Elements of properties of matter by ds mathur pdf

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Elements Of Properties Of Matter Bookyards is the world's biggest online library where you can find Download Free PDF D. S. Mathur Physics Convert to Kobo. Elements Of Properties Of Matter. byMathur, D. S. Publication date Topics NATURAL SCIENCES, Physics, Physical nature of matter. PublisherS. Chand. January 12, Posted in niter te level 1 term 1 pdf link. Smart fibres, fabrics and clothing by tao pdfIn "niter te level-3 term-2 pdf" a textbook of electrical technology by bl theraja pdf volume 1In "niter te level-2 term-2 pdf".

Metals and alloys An alloy is a metal composed of more than one element. At times you my not necessarily follow the order in which the activities are presented. A minimum of two video, audio with an abstract in text form is provided in this section. Buy New Price: It is usual to refer to this as due to the internal friction of solids.

Any body completely or partially submerged in a fuid is buoyed up by a force equal to the weight of the fuid displaced by the body. In other words the magnitude of the buoyant force is equal to the weight of the fuid displaced by the object. Hence the density of the object is less than the density of the fuid, the unsupported object will accelerate upward.

If the density of the object is greater than the density of the fuid, the unsupported object will sink. Case II: A foating object Consider an object in static equilibrium foating on a fuid; that is one which is partially submerged. In this case, the upward buoyant force is balanced by the downward weight of the object. Stream Lines The path taken by a fuid particle under steady fow is called a stream line.

A particle at P fows one of thesestreamlines, and its velocity V is tangent to the streamline at each point along its path. The particles in the fuid move along the streamlines in steady fow. At all points the velocity of the particles is tangent to the stream line along which it moves.

We shall assume that the fuid is incompressible and nonviscous and that it fows in an irrotational and steady manner. Therefore the force on the lower end of the fuid is P 1 A 1 where P 1 is the pressure at point 1.

This work is negative since the fuid force opposes the displacement. Calculation of speed in fluid flow a A water hose 2cm in diameter is used to fll a 20 litre bucket.

If it takes 1min to fll the bucket, what is the speed v at which the water leaves the hose? Task 2. Using Archimedes principle to compare densities a A plastic sphere foats in water with 0. This same sphere foats in oil with 0. Determine the ratio of densities of the oil and the sphere. Using fluid dynamics equations to solve problems 1.

Mathur elements of by of ds properties pdf matter

Determine the absolute pressure at the bottom of a lake that is 30m deep. A swimming pool has dimensions 30m X 10m and a fat bottom. When the pool is flled to a depth of 2m with fresh water, what is the total force due to the water on the bottom? On each end? On each side? Find the depth in water for which the spring is compressed by 0. Determine the velocity of fow at a point where the diameter of the pipe is a 10cm b 5cm 2.

What is the hydrostatic force on the back of Grand Coulee Dam if the water in the eservoir is m deep and width of the dam is m? Calculate the buoyant force on a solid object made of copper and having a volume of 0. What is the result if the object is made of steel?

In air an object weighs 15N. When immersed in water, the same object weighs 12N. When immersed in another liquid, it weights13N. Find a. The density of the object and b. The density of the other liquid African Virtual University 51 Activity 3: Transport Properties You will require 25 hours to complete this activity.

In this activity you are guided with a series of readings, Multimedia clips, worked examples and self assessment questions.. You are strongly advices to go through the activities and consult all the compulsory materials and as many as possible among useful links and references. In addition you will in detailed describtion of conduction and thermal expansion of metals using mathematical approach. The transportaion of electron is discussed in terms of the effective concentration of mobile electrons in metals, alloys and and semiconductors Key Concepts Diffusion: Is the movement of particles from higher chemical potential to lower chemical potential chemical potential can in most cases of diffusion be repre- sented by a change in concentration.

An electric charge is an attribute of matter that produces a force.

Elements of Properties of Matter

If two solutions of different concentration are separated by a semi- permeable membrane which is permeable to the smaller solvent molecules but not to the larger solute molecules, then the solvent will tend to diffusion across the membrane from the less concentrated to the more concentrated solution this process is called osmosis. Electron diffusion: The conduction of heat is also a process of diffusion in which random thermal energy is transferred from a hotter region to a colder one without bulk movement of the molecules themselves.

