Notes

Heat:

          Heat is the energy that is transferred from the body to others in thermal contact with each other as a result of the difference in temperature between them.

Temperature:

          The temperature of a body is the degree of hotness or coldness of the body.

Thermal conduct:

           In heat transfer and thermodynamics, a thermodynamic system is said to be in thermal conduct with another system if it can exchange energy with it through the process of heat.

Thermal equilibrium:

           Thermal equilibrium - When two objects A and B are in thermal contact and there is no net transfer of thermal energy from A to B or from B to A, they are said to be in thermal equilibrium.

Energy in transit:

             The form of energy that is transferred from a hot body to a cold body is called heat. Thus, Heat is, therefore, called the energy in transit.

             Once heat enters a body, it becomes its internal energy and no longer exists as heat energy.

Internal energy:

                The sum of kinetic energy and potential energy associated with the atoms, molecules, and particles of a body is called its internal energy.

                The internal energy of a body depends on many factors such as the mass of the body, kinetic and potential energies of molecules, etc.

Heat:

Heat (symbol: Q) is energy. It is the total amount of energy (both kinetic and potential) possessed by the molecules in a piece of matter. Heat is measured in Joules.

Temperature:

Temperature (symbol: T) is not energy. It relates to the average (kinetic) energy of microscopic motions of a single particle in the system per degree of freedom. It is measured in Kelvin (K), Celsius (°C), or Fahrenheit (°F).

Explanation:

Heat is the total energy of molecular motion in a substance while the temperature is a measure of the average of the molecular motion in a substance. Heat energy depends on the speed of the particles, the number of particles (the size or mass), and the type of particles in an object. Temperature does not depend on the size or type of object. For example, the temperature of a small cup of water might be the same as the temperature of a large tub of water. But the tub of water has more heat because it has more water and thus more total thermal energy.

Note:  Temperature is not energy, but a measure of it. Heat is energy.

DO YOU KNOW?

The crocus flower is a natural thermometer. It opens when the temperature is precisely 23°C and closes when the temperature drops.

Mini Exercise

1. Which of the following substances have a greater average kinetic energy of its molecules at 10°C?

(a)  steel    (b) copper         (c)   water       (d)   mercury

 Ans:   At 10°C water molecules have greater kinetic energy. Due to lesser intermolecular forces as compared to steel, copper, and mercury.

2. Every thermometer makes use of some property of a material that varies with temperature. Name the property used in:

(a) strip thermometers (b) mercury thermometers

(a) strip thermometers:

              Liquid-crystal thermometers use liquid crystals that change color in response to temperature changes. A mixture of liquid crystals is enclosed in separate partitions. Numbers on the partitions indicate temperatures according to the amount of heat present.

(b) Mercury thermometers:

Mercury thermometers are based on the fact that materials (in this case, the liquid mercury) expand when heated.

Mercury has boiling point and less specific heat.

Note:  Due to these properties’ mercury is used in mercury thermometers. Since it is opaque, it is easy to see the capillary.

Thermometer:

             A device that is used to measure the temperature of a body is called a thermometer.

Principle of thermometer:

          Mercury thermometer is based on the fact that material (in this case, the liquid mercury) expands when heated.

Basic properties of thermometric liquid:

 A thermometric liquid should have the following properties:

• It should be visible.
• It should have uniform thermal expansion.
• I should have a low freezing point.
• It should have a high boiling point.
• It should not wet glass.
• I should be a good conductor of heat.
• It should have a small specific heat capacity

Preference for mercury:

         Mercury has a uniform thermal expansion, is easily visible, has a low freezing point, has a high boiling point, and has less specific heat.

Note:  Due to these properties’ mercury is used in a mercury thermometer. Since it is opaque, it is easy to see the capillary.

liquid-in-glass thermometer:

A liquid-in-glass thermometer has a bulb with a long capillary tube of uniform and fine bore. A suitable liquid is filled in the bulb. When the bulb contacts a hot object, the liquid in it expands and rises in the tube. The glass stem of a thermometer is thick and acts as a cylindrical lens. This makes it easy to see the liquid level in the glass tube.

