Thermodynamic Scale of Temperature :- ABSOLUTE

Thermodynamic Scale of Temperature :- ABSOLUTE 


          An absolute temperature scale is independentof the properties of the substances.The temperatures are always measured by making use of properties e.g. thermal expansion of liquids and gases, the variation of thermo e.m.f. and electrical resistance with temperature etc. 


          Lord kelvin from the study of the effeciency of reversible engion could define a new scale of temperature which a independent of the particular substance because the efdficency of a reversible engion itself is independent of the working substance

6.2 The Thermodynamic Temperature Scale;-

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Absolute temperature scale, any thermometric scale on which a reading of zero coincides with the theoretical absolute zero of temperature—i.e., the thermodynamic equilibrium state of minimum energy. The standard measure of temperature in the International System of Units is the Kelvin (K) scale, on which the only point established by arbitrary definition is the unique temperature at which the liquid, solid, and vapour forms of water can be maintained simultaneously. The interval between this temperature and absolute zero is defined as 273.16 kelvins, and the temperature of this “triple point” is designated 273.16 K (since 1967, no longer written °K). In essence, the Kelvin scale is the Celsius (°C) temperature scale shifted by 273.15 degrees (because the triple point of water is actually 0.01 °C), with the same size unit of temperature.

          (The considerations of Carnot cycles in this section have not mentioned the working medium. They are thus not limited to an ideal gas and hold for Carnot cycles with any medium. )

        More specifically, we can define a thermodynamic temperature scale that is independent of the working medium. Earlier we derived the Carnot efficiency with an ideal gas as a medium and the temperature definition used in the ideal gas equation was not essential to the thermodynamic arguments. To see this, consider the situation shown below in Figure 6.2, which has three reversible cycles. There is a high temperature heat reservoir at  and a low temperature heat reservoir at  . For any two temperatures  ,  , the         Ratio of the magnitudes of the heat absorbed and rejected in a Carnot cycle has the same value for all systems.

Figure : Arrangement of heat engines to demonstrate the thermodynamic temperature scale

We choose the cycles so  is the same for A and C. Also  is the same for B and C. For a Carnot cycle

Also

But

Hence

We thus conclude that  has the form  , and similarly  . The ratio of the heat exchanged is therefore

In general,

       so that the ratio of the heat exchanged is a function of the temperature. We could choose any function that is monotonic, and one choice is the simplest:  . This is the thermodynamic scale of temperature,  . The temperature defined in this manner is the same as that for the ideal gas; the thermodynamic temperature scale and the ideal gas scale are equivalent..

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De broglie wavelength equation (De-Broglie equation )

De Broglie Wavelength Formula

        In some situations, light behaves like a wave, while in others, it behaves like particles. The particles of light are called photons, and they can be thought of as both waves and particles. Louis de Broglie (1892-1987) developed a formula to relate this dual wave and particle behavior. It can also be applied to other particles, like electrons and protons. The formula relates the wavelength to the momentum of a wave/particle.

For particles with mass (electrons, protons, etc., but not photons), there is another form of the de Broglie wavelength formula. At non-relativistic speeds, the momentum of a particle is equal to its rest mass, m, multiplied by its velocity, v.

The unit of the de Broglie wavelength is meters (m), though it is often very small, and so expressed in nanometers (1 nm = 10(-9) m), or Angstroms  

 De broglie wavelength equation (De-Broglie equation )

     In 1924, Louis de-Broglie give the idea that matter should also posses dual nature. According to Louis de-Broglie a moving matter particle is surrounded by a wave whose wavelengths depend upon the mass of the particle and its velocity. These waves associated with the matter particles are known as matter waves or de-Broglie waves. The wavelength of the particle can be find through the following relation - 

                  

where h is the Planck's constant and p is the momentum of particle. The value of Planck's constant is 

 The de-Broglie concept of matter waves was based on the following facts- 

(i) Matter and light, both are forms of energy and each of them can be transformed into the other.

(ii) Both are governed by the space time symmetries of the theory of relativity.

Derive an expression for the de broglie wavelength:-

Considering the Planck's theory of radiation, the energy of the a photon (quantum) is given by

                              ......(1)

where c is the  velocity of light in vacuum and  is its wavelength. 

According to Einstein energy mass relation 

                              ........(2)

From equation (1) & (2), we get 

             ........(3)

where mc = p (momentum associated with photon).

If we consider the case of a material particle of mass m and moving with a velocity v, then the wavelength associated with this particle is given by 

                       ..........(4)

If E is the kinetic energy of the material particle then 

                      

            .........(5)

Substituting the value of p in equation (4), we get  de broglie wavelength,

                ...........(6)

According to kinetic theory of gases, the average kinetic energy of particle is given by 

where, K=  Boltzmann's constant = 

Putting the value of E in equation (4)

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Home rothery's rules and regulations (physics)

Hume-Rothery rules:-

HUME-ROTHERY'S RULES:- 

             In the course of an alloy development, it is frequently desirable to increase the strength of the alloy by adding a metal that will form a solid solution. In the choice of such alloying elements, a number of rules govern the for- mation of substitutional work of Hume-Rothery. Unfortunately, if an alloying element is chosen at random, intermediate phase instead of a solid solution. 

Hume-Rothery's Rules are described below. is likely to form an objectionable.

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CHEMICAL AFFINITY FACTOR 

             The greater the chemical affinity of two metals the more restricted is their solid solubility. When their chemical affinity is great, two metals tend to form an intermediate phase rather than a solid solution.