Viscous motion: African Virtual University 52 Thermal expansion of solids or a body: Is a consequence of the change in the average separation between its constituent atoms or molecules Electrical conductivity: Is the ability of different types of matter to conduct an electric current Semiconductors: Viscosity is the resistance or the internal friction between molecules.

Some liquids like water have a low viscosity whereas other liquids like honey have a high viscosity.

At higher temperatures the viscosity decreases as the molecules take on more kinetic energy allowing them to move past each other faster List of Relevant Resources Reference: This resource is video show on electric charges Reference: If mole- cules of a chemical are present in an apparently motionless fuid, they will exhibit microscopic erratic motions due to being randomly struck by other molecules in the fuid.

That is, there will be a net transport of that chemical from regions of high concentration to regions of low concentration. An analogous form of diffusion is called conduction. As in chemical diffusion, heat migrates from regions of high heat to regions of low heat. The mathematics describing both conduction and diffusion is the same. Figure 1 Consider two containers of gas A and B separated by a partition.

The molecules of both gases are in constant motion and make numerous collisions with the partition Detailed Description of The Activity Main Theoretical Elements Gases Liquids and Solids As a useful, though not complete, classifcation it can be said that matter exists in three states, as gas, liquid or solids.

This statement is justifed by the fact that there exist many substances which can undergo sharp, easily identifable, repro- ducible and reversible transitions from one state to the other.

Water is the classical example: There are obvious contrast between the properties of ice, water and steam or water vapour which make their description as solid, liquid and gas quite unambiguous. Similarly, most metals are solid, they melt under well defned conditions of temperature and pressure to form liquids and boil at higher temperatures to produce gases.

African Virtual University 54 If all substances possessed such clear demarcations, it would be easy to defne the different states of matter. But there are very many substances like glasses or glues which one normally thinks of as being solid but which do not melt at sharply defned temperatures; when heated they gradually become plastic, till they become recognizably liquid.

Other solids such as wood or stone are inhomogeneous and it is diffcult to describe their structure in detail. Prosperities and structures of gases Gases have low densities they are highly compressible over wide ranges of volume, they have no rigidity and low viscosities. The molecules are usually a large distance apart compared with their diameter and there is no regularity in their arrangement in space. Given the positions of two or three molecules, it is not possible to predict where a further one will be found with any precision.

The molecules are distributed at random throughout the whole volume. The low density can be readily understood in terms of the comparatively small number of molecules per unit volume. The high compressibility follows from the fact that the average distance between molecules can be altered over wide limits.

The molecules can move long distances without encountering one another, so there is little resistance to motion of any kind, which is the basis of the explanation of the low viscosity.

Properties and structure of liquids Liquids have much higher densities than gases and their compressibility is low. They have no rigidity but their viscosity is greater than that of ordinary gases.

The molecules are packed quite closely together and each molecule is bonded to a number of neighbors but still the pattern as a whole is a disordered one. The molecules are moving with just the same order of velocity as in a gas at the same temperature, though the motion is now partly in the form of rapid vibrations and partly translational. Properties and structure of solids Solids have practically the same densities and compressibilities as liquids.

In addition they are rigid; under the action of small forces they do not easily change their shape. An important property of those solids which have a well-defned melting — point is that they are close packed, and the arrangement is highly regular. Substances which do not melt sharply but show a gradual transition to the liquid when heated are said to be amorphous and show no trace of regularity of external shape.

In crystalline solids, the molecules are arranged in regular three dimensional patterns or lattices, If the crystal has been carefully prepared, the regular arran- African Virtual University 55 gement persists over distances of several thousand molecules in any direction before there is an irregularity, but if it has been subjected to strains or distortions the regular arrangement may be perfect and uninterrupted only over much shor- ter average distances.

In metals the ions are closely packed together, so that the distance between the centre of an ion and that of one of its nearest neighbours is equal to the diameter of one ion, or something close to it. In other crystals, the packing together of the molecules may be relatively open, but even in light solids such as ice the distance between the centers of any molecule and its near neighbors in only twice the diameter of a molecule.

In solids, the molecules are again moving with the same order of magnitude of velocity as in gases or liquids, but the motion is confned to vibrations about their mean positions.

Transport Processes So far we have learned the properties of solids, liquids and gases which are in equilibrium. In this activity we will deal with systems which are nearly but not quite in equilibrium in which the density or the temperature or the average mo- mentum of the molecules varies from place to place.