Uses:

Thus, mercury is one of the most suitable thermometric materials. The mercury-in-glass thermometer is widely used in laboratories, clinics, and houses to measure temperature in the range from -10°C to 150°C.

Lower and upper fixed points:

               A thermometer has a scale on its stem. The scale has two fixed points. The lower fixed point is marked to show the position of liquid in the thermometer when it is placed in ice.

               Similarly, upper fixed points are m marked to show the position of liquid in the thermometer when it is placed in steam at standard pressure above boiling water.

Scales of temperature:

A scale is marked on the thermometer. The temperature of the body in contact with the thermometer can be read on that scale. Three scales of temperature are in common in use. These are:

• Celsius scale or centigrade scale
• Fahrenheit scale
• Kelvin Scale

Celsius scale:

On the Celsius scale, the interval between lower and upper fixed points is divided into 100 equal parts. The lower fixed point is marked as 0°C and the upper fixed point is marked as 100°C.

Fahrenheit scale:

On the Fahrenheit scale, the interval between lower and upper fixed points is divided into 180 equal parts. The lower fixed point is marked as 32°F and the upper fixed point is marked as 212°F.

Kelvin scale:

In SI units, the unit of temperature is Kelvin (K) and its scale is called the Kelvin scale of temperature. The interval between lower and upper fixed points is divided into 100 equal parts. Thus, a change in 1°C is equal to a change of 1K. The lower fixed point on this scale corresponds to 273 K and the upper fixed point is referred to as 373 K. The zero on this scale is called the absolute zero and is equal to -273°C.

DO YOU KNOW?

Conversion of temperature from one scale into another temperature scale:

From Celsius to Kelvin scale:

              The temperature (T) on the Kelvin scale can be obtained by adding 273 to the temperature C on the Celsius scale. Thus

                       T (K)    =        273 + C     …………  (i)

From Kelvin to Celsius scale:

             The temperature on the Celsius scale can be found by subtracting 273 from the temperature on the Kelvin scale. Thus

                       C    =        T (K) - 273    …………  (ii)

From Celsius to Fahrenheit Scale:

             Since 100 divisions on the Celsius scale are equal to 180 divisions on the Fahrenheit scale. Therefore, each division on the Celsius scale is equal to 1.8 divisions on the Fahrenheit scale. Moreover, 0°C corresponds to 32°F.

                     F     =        1.8C  +   32    ………  (iii)

            Here F is the temperature on the Fahrenheit scale and C is the temperature on the Celsius scale.

DO YOU KNOW?

                  A clinical thermometer is used to measure, the temperature of the human body. It has a narrow range from 35°C to 42°C. It has a constriction that prevents the mercury to return. Thus, its reading does not change until reset.

USEFUL INFORMATION

Specific heat:
        Specific heat of a substance is the amount of heat required to raise the temperature of 1kg mass of that substance through 1K.
         It has been observed that the quantity of heat $\triangle Q$ required to raise the temperature $ \triangle T$ of a body is proportional to the mass of the body.

Thus,
                    $\triangle Q \alpha m \triangle T$
                     $\triangle Q$ = c m \triangle T$   ……………….. (i)

           Here $ \triangle Q$ is the amount of heat absorbed by the body and c is the constant of proportionality called the specific heat capacity or simply specific heat.

Mathematically,
   c =$\frac{\triangleQ}{(m\triangle T )}$              (ii)

Unit of specific heat:
    SI unit of specific heat is J〖kg〗$^{-1} K^{-1}$.

Importance of large specific heat capacity of water:

The specific heat of water is 4200Jk  and that of dry soil is about 810Jk  As a result, the temperature of soil would increase five times more than the same mass of water with the same amount of heat. Thus, the temperature of land rises and falls more rapidly than that of the sea. Hence, the temperature variations from summer to winter are much smaller at places near the sea than on land far away from the sea.

