WHAT IS ELASTICITY AND MICROSCOPIC REASON OF ELASTICITY

WHAT IS ELASTICITY 

We have use the concept of a a rigid solid body in which the distance between any two particles is always fixed. Real solid bodies do not exactly fulfil this condition. When external forces are applied, the body may get deformed. When deformed, internal forces develop which try to restore the body in its original shape. The extent to which the shape of a body is restored when the deforming force are removed varies from material to material. The property to restore the natural shape or oppose the deformation is called elasticity.

If a body completely gains its nature shape after the removal of the deforming forces, it is called a perfectly elastic body. If a body remains in the deformed state and does not even partially regain its original shape after the removal of the deforming forces, it is called a perfectly inelastic or plastic body.

Quite often, when the deforming forces are removed, the body partially regains the original shape. Such bodies are partially regains the original shape. Such bodies are partially elastic.

Microscopic Reason of Elasticity

A solid body is composed of a great many molecules or atom arranged in a particular fashion. Each molecule is acted upon by the force due to the neighbouring molecules. The solid taken such a shape that each molecule finds itself in a position of stable equilibrium. When the body is deformed, the molecules are displaced from their original positions of stable equilibrium. The intermolecular distances change and restoring force start acting on the molecules which drive them back to their original positions and the body taken its natural shape.

 One can  compare this situation to a spring-mass system. Consider a particle connected to several particles through springs. If this particle is displaced a little, the springs exert a resultant force which tries to bring the particle towards its natural position. In fact, the particle will oscillate about this position. In due course, the oscillations will be damped out and the particle will regain its original position.

 

WHAT IS SPECTRUM AND IT'S KINDS

WHAT IS SPECTRUM AND IT'S KINDS

When light coming from a source is dispersed by a prism or any other dispersing element, light of different wavelengths are deviated through different angles and get separated. Such a dispersed light may be received on a screen, on a photographic plate or it may be viewed directly by the eye. A collection of dispersed light giving its wavelength composition is called a spectrum.As a very simple demonstration, let white light fall on a prism and collect the transmitted light on a white wall or a white paper. A spectrum consisting of different colours from red to violet is obtained.

KINDS OF SPECTRA

There are two types of spectra

A.  Emission Spectra

Light is emitted by an object when it is suitably excited by heating or by passing an electric discharge. When a light beam emitted by such a source is dispersed to get spectrum, it is called an emission spectrum. An emission spectrum carries information about the source material. An emission spectrum can be of three types:

(a) continuous spectrum 

Quite often a source emits light which has continuously varying wavelengths in it. electric bulb, a candle or a red hot iron piece emits light of this type. When such a light is dispersed, a bright spectrum continuously distributed on a dark background is obtained. The colours gradually change and there are no sharp boundaries in between. Such a spectrum is known as a continuous emission spectrum.

(b) line spectrum

All objects are made of atoms and molecules. The atoms and molecules can have certain fixed energies. An atom or a molecule having the lowest possible energy is said to be in its ground state, otherwise, in an excited state. An atom or molecule, in an excited state can emit light to lower its energy. Light emitted in such a process has certain fixed wavelengths. The light emitted by one kind of atoms generally have widely separated wavelength components (figure3.1a). When such a light is dispersed, we get certain sharp bright lines on a dark background. Such a spectrum is called line emission spectrum. It carries information about the atoms of the source. For example, when electric discharge is passed through sodium vapour, the vapour emits light of the wavelengths 589.0 nm and 589.6 nm. When dispersed by a high resolution grating, one obtains two bright yellow lines on a dark background.

(c) Band spectrum

The molecular energy levels are generally grouped into several bunches, each bunch widely separated from the other, and the levels in a bunch being close to each other. Thus, the wavelengths emitted by such molecules are also grouped, each group being well separated from the other. The wavelengths in a group are close to one another and appear as continuous. The spectrum looks like separate is called a band emission spectrum. Figure(3.1b) shows schematically the production and appearance of band spectra.

B. Absorption spectrum

When white light having all wavelengths is passed through an absorbing material, the material may absorb certain wavelengths selectively. When the transmitted light is dispersed, we get dark lines or bands at the position of the missing wavelengths superposed on an otherwise bright continuous coloured background (figure 3.2).

The missing wavelengths provide information about the absorbing materrial. Such a spectrum is called an absorption spectrum. 

Absorption spectrum may be of two types depending on the absorbing material and the conditions, such as temperature, of the experiment.