Under these circumstances there is a tendency for the non-uniformities to die away through the movement the transport of molecules down the gradient of concentration or of their mean energy down the temperature gradient or their mean momentum down the velo- city gradient. Diffusion Diffusion is the movement of molecules from a region where the concentration is high to one were it is lower, so as to reduce concentration gradients. This process can take place in solids, liquids and gases though this part you will be mostly concerned with gases.

Diffusion is quite independent of any bulk movements such as winds or convection currents or other kinds of disturbance brought about by differences of density or pressure or temperature although in practice these often mask effects are due to diffusion. One gas can diffuse through another when both densities are equal. For example, carbon monoxide and nitrogen both have the same molecular weight, 28, so that there is no tendency for one or other gas to rise or fall because of density diffe- rences: Diffusion can also take place when a layer of the denser of two fuids is initially below a layer of the lighter so that the diffusion has to take place against gravity.

Thus, if a layer of nitrogen is below a layer of hydrogen, a heavy stratum below a light one, then after a time it is possible to detect some hydrogen at the bottom and some nitrogen at the top, and after a very long time both layers will be practically uniform in concentration.

If the rates of change of concentration with time are plotted, the diffusion coeffcient can be deduced; the equations describing the process are given in diffusion equation. Figure 2 Concentration as a function of x for different values of time t The diffusion equation We will begin by taking a macroscopic view of the phenomenon, that is, we will write down equations which involve such variables as concentrations or fuxes but will not specifcally mention individual molecules.

Let us consider the simple case where n varies with one coordinate only the x-axis. In Figure 1. Then diffusion takes place down the concentration gradient, from high to low concentration; we are assuming that bulk disturbances are absent. We next defne the fux J of particles as the number of particles on average crossing unit area per second in the direction of increasing x.

Notice that both concentration and fux can be measured in moles instead of numbers of molecules: In other words, J may be a function of x and t so we write it as J x,t. Of course, there are circumstances where J may be the same for all x, or where it is constant with time, but the most general situation is that j depends on both. It is an experimental fact that, at any instant that fux at any position x is propor- tional to the concentration gradient there: By itself, Eq.

Consider, however, the much more general situation where initially a certain distribution of concentration is set up and then subsequently the molecules dif- fuse so as to try to reach a uniform concentration.

The rate of movement of molecules from the slice is equal to the difference between the two values of AJ, and also equal to the volume of the slice, A dx, times the rate of decrease of n: This is called the diffusion equation, and since n depends on x and t it could be written n x,t. Eliminating J: These are typical of transport equations with the provision that for energy and momentum diffusion, the coeffcients in the three equations are not all identical as they are here.

African Virtual University 59 Heat conduction Heat can be transferred by conduction, convection or radiation. The process of transferring heat through a body is called thermal conduction. The physical pro- perty known as thermal conductivity is a measure of how effcient the material will conduct heat through it.

The thermal conductivity of a substance is defned as the amount of heat transfer per unit area per unit time per unit temperature gradient through a body. Mathematically, thermal conductivity can be treated in a very similar way to diffusion leading to very similar types of mathematical functions.

Thermal conductivity is very important when designing for thermal insulation, thermal isolation, effcient heat transfer and cooling systems The conduction of heat is also a process of diffusion in which random thermal energy is transferred from a hotter region to a colder one without bulk movement of the molecules themselves.

In a hot region of a solid body, they have extra kinetic energy. By a collision process, this energy is shared with and transferred to neighbouring molecules, so that the heat diffuses through the body though the molecules themselves do not migrate. Combining these two equations to eliminate Q: But when conditions are not steady, and T varies with time as well as position, Eq. Viscosity For completeness, a third simple transport process the diffusion of momentum by viscous forces will be mentioned here, briefy.

Viscous motion of fuids can be far more complicated than diffusion or heat conduction and we will be forced to consider only the steady state equation. Figure 4 Coordinates used in the defnition of viscosity.

Consider a gas or liquid confned between two parallel plates Fig 4. Let the lower plate be stationary and the upper plate be moving in the direction shown, which we will call the x-direction. Molecules of fuid very near the plate will be dragged along with it and have a drift velocity, U x parallel to x, superposed on their thermal velocity. We will assume that U x is much less than the mean thermal speed or the speed of sound. Molecules of fuid near the stationary plate will, however, remain more or less with zero drift velocity.