Storing and carrying thermal energy:

Water has a large specific heat capacity. For this reason, it is very useful in storing and carrying thermal energy due to its high specific heat capacity. The cooling system of automobiles uses water to carry away unwanted thermal energy. In an automobile, a large amount of heat is produced by its engine due to which its temperature goes on increasing. The engine would cease unless it is not cooled down. Water circulating the engine by arrows maintains its temperature. Water absorbs unwanted thermal energy of the engine and dissipates heat through its radiator.

Central heating systems:

In central heating systems, hot water is used to carry thermal energy through pipes from the boiler to the radiators. These radiators are fixed inside the house at suitable places.

DO YOU KNOW?

The presence of large water reservoirs such as lakes and seas keeps the climate of nearby land moderate due to the large heat capacity of these reservoirs.

Heat capacity:

             The heat capacity of a body is the quantity of thermal energy absorbed by it for one Kelvin (1K) increase in its temperature.
             If the temperature of a body increases through $\triangle T$ on adding $\triangle Q$ amount of heat, then its heat capacity will be $\frac{\triangle Q}{(\triangle T)}$. Putting the value of $\triangle Q$.

We get: 

            Heat capacity =      $\triangle Q/(\triangle T )$   =  $ \frac{mc\triangle T}{(\triangle T )}$
            Heat capacity =     mc …………   (i)

Equation (i) shows that the heat capacity of a body is equal to the product of the mass of the body and its specific heat capacity.

           For example, the heat capacity of 5kg of water is (5 kg \times 4200 Jkg^{-1} K^{-1}) 21000 JK^{-1}. That is; 5kg of water needs 21000 joules of heat for every 1 K rise in its temperature. Thus, the larger the quantity of a substance, the larger will be its heat capacity.

Change of state:

Matter can be changed from one state to another. For such a change to occur thermal energy is added to or removed from a substance.

Activity:

Take a beaker and place it over a stand. Put small pieces of ice in the beaker and suspend a thermometer in the beaker to measure the temperature of the ice.

Now place a burner under the beaker. The ice will start melting. The temperature of the mixture containing ice and water will not increase above 0°C until all the ice melts and we get water at 0°C. If this water at 0°C is further heated, its temperature will begin to increase above 0°C as shown by the graph in the figure. 8.9.

Part AB: On this portion of the curve, the temperature of ice increases from 30°C to 0°C.

Part BC: When the temperature of ice reaches 0°C, the ice water mixture remains at this temperature until all the ice melts.

Part CD: The temperature of the substance gradually increases from 0°C to 100°C. The amount of energy so added is used up in increasing the temperature of the water.

Part DE: At 100°C water begins to boil and changes into steam. The temperature remains 100°C until all the water changes into steam.

Fusion point or melting point:

                          When a substance is changed from a solid to a liquid state by adding heat, the process is called melting or fusion.

                           The temperature at which a solid start melting is called its fusion point or melting point.

Freezing point:

                  The temperature at which a substance is changed from liquid to solid state is called the freezing point. However, the freezing point of a substance is the same as its melting point.

Latent heat of fusion:
            The heat energy required to change a unit mass of a substance from solid to liquid state at its melting point without a change in its temperature is called its latent heat of fusion.

It is denoted by H_f.
                                      H_f  = $\frac{( \triangle Q_{f})}{(m)}$  
   Or                   $\triangle Q_{f}$=  $m H_{f}$   …………   (i)

Ice changes at 0°C into water. Latent heat of fusion of ice is:
$3.36\times 10^{5}$  $Jkg^{-1}$.  That is, $3.36 \times 10^{5}$  joule heat is required to melt 1kg of ice into the water at 0°C.