(a) Line Absorption spectrum

light may be absorbed by atoms to take them from lower energy states to higher energy states. In this case, the missing wavelengths are widely separated and we get sharp dark lines on a continuous bright background. Such a spectrum is called a line absorption spectrum. When light coming from the sun is dispersed, it shows certain sharply defined dark lines. This shows that certain wavelengths are absent. These missing lines are called Fraunhofer lines.

(b) Band absorption spectrum

If light is absorbed by molecules of the absorbing material, exciting them from lower energy to higher energy states, the missing wavelengths are grouped into bunches. Thus, when the transmitted light is dispersed, we get separate dark bands on a continuous bright background. Such a spectrum is called a band absorption spectrum. Light passing through hydrogen gas at moderate temperature or through certain solutions of organic and inorganic compounds shows such a spectrum.

 

THE SECOND LAW OF THERMODYNAMICS

THE SECOND LAW OF THERMODYNAMICS

When a body at 100*c is kept in contact with a similar body at 0*c, heat flows from the hotter body to the colder body and both come to 50*c. Is the reverse process possible ? That is, if we put two similar bodies both at 50*c in contact, can heat flow from one body to the other so that one body reaches 0*c and the other 100*c ? A block moving at a speed v0 on a rough table eventually stops and the table and the block warm up. The kinetic energy of block appears as the internal energy of the table and the block. Can the reverse process be possible ? That is, we heat the block and the table and put the block on the table. Can the bodies cool down and the block start sliding with speed on the table converting the internal energy into kinetic energy ? Consider a container with rigid walls divided in two parts by a partition having a valve. A gas is put in one part and vacuum is created in the other part. The valve is now opened. The gas eventually occupies both the part of the container. Is the reverse process possible ? We put the gas distributed in both the parts with the valve open. Can the gas go into one part evacuating the other part all by itself ?

The answer to all these questions is NO. of course, the first law of thermodynamics is not violated in any of these proposed reverse processes. The energy is conserved in the direct process as well as in the reverse process. still the reverse process is not possible. There must be a law nature other than the first law which decides, whether a given process, allowed by the first law, will actually take place or not. This law is the second law of the thermodynamics. This law may be stated in various ways. We give here one statement in terms of working of heat engines. We know that a heat engine taken Q1 amount of heat energy from a hot body, converts a part of it into mechanical work and rejects the rest amount Q2 to a cold body. The efficiency of the engine is 1 - Q2 / Q1. The efficiency would be 1, that is, 100% if Q2 = 0./ Such an engine would not need any "low- temperature body" to which it needs to reject heat. Hence, it needs only one body at a single temperature, from which it will take heat and covert it completely into mechanical work. This temperature can even be temperature of the surrounding and hence we will not have to burn any fuel to prepare steam or gases at high temperature to run the engine. A scooter could be run by an engine taking heat from the body of the scooter without needing any petrol. A ship could be run by an engine taking heat from the ocean. However, all attempts to construct such a 100% efficient engine failed. In fact, it is not possible to have such an engine and this is one from of the second law of thermodynamics stated more precisely as follows:

It is not possible to design a heat engine which works in cyclic process and whose only result is to take heat from a body at a single temperature and convert it completely into mechanical work.

This statement of the second law is called the Kevin-planck statement.

One can convert mechanical work completely into heat but one cannot convert heat completely into mechanical work. In this respect, heat and work are not equivalent. We shall now study some other aspects of the second law of thermodynamics. 

THE FIRST LAW OF THERMODYNAMICS

The First Law Of Thermodynamics

We have seen that heat is just a form of energy. A system can be given energy either by supplying heat to it (by placing it in contact with a hotter object) or by doing mechanical work on it. consider an ideal gas in a cylindrical container fitted with a piston (figure 2.1). Suppose the piston is fixed in its position and the walls of the cylinder are kept at a temperature higher than that of the gas. The gas molecules strike the wall and rebound. The average kinetic energy of a wall molecule is larger than the average kinetic energy of a gas molecule. Thus, on collision, the gas molecules receive energy from the wall molecules.This increased kinetic energy is shared by other molecules of the gas and in this way the total internal energy of the gas increases.

Figure 2.1

Next, consider the same initial situation but now the walls are at the same temperature as the gas. Suppose the piston is pushed slowly to compress the gas. As a gas molecule collides with the piston coming toward it, the speed of the molecule increases on collision (assuming elastic collision, v2 + v1 +2u in figure 2.2). This way the internal energy of the molecules increases as the piston is pushed in.

