THERMAL PROPERTIES OF MATTER
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 process 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 horse 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.THERMAL PROPERTIES OF MATTER
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 other 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 degree Celsius (°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.THERMAL PROPERTIES OF MATTER
3• MEASUREMENT OF TEMPERATURE
A measure of temperature is obtained using a thermometer. Many physical properties of materials change sufficiently with temperature.
Some such properties are used as the basis for
constructing thermometers. The commonly used property is variation of the volume of a liquid with temperature. For example, in common liquid–in–glass thermometers, mercury, alcohol etc., are used whose volume varies linearly with temperature over a wide range.
Thermometers are calibrated so that a
numerical value may be assigned to a given
temperature in an appropriate scale. 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 the
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, respectively. 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.THERMAL PROPERTIES OF MATTER
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 French scientist Jacques Charles (1747– 1823). Low-density gases obey these laws, which may be combined into a single relationship. 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 low-density gas and is known as ideal-gas equation. THERMAL PROPERTIES OF MATTER
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 some
time to open it. This would allow the metallic lid 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 slightly warm water. If we take out the thermometer from the warm water the level of mercury falls again. Similarly,
in 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.THERMAL PROPERTIES OF MATTER
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 . THERMAL PROPERTIES OF MATTER
Some important questions
Question 1:
The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively.
Express these temperatures on the Celsius and Fahrenheit scales.
Answer:-
Kelvin and Celsius scales are related as:
°C = °K – 273.15 … (i)
Celsius and Fahrenheit scales are related as:
°F=9/5(°C) +32
For neon:
°K = 24.57 K
°C = 24.57 – 273.15 = –248.58°C
°F=9/5(-248.58) +32
=415.44°F
For carbon dioxide:
°K = 216.55 K
°C= 216.55 – 273.15 = –56.60°C
=9/5(-56.60) +32
=-69.88°F
Question. 2
A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and then
placed on a large ice block. What is the maximum amount of ice that can melt? (Specific
heat of copper = 0.39 J g–1 K–1; heat of fusion of water = 335 J g–1).
Answer:-
Mass of the copper block, m = 2.5 kg = 2500 g
Rise in the temperature of the copper block, Δθ
= 500°C
Specific heat of copper, C = 0.39 J g–1 °C–1
Heat of fusion of water, L = 335 J g–1
The maximum heat the copper block can lose, Q = m C Δ
= 2500 × 0.39 × 500
= 487500 J
Let m1 g be the amount of ice that melts when the copper block is placed on the ice
block.
The heat gained by the melted ice, Q = m1 L
m=Q/L = 487500/335 = 145.22g
Hence, the maximum amount of ice that can melt is 1.45 kg.
THERMAL PROPERTIES OF MATTER
Some important questions:
1. Two absolute scales A and B have triple points of water defined to be 200 A and 350 B.
What is the relation between TA and TB?
2.The electrical resistance in ohms of a certain thermometer varies with temperature
according to the approximate law:
R = R o [1 + α (T – To)]
The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the
normal melting point of lead (600.5 K). What is the temperature when the resistance is
123.4 Ω?
3.A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a
steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature
is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of
the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear
expansion of steel = 1.20 × 10–5 K
–1
.
4. A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same
length and diameter. What is the change in length of the combined rod at 250 °C, if the
original lengths are at 40.0 °C? Is there a ‘thermal stress’ developed at the junction? The
ends of the rod are free to expand (Co-efficient of linear expansion of brass = 2.0 × 10–5
K
-1
, steel = 1.2 × 10–5 K
-1
).
5. The coefficient of volume expansion of glycerin is 49 × 10–5 K-1. What is the fractional
change in its density for a 30 °C rise in temperature?
Some important links:
» MECHANICAL PROPERTIES OF SOLIDS
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