Experiment:

Take a beaker and place it over a stand. Put small pieces of ice in the beaker and suspend a thermometer in the beaker to measure the temperature. Place a burner under the beaker. The ice will start melting. The temperature of the mixture containing ice and water will not increase above 0°C until all the ice melts. Note the time which the ice takes to melt completely into the water at 0°C

Continue heating the water at 0°C in the beaker. Its temperature will begin to increase. Note the time which the water in the beaker takes to reach its boiling point at 100°C from 0°C.

Draw a temperature-time graph as shown in figure 8.11. Calculate the latent heat of fusion of ice from the data as follows:

Let, the mass of ice = m

Finding the time from the graph:

Time taken by ice to melt completely at 0°C =$ t_{f} = t_{2-} t_{1} $ =  3.6 min.
Time taken by water to heat from 0°C to 100°C =$ t_{0} = t_{3-} t_{2}$ =  4.6 min.
Specific heat of water c = $4200 J〖kg〗^{-1} K^{-1}$.
Increase in the temperature of water = $\triangle T$ = 100°C =100 K
Heat required by water from 0°C to 100°C =$ \triangle Q$ = $ mc \triangle T$
=$m \times 4200 Jkg^{-1} K^{-1} \times 100K$
= $m\times 420 000 Jkg^{-1}$
= $m \times 4.2 \times 10^{5} Jkg^{-1}$

Heat $ \triangle Q$ is supplied to water in time $t_{0}$ to raise its temperature from 0°C to 100°C. Hence, the rate of absorbing heat by the water in the beaker is given by:

Rate of absorbing heat =  $ \triangle Q/(t_{0})$
∴ Heat absorbed in time  $t_{f} = Δ Q = (ΔQ× t_{f})/(t_{0})$ =$\frac{\triangle Q \times ( t_{f})}{(t_{0})}$ 
Since, $\triangle Q_{f}$ = $ m \times H_{f}$                  (from eq. 8.7)

Putting the values, we get:

$m \times H_{f}$  =  $m \times 4.2\times 10^{} Jkg^{-1}\times ( t_{f})/(t_{0})$
or, $H_{f}$= $\frac{4.2 \times 10^{5} Jkg^{-1} \times ( t_{f})}{(t_{0})}$ 
The values of $t_{f}$ and$ t_{0}$ can be found from the graph. Put the values in the above equation to get
$H_{f}$ = $4.2 \times 10^{5} Jkg^{-1} \times ( 3.6min)/(4.6min )$
= $3.29 \times 10^{5}  Jkg^{-1}$

     
The latent heat of fusion of ice found by the above experiment is $3.29 \times 10^{5}  Jkg^{-1}$   while its actual value is $3.36 \times 10^{5} Jkg^{-1}$.

Latent heat of vaporization:

           The quantity of heat that changes the unit mass of a liquid completely into as at its boiling point without any change in its temperature is called its latent heat of vaporization.

Melting point, boiling point, latent heat of fusion, and latent heat of vaporization of some common substances.

Experiment:

At the end of experiment 8.1, the beaker contains boiling water. Continue heating water till all the water changes into steam. Note the time which the water in the beaker takes to change entirely into steam at its boiling point of 100°C

Extend the temperature-time graph as shown in the figure. Calculate the latent heat of fusion of ice from the data as follows:

 Let, Mass of ice = m

Time $ t_{0}$ taken to heat water from 0°C to 100°C (melt) = t_{0} = $t_{3-} t_{2}$ =  4.6 min.
Time taken by water at 100°C to change it into steam = $t_{4}= t_{4-} t_{3}$ =  24.4 min.
Specific heat of water c  = $4200 J〖kg〗^{-1} K^{-1}$.
Increase in the temperature of water = $\triangle T$ = 100°C =100 K
Heat required by water from 0°C to 100°C = $\triangle $Q = $mc \triangle T$

=m $ \times 4200 Jkg^{-1} K^{-1} \times 100K$
= $m \times 420 000 Jkg^{-1}$
= $m \times 4.2 \times 10^{5} Jkg^{-1}$