Figure 2.2

We see that the total internal energy of the gas may be increased because of the temperature difference between the walls and the gas (heat transfer) or because of the motion of the piston (work done on the gas).

In a general situation both modes of energy transfer may go together. As an example, consider a gas kept in a cylindrical can fitted with a movable piston. If the can is put on a hot stove, heat is supplied by the hot bottom to the gas and the piston is pushed out to some distance. As the piston moves out, work is done by the gas on it and the gas loses this much amount of energy. Thus the gas gains energy as heat is supplied to it and it loses energy as work is done by it.

Suppose, in a process, an amount ∆Q of heat is given to the gas and an amount ΔW of work is done by it. The total energy of the gas must increase by ΔQ - ∆W. As result, the entire gas together with its container may start moving (systematic motion) or the internal energy (random motion of the molecules) of the gas may increase. If the energy does not appear as a systematic motion of the gas then this net energy ΔQ - ∆W must go in the form of its internal energy. If we denote the change in internal energy by ∆U, we get.

ΔU = ∆Q - ∆W

or.      ΔQ = ∆U + ∆W ...........(2.3) 

equation (2.3) is the statement of the first law of thermodynamics. In an ideal monatomic gas, the internal energy of the gas is simply translational kinetic energy of all its molecules. In general the internal energy may get contributions from the vibrational kinetic energy of molecules, rotational kinetic energy of molecules as well as from the potential energy corresponding to the molecular forces. Equation (2.3) represents a statement of conservation of energy and is applicable to any system, however complicated. 

DIFFERENCE BETWEEN AMMETER AND VOLTMETER AND IT'S WORKING

AMMETER AND VOLTMETER

Ammeter is a device to measure an electric current and voltmeter is a device to measure a potential difference. In both the instrument there is a coil, suspended between the poles of a magnet. When a current is passed through the coil, it deflects. The angle of deflection is proportional to the current going through the coil. A needle is fixed to coil.  when the coil deflects, the needle moves on a graduated scale.

Ammeter

In an ammeter, a resistor having a small resistance is connected in parallel with the coil. This resistor is called the shunt. The current to be measured is passed through the ammeter by connecting it in series with the segment which carries the current. Plus and minus signs are marked near the terminals of the ammeter. The current should enter the ammeter through the terminal marked "plus". When no current passes through the ammeter, the needle stays at zero which is marked at the left extreme of the scale.

figure1.1

Suppose the coil has a resistance Rc and the small resistance connected in parallel (shunt) has a value r. When a current i is sent through the ammeter, the current gets divided in two parts. A part i1 goes through the coil and the rest, i - i1, through the shunt. As the potential difference across Rc  is the same as that across r,

i1Rc = (i - i1)r

or,

   i1 = R/Rc + r  i.

The deflection is proportional to i1 and hence to i. The scale is graduated to read the value of i directly. The equivalent resistance of an ammeter is given

Req = Rcr/ Rc + r 

When the ammeter is connected in a segment of a circuit the resistance of the segment increases by this amount Req. This reduces the main current which we wish to measure. To minimise this error, the equivalent resistant Req should be small. This is one reason why the shunt having a small resistance r is connected in parallel to the coil. This makes Req small.

Galvanometer is very similar to an ammeter in construction. When no current passes through it, the needle stays in the middle of the graduated scale. this point is marked zero. Current can be passed through the galvanometer in either direction. the needle deflects accordingly towards left or towards right.

Voltmeter

in a voltmeter, a resistor having a high resistance R is connected in series with the coil. The end points (terminals) are connected to the points A and B between which the potential difference is to be measured. plus and minus signs are marked on the terminals. The terminal marked "plus" should be connected to the point at higher potential. when no potential difference is applied between the terminals, the needle stays at zero which is marked at the left extreme of the scale. when the potential difference is applied, a current passes through the coil and the high resistance. If Rc be resistane of the coil and V be the potential difference applied to the voltmeter, the current in the coil is

i = V/ Rc +R 

The deflection is proportional to the current i and hence to V. The scale is graduated to read the potential difference directly.

figure1.2

When the voltmeter is used in a circuit, its resistance Req = Rc + R is connected in parallel to some element of the circuit. This changes the overall current in the circuit and hence, the potential difference to measured is also changed. To minimise the error due to this, the equivalent resistance Req of the voltmeter should be large. (When a large resistance is connected in parallel to a small resistance, the equivalent resistance is only slightly less than the smaller one.) That is why, a large resistance R is added in series with the coil of a voltmeter.