Eventually a regime will be set up in which there is a continuous velocity gradient across the fuid from bottom to top. In this state, molecules will be continuously diffusing across the space between the plates and taking their drift momentum with them. Considering an area of a plane parallel to the xy plane in the fuid, molecules which diffuse across from above to below will carry more drift mo- mentum than those which diffuse from underneath to the top.

In other words, the more rapidly moving layer tends to drag a more slowly moving layer with it, because of this diffusion of momentum.


In macroscopic terms, a shearing stress force per unit area is necessary to main- tain this state of motion. Provided the direction Moving plate x U Z Y X Stationary plate African Virtual University 61 of the force is clearly understood, it is not necessary to include a minus sign, as this depends on the convention for the choice of axes. We started by considering a fuid in Figure4, but Eq.

It is diffcult to imagine a solid subjected to a shear which goes on increasing with time, but it is quite common for solids to be sheared to and for in an oscillatory fashion. Forces are then required to provide the accelerations, but in any case the viscosity gives rise to the dissipation of energy and the production of heat. It is usual to refer to this as due to the internal friction of solids.

It is implied in Figure 4. For one thing, there are always mass-acceleration terms which have no analogue in the other phenomena. For another, a kind of regime may be set up where the fow is not streamline as illustrated in Figure 4 but turbulent, and vortices or eddies are present which add an element of randomness to the fow pattern. We can, however, usefully adopt a mathematical representation of the simple situation of Fig 4.

Of matter elements ds of properties pdf by mathur

We can imagine the liquid divided into layers, each one sliding over the one underneath it on imaginary rollers like long axle rods parallel to the y-axis.

These rollers are not there in any real sense, but they can lead one to defne a quantity called the vorticity which is always present in a fowing fuid even when no macroscopic vortices are present. In a simple case like Fig. Now in the general case of an accelerating fuid with non-uniform velocity it is the vorticity which diffuses throughout the fuid, though the equation it obeys is not of a simple form African Virtual University 62 Task 3.

He found the damping coeffcient of the oscillations. If we neglect the energy loss in the torsion wire itself and assume that the discs would go on swinging for a very long time if all the gas were removed, we can calculate the damping as follows. Figure 5 Principle of the apparatus for measurement of viscosity by the damping of torsional oscillation. The contribution to the couple is the couple is the radius times the force: If there are n discs, each with two surfaces, there are 2n such contributions.

The t Law Consider fgure3. Then the appropriate solution of Eq. This is perhaps an unexpected result: Of course, some molecules go much further than this, other less far, and it is the mean which we have calculated.

Stated differently , our results shows that to diffuse a mean distance. X, the time required is proportional to x 2.

This is an important characteristic of the diffusion process. Thermal Expansions of solids and liquids. Most solids expand as their temperature increases.

The thermal expansion of solids or a body is a consequence of the change in the average separation between its constituent atoms or molecules. Suppose the linear dimension of the body along some direction is l at some temperature. The linear dimension of the body also change with temperature, it fol- lows that area and volume of a body also change with temperature. The electrical conductivity of a material is defned as the ratio of the current per unit cross-sectional area to the electric feld producing the current.

Electrical conductivity is an intrinsic property of a substance, dependent on the temperature and chemical composition, but not on the amount or shape. Electrical conductivity is the inverse quantity to electrical resistivity. For any object conducting electricity, one can defne the resistance in ohms as the ratio of the electrical potential difference applied to the object to current passing through it in amperes.

For a cylindrical sample of known length and cross-sectional area, the resistivity is obtained by dividing the measured resistance by the length and then multiplying by the area.

Conductivity is temperature dependent. The electrical conducti- vity of copper at room temperature, for instance, is over 70 million siemens per meter. On an atomic level this high conductivity refects the unique character of the metallic bond in which pairs of electrons are shared not between pairs of atoms, but among all the atoms in the metal, and are thus free to move over large distances.

Many metals undergo a transition at low temperatures to a supercon- ducting state, in which the resistance disappears entirely and the conductivity becomes infnite. The superconduction process involves a coupling of electron motion with the vibration of the atomic nuclei and inner-shell electrons, to allow net current fow without energy loss.