As burner supplies heat $\triangle$ Q to water in time t_{0}  to raise its temperature from 0°C to 100°C. Hence, the rate at which heat is absorbed by the beaker is given by
Rate of absorbing heat  =   $\triangle Q/(t_{0})$
∴ Heat absorbed in time  $t_{v}$ = $ \triangle Q_{v}$   =  $\frac{(\triangle Q\times t_{v})}{(t_{0})}$ 

=$ \frac{ \triangle Q \times(t_{v})}{(t_{0})}$
Since, $\triangle Q_v$ = $m \times H_{v}$                  (from eq. 8.8)

Putting the values, we get

$ m \times H_{v}$  = $\frac{m \times 4.2 \times 10^{5} Jkg^{-1}\times ( t_{v})}{(t_{0})}$ 
or, $H_{v}$  = $ \frac{4.2 \times 10^{5} Jkg^{-1} \times ( t_{v})}{(t_{0})}$
Putting the values of $ t_{v}$  and $ t_{0} $ from the graph, we get

$H_{v}$  = $\frac{4.2 \times 10^{5} Jkg^{-1}\times ( 24.4min)}{(4.6min )}$ 
= $2.23 \times 10^{6}  Jkg^{-1}$       

The latent heat of vaporization of water found by the above experiment is $2.23 \times 10^{6} Jkg^{-1}$ while its actual value is $2.23 \times 10^{6}  Jkg^{-1}$.

The evaporation:

Evaporation is the changing of a liquid into vapors (gaseous state) from the surface of the liquid without heating it.

Evaporation causes cooling:

Evaporation plays an important role in our daily life. Ours clothe dry up rapidly when spread. During evaporation; fast-moving molecules escape out from the surface of the liquid. Molecules that have lower kinetic energies-l are left behind. This lowers the average kinetic energy of the liquid molecules and the temperature of the liquid. Since the temperature of a substance depends on the average kinetic energy of its molecules. Evaporation of perspiration helps to cool our bodies.

$T \alpha K.E$

Evaporation takes place at all temperatures from the surface of a liquid. The rate of evaporation is affected by various factors.

Factors affecting the rate of evaporation:

1. Temperature:

Why do wet clothes dry up more quickly in summer than in winter? At a higher temperature, more molecules of a liquid are moving with high velocities. Thus, evaporation is faster at high temperatures than at low temperatures.

2. Surface area:

Why does water evaporate faster when spread over a large area? The larger the surface area of a liquid, the greater number of molecules have the chance to escape from its surface.

3. Wind:

Wind blowing over the surface of liquid sweeps away the liquid molecules that have just escaped out, this increases the chance for more liquid molecules to escape out.

4. Nature of the liquid:

Do spirit and water evaporate at the same rate? Liquids differ in the rate at which they evaporate and spread a few drops of ether or spirit on your palm. You feel cold, why?

Mini Exercise

1. How does specific heat differ from heat capacity?

2. Give two uses of the cooling effect of evaporation.

Ans:   Uses of cooling effect by evaporation:

1. During hot summers, the water is usually kept in the earthen pot to keep it cool. Water is cooled in the pot since the surface of the pot contains large pores and water seeps via their pores to the outside of the pot. This water evaporates and takes the latent heat for vaporization hence retaining the water inside the pot to be cooled.
2. Especially in villages, people often sprinkle water on the round in front of their homes during hot summers.
3. Water vaporization from leaves of trees also cools the surroundings.
4. A desert cooler cools better on a hot and dry day.
5. It is a common observation that we can sip hot tea (or milk) faster from a saucer than from a cup.
6. Wearing cotton clothes on summer days to keep the body cool and comfortable.
7. Put a little spirit on your hand and wave around, the spirit evaporates rapidly and our hands feel cooler.

