adiabatic process;
1. No heat is supplied or rejected during the process.
2. The temperature of the gas changes, as the work is done at
the cost of internal energy.

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3. The process is assumed to be frictionless and the change in
internal energy is equal to the mechanical work done.
We know that
Q = AU + W
0 = AU + W {Q=0}
AU = - W
Minus sign indicates that for increase in internal energy work must
be done on the gas (i.e., -ve work must be done by the gas).
Similarly, for decrease in internal energy, work must be done by
the gas.
Steam
Steam is a vapor of water and is invisible when pure and dry. It is
used as the working substance in the operation of steam engines
and steam turbines. Steam does not obey laws of perfect gases,
until it is perfectly dry. When the dry vapor is heated further it
becomes super-heated vapor, which behaves, more or less, like a
perfect gas.
Classification of Steam
Steam may be classified as wet steam, dry saturated steam &
super-heated steam.

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1. Wet Steam:
When the steam contains moisture or particles of water in
suspension, it is said to be wet steam. It means that the
evaporation of water is not complete, and the whole of the latent
heat has not been absorbed.
2. Dry Saturated Steam:
When the wet steam is further heated, and it does not contain any
suspended particles of water, it is known as dry saturated steam.
The dry saturated steam has absorbed its full latent heat and
behaves practically, in the same way as a perfect gas.
3. Superheated Steam:
When the dry saturated steam is further heated at a constant
pressure, thus raising its temperature, it is said to be superheated
steam. Since the pressure is constant, therefore the volume of
superheated steam increases. It may be noted that one Kg of
superheated steam is considerably greater than the volume of
one Kg of dry saturated steam at the same pressure.
In actual practice, the superheated steam is produced in a
separate apparatus known as superheater, so that it is out of
contact with water from which it was formed.

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Saturated Vapor
A saturated vapor is one which is in a state of dynamic equilibrium
with its own liquid or solid. During the evaporation of liquid, some
of the molecules again come back to the liquid after escaping
from the surface. If the rate at which the molecules leave the
liquid equals the rate at which molecules re-enter the liquid, then,
the air over the surface of the liquid is said to be saturated with
the vapors of the liquid.
Dryness Fraction of Steam
It is the ratio of the weight of actual dry steam to the weight of
same quantity of wet steam. The value of dryness fraction, in
case of dry steam, is unity. At this stage, the weight of water on
suspension is zero.
Boiling Point
The boiling point (B.P.) of a substance is defined as the
temperature at which its saturated vapor pressure becomes equal
to the external atmospheric pressure.
Effect of Pressure on Boiling Point
Boiling point of a liquid increases by increasing the pressure on its
surface. Similarly, boiling point of a liquid decreases with the
decrease of pressure on its surface.

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At standard pressure, the boiling point of water is 100°C. But, if
the pressure is doubled, then, its boiling point becomes 120°C.
Experiment
Fill a round bottom flask with water to half of its capacity as shown
in figure (1). Heat it with a spirit lamp till water starts to boil. After
the water has been boiling for a couple of minutes, remove the
spirit lamp and cork the flask. The water will stop boiling after a
little while and its temperature will fall below 100°C. Now invert
the flask and pour some cold water on its bottom. Water will start
to boil again although no more heat has been provided to it. At
this stage, the boiling point of water has fallen below 100°C.
Fig: (1) The pressure effects the boiling point
Reason
The boiling of water for the first time expels all the air in the flask
replacing it with steam. When the spirit lamp is removed and flask
corked and allowed to cool, the internal steam starts to condense

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into water. As no air can enter in the flask, so, the air pressure in
the flask falls. The boiling point of water lowers and it starts to boil
below 100°C without any fresh supply of heat.
Example
Pressure cooker is made on the basis of this principle. The steam
formed exerts a pressure much above the normal atmospheric
pressure inside the pressure cooker. Due to this, the boiling point
of water becomes more than 100°C. Thus, in it, pulses, meat and
other tough eatables can be cooked in much shorter time.
Effect of Pressure on Melting Point
The melting point of those materials which expand on being
frozen get lowered when pressure over one atmosphere is
exerted on them. We shall explain this fact by performing a simple
experiment.
Experiment
Take a fine bare copper wire and attach to its end the largest
weight which the wire will support without breaking. Place the wire
across a block of ice as shown in fig :( 1). The copper wire sinks
slowly through the block and the weight falls to the floor. The ice
block, however remains in one piece.

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Fig: (1) Block of ice allowing copper wire to pass
(Regelation Experiment)
Reason
The large pressure exerted by wire lowers the freezing point of ice
and so the ice beneath the wire melts. But, above the wire, the
water refreezes. It releases the latent heat which is conducted
through the copper wire which helps to melt the ice beneath. This
process continues till the wire cuts through the ice block.
Examples
(1) Sweetened ice-balls are prepared under this principle. When
fluffy ground ice is pounded together, some of the ice flakes in
between tiny ice blocks melt under increased pressure. When the
pressure is released, the water refreezes forming an ice ball.
(2) Skating is also possible due to this principle. Because, ice
beneath feet melts and forms a thin layer of water, therefore, due
to this, a skater moves quickly.