Electrical conductivity in the liquid state is generally due to the presence of ions. Substances that give rise to ionic conduction when dissolved are called electroly- tes. The conductivity of one molar electrolyte is of the order of 0. Sodium chloride common table salt , composed of sodium ions and chloride ions, is a very poor conductor in the solid state.

If it is dissolved in water, however, it becomes a good ionic conductor. Likewise, if it is melted, it becomes a good conductor. Substances such as hydrogen chloride or acetic acid are non- conductors in the pure state but give rise to ions and thus electrical conductivity when dissolved in water.

In modern electrochemistry, substances of the sodium chloride type, which are actually composed of ions, are termed true electrolytes, while those that require a solvent for ion formation, like hydrogen chloride, are termed potential electrolytes.

An older name for the siemens is the mho, which, of course, is ohm spelled backwards which was written as an inverted Greek omega.

Semiconductors are materials which have a conductivity between conductors generally metals and nonconductors or insulators such as most ceramics. Semi- conductors can be pure elements, such as sillicon or germanium, or compounds such as gallium arsenide or cadmium selenide. In a process called doping, small amounts of impurities are added to pure semiconductors causing large changes in the conductivity of the material. Metals and alloys An alloy is a metal composed of more than one element.

Engineering alloys include the cast-irons and steels, aluminum alloys, magnesium alloys, titanium alloys, nickel alloys, zinc alloys and copper alloys.


For example, brass is an alloy of copper and zinc. This versatile construction material has several characteristics, or properties, that we consider metallic: African Virtual University 67 1 It is strong and can be readily formed into practical shapes. Many Ca- lifornians have been able to observe moderate earthquake activity that leaves windows of relatively brittle glass cracked while steel support framing still functions normally.

Although structural steel is a special common example of metals for engineering, a little thought produces numerous others [such as gold, platinum, lead and tin].

The mean distance travelled by a molecule at any time t. Consider a composite structure shown on below. Conductivities of the layer are: Calculate the total resistance and the heat flow through the composite. An aluminum tube is 3m long at 20 0 C.

What is its length at 0 C. A metal rod made of some alloy is to be used as a thermometer. At 0 0 C its length is 40cm, and at 0 C its length is What is the linear expansion coeffcient of the alloy? What is the temperature when its length is At 20 0 C, an aluminum ring has an inner diameter of 5cm, and a brass rod has a diameter of 5.

To what temperature must the aluminum ring be heated so that it will just slip over the brass rod? To what temperature must both be heated so the aluminum ring will slip off the brass rod? Would this work? First, draw the thermal circuit for the composite. Next, the thermal resistances corresponding to each layer are calculated: These three layers are combined in series: The equivalent resistor R 1,2,3 is in parallel with R 4: Finally, R 1,2,3,4 is in series with R 5.

The total resistance of the circuit is: What is the properties of semiconductor a it is an in sulators b it is con ductors C it is material which has a conduc- tivity between conductors generally metals and nonconductors or insu- lators 2. The hollw cylinder as shown in the fgure has the length L and inner and outer radii a and b.

By mathur ds properties of matter elements pdf of

A potential difference is set up between the inner and outer surface of the cylinder so that current fow radially through the cylinder. Derive the diffusion equation in 1D 4. Summative Evaluation Summative evaluation 1. Asteel wire 2mm in diameter is just stretched between two fxed points at a temperature of 20 0 C. Determine its tension when the temperature falls to 10 0 C.

If a weight of 10kg is attached to one end what extension is produced? Find the work done in joules in stretching a wire of cross-section 1sq. Water fows along a horizontal pipe, whose cross- section is not costant. Defne the coeffcient of viscosity.

Give examples of some viscous substances. How would you determine the coeffcient of a liquid? State a the law of fuid pressure b The principle of Archimedes A string supports a solid iron object of mass gm totally immersed in a liquid of density kg m References Finn, C.

P Raymond A. Serway Updated Version. Douglas D. Giancoli Physics for Scientists and Engineers. Prentice Hall. | Elasticity (Physics) | Deformation (Mechanics)

Sears, Zemansky and Young, College Physics, 5th ed. Sena L. Godman A, and Payne E. F, Longman Dictionary of Scientifc Usage. Siegel R. Kittel C. Freeman and Co. Zemansky M. Halliday D. Main Author of the Module About the author of this module: Box personal , Institutional E-mail: You are always welcome to communicate with the author regarding any question, opinion, suggestions, etc about this module.

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