3. How does evaporation differ from vaporization?

Ans:    Difference between vaporization and evaporation:

Vaporization:

Vaporization is a transitional phase of an element or compound from a solid phase or liquid phase to a gas phase. It changes matter from one state or phase into another without changing its chemical composition.

Vaporization has three types:

(i) Boiling ii.    Evaporation iii.   Sublimation

Evaporation:

Evaporation, wherein the transition from the liquid phase to the gas phase takes place below the boiling temperature at a given pressure and occurs on the surface.

COOLING IN REFRIGERATORS

Cooling is produced in refrigerators through evaporation of liquefied gas. This produces a cooling effect. Freon, a CFC, was used as a refrigerator gas. But its use has been forbidden when it was known that CFC is the cause of ozone depletion in the upper atmosphere which increases the number of UV rays from the Sun. The rays are harmful to all living matter. Freon gas is now replaced by Ammonia and other substances which are not harmful to the environment.

Thermal expansion:

              Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.

              On heating, the amplitude of vibration of the atoms and molecules of an object increases. They push one another farther away as the amplitude of vibration increases. Thermal expansion results in an increase in the length, breadth, and thickness of a substance.

Linear thermal expansion in solids:

             Consider a metal rod of length $L_{0}$ at a certain temperature $T_{0}$. Let its length on heating to a temperature T becomes L Thus
Increase in length of the rod =$ \triangle L = L - L_{0}$
Increase in temperature       = $\triangle T = T - T_{0}$
It is found that the change in length $ \triangle L$ of a solid is directly proportional to its original length$ L_{0}$, and the change in temperature $\triangle T $.

That is;
$ \triangle L \alpha L_{0} \triangle $ T

or                                                              $ \triangle L = \alpha L_{0} \triangle T $ ……….  (i)
or                                                              $ L - L_{0}= \alpha L_{0} \triangle T $
or                                                               L =$ L_{0}+ \alpha L_{0} \triangle T$
or                                                               L =$ L_{0} (1+\alpha  \triangle T)$ ……….  (ii) 

Where α is called the coefficient of linear thermal expansion of the substance.

          From equation (i), we get 
          $\alpha$ = $ ( \triangle L )/(L_{0} \triangle T )$                           (iii)

Coefficient of linear expansion $\alpha$:
  We can define the coefficient of linear expansion$ \alpha$  of a substance as the fractional increase in its length per kelvin rise in temperature.

Table gives the coefficient of linear expansion of some common solids.

Volumetric thermal expansion:

          The volume of a solid also changes with the temperature change and is called volume thermal expansion or cubical thermal expansion.
          Consider a solid of the initial volume$ V_{0}$ at a certain temperature $ T_{0}$. On heating, the solid to a temperature T, let its volume becomes V, then
Change in the volume of a solid $ \triangle V = V - V_{0}$
And change in temperature $ \triangle T$ =$ T - T_{0}$

         Like linear expansion, the change in $ \triangle V$ is found to be proportional to its original volume $ V_{0}$ and change in temperature $ \triangle T $. Thus 
 $ \triangle V \alpha V_0 \triangle T $

or                                                              $ \triangle V $ = $ \beta V_0 \triangle T $ ……….  (i)
or                                                            $ V - V_{0} =  〖\beta V〗_{0} \triangle T$
or                                                               $V = V_{0}+\beta V_{0} \triangle T $
or                                                              $ V = V_{0} (1+ \beta \triangle T)$ ……….  (ii) 

          where \beta is the temperature coefficient of volume thermal expansion, using equation (i), we get 
         $ \beta $ = $ (\triangle V )/(V_{0} \triangle T )$                           (iii)

Coefficient of volume expansion $ \beta$:

           Thus, we can define the temperature coefficient of volume expansion $ \beta $ as the fractional change in its volume per kelvin change in temperature. The coefficient of linear expansion and volume expansion are related by the equation:
   $\beta = $3 \alpha$ ……………..  (iv)

Values of $ \beta$ for different substances are given in Table

Gapes are left on railway tracks to compensate for thermal expansion during the hot season. Railway tracks buckled on a hot summer day due to expansion if it is not left between sections.

Bridges made of steel girders also expand during the day and contract during the night. They will bend if their ends are fixed. To allow thermal expansion, one end is fixed while the other end of the girder rests on rollers in the gap left for expansion.

Overhead transmission lines are also given a certain amount of sag so that they can contract in winter without snapping.

Application of thermal expansion:

1. In thermometers, thermal expansion is used in temperature measurements.
2. To open the cap of a bottle that is tight enough, immerse it in hot water for a minute or so. The metal cap expands and becomes loose. It would now be easy to turn it to open.
3. To join steel plates tightly together, red hot rivets are forced through holes in the plates. The end of the hot rivet is then hammered. On cooling, the rivets contract and brings the plates tightly gripped.
4.  Iron rims are fixed on wooden wheels of carts. Iron rims are heated. The thermal expansion allows them to slip over the wooden wheel. Water is poured on it to cool. The rim contracts and becomes tight over the wheel.

Bimetal strips:

A bimetal strip consists of two thin strips of different metals such as brass and iron joined together. On heating the strip, brass expands more than iron. This unequal expansion causes bending of the strip.

(a) A bimetal strip of brass and iron

(b) Bending of the brass-iron bimetal strip on heating due to the difference in their thermal expansion.

Uses of bimetal strips:

• Bimetal thermometers are used to measure temperatures, especially in furnaces and ovens.
• Bimetal strips are also used in thermostats.
• Bimetal thermostat switch is used to control the temperature of the heater coil in an electric iron.

DO YOU KNOW

Anomalous expansion of water:

Water on cooling below 4°C begins to expand until it reaches 0°C. On further cooling, its volume increases suddenly as it changes into ice at 0°C. When ice is cooled below 0°C, it contracts i.e. its volume decreases like solids. This unusual expansion of water is called the anomalous expansion of water.

The molecules of liquids are free to move in all directions within the liquid. On heating, the average amplitude of vibration of its molecules increases. The molecules push each other and need more space to occupy. This accounts for the expansion of the liquid when heated. The thermal expansion in liquids is more significant than in solids due to the weak forces between their molecules. Therefore, the coefficient of volume expansion of liquids is greater than solids.

        Liquids have no definite shape of their own. A liquid always attains the shape of the container in which it is poured. Therefore, when a liquid is heated, the liquid and the container change their volume.

Thermal expansion of liquids:

Thus, there are two types of thermal volume expansion for liquid

• Apparent volume expansion
• Real volume expansion

Activity:

Take a long-necked flask. Fill it with some colored liquid up to mark A on its neck as shown in the figure. Now start heating the flask from the bottom. The liquid level first falls to B and then rises to C.

The heat first reaches the flask which expands and its volume increases. As a result, liquid descends into the flask and its level falls to B. After some time, the liquid begins to rise above B on gets hot. At a certain temperature, it reaches C. the rise in level from A to C is due to the apparent expansion in the volume of the liquid. The actual expansion of the liquid is greater than that due to the expansion because of the expansion of the glass flask. Thus, the real expansion of the liquid is equal to the volume difference between A and C in addition to the volume expansion of the flask. Hence

The expansion of the volume of a liquid taking into consideration the expansion of the container also is called the real volume expansion of the liquid. The real rate of volume expansion $\beta_{r}$ of a liquid is defined as the actual change in the unit volume of a liquid for a 1K (or 1°C) rise in its temperature. The real rate of volume expansion $\beta_{r}$ is always greater than the apparent rate of volume expansion $ \beta_a$ by an amount equal to the rate of volume expansion of the container \beta_{g}.

Thus, $\beta_{r}$  = $ \beta_{a}$+ $ \beta_{g}$   ………………  (ii)

It should be noted that different liquids have different coefficients of volume expansion.