             Chemical Affinity Factor-The greater the chemical affinity of two metals, the more restricted is their solid solubility. When their chemical affinity is great, two metals tend to form an intermediate phase rather than a solid-solution. Generally, the farther apart the elements are in the periodic table, the greater is their chemical affinity.

RELATIVE VALENCY FACTOR 

              If the alloying element has a different valence from that of the base metal, the number of valence electrons per atom, called the electron ratio, will be changed by alloying. Crystal structures are more sensitive to a decrease in the electron ratio than to an increase. Therefore, a metal of high valence can dissolve only a small amount of lower valance metal, while the lower valence metal may have good solu- bility for a higher valence metal. 

              Relative Valence (Valency) Factor - It has been found that the metal of high valence can dissolve only a small amount of a lower valence metal, while the lower valence metal may have good solubility for the higher valence metal. For example in the Al-Ni alloy system both metals have FCC structure. The relative size factor is approximately 14%. However, Ni is lower n valence than Al and thus solid nickel dissolves 5% aluminium, but the higher valence Al dissolves only 0.04% Ni.

RELATIVE SIZE FACTOR 

            If the size of two metallic atoms (given approxima- tely by their constants) differs by less than 15 percent, the metals are said to have a favourable size factor for solid solution formation. So far as this factor is concerned, each of the metals will be able to dissolve apprecia- bly (to the order of l0%) in the other metal. If the size factor is greater than 15°, solid solution formation tends to be severely limited and is usually only a fraction of one percent.

               Relative Size Factor- If the two metals are to exhibit extensive solid solubility in each other, it is essential, that their atomic diameters shall be fairly similar, since atoms differing greatly in size cannot be accommodated readily in the same structure (as a substitutional solid solution) without producing excessive strain and corresponding instability. This is what referred as the term size factor. The extensive solid solubility is encountered only when the two different atoms differ in size by less than 15%, calleda favourable size factor (e.g. Cu-Ni, Au-Pt). If the relative size factor is between 8% and 15 % , the alloy system usually shows a minimum and if this is greater than 15 % , substitutional solid solution formation is very limited. 

LATTICE-TYPE FACTOR 

           Only metals that have the same type of lattice (FCC for example) can form a complete series of solid solutions. Also, for com- plete solid solubility, the size factor must usually be less than 8 percent. Copper-nickel and silver-gold-platinum are examples of binary and ter- nary systems exhibiting complete solid solubility.

              Crystal Structure Factor The crystal lattice structure of the two elements (metal) should be same (i.e. both should be of BCC, FCC, or HCP structure) for complete solubility, otherwise the two solutions would not merge into each other. Also for complete solid solubility the size must usually be less than 8%.

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Hume-Rothery's Rules are described below. is likely to form an objectionable.

रासायनिक प्रभाव क्षेत्र

             दो धातुओं का रासायनिक आत्मीयता जितना अधिक प्रतिबंधित है, उनकी ठोस घुलनशीलता है। जब उनकी रासायनिक आत्मीयता महान होती है, तो दो धातुएं एक ठोस समाधान के बजाय एक मध्यवर्ती चरण बनाती हैं।

रिश्ता वैधता का कारखाना

              यदि मिश्र धातु तत्व का आधार धातु से भिन्न भिन्नता है, तो प्रति परमाणुओं में वैलेंस इलेक्ट्रॉनों की संख्या, जिसे इलेक्ट्रॉन अनुपात कहा जाता है, को मिश्रधातु द्वारा बदल दिया जाएगा। वृद्धि की तुलना में क्रिस्टल संरचनाएं इलेक्ट्रॉन अनुपात में कमी के प्रति अधिक संवेदनशील हैं। इसलिए, उच्च वैलेंस की एक धातु केवल कम वैलेंस धातु को भंग कर सकती है, जबकि कम वैलेंस धातु में उच्च वैलेंस धातु के लिए अच्छा सॉल्यू-बाइट हो सकता है।

विश्वसनीय आकार फैक्टरी

            यदि दो धात्विक परमाणुओं का आकार (उनके स्थिरांक द्वारा अनुमानित रूप से दिया गया) 15 प्रतिशत से कम होता है, तो धातु को ठोस घोल बनाने के लिए अनुकूल आकार कारक कहा जाता है। जहाँ तक इस कारक का संबंध है, प्रत्येक धातु दूसरे धातु में apprecia- bly (l0% के क्रम में) को भंग करने में सक्षम होगी। यदि आकार का कारक 15 ° से अधिक है, तो ठोस समाधान गठन गंभीर रूप से सीमित हो जाता है और आमतौर पर केवल एक प्रतिशत का एक अंश होता है।

लेटिस-टाईप फैक्टर

           केवल धातुएँ जिनमें एक ही प्रकार की जाली होती है (उदाहरण के लिए FCC) ठोस समाधानों की एक पूरी श्रृंखला बना सकती है। इसके अलावा, कॉम-पिल सॉलिड सॉल्युबिलिटी के लिए, साइज फैक्टर आमतौर पर 8 प्रतिशत से कम होना चाहिए। कॉपर-निकेल और सिल्वर-गोल्ड-प्लैटिनम बाइनरी और टेर-नैरी सिस्टम के उदाहरण हैं जो पूर्ण ठोस घुलनशीलता प्रदर्शित करते हैं।

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Types of SAND in civil Engineering

Types of sand according to size:-

GREEN SAND

DRY SAND

LOAM SAND

FACING SAND

BACKING SAND

SYSTEM SAND

PARTING SAND

CORE SAND


Define all types SAND:_-

          GREEN SAND- It is a mixture of silica sand with 18 to 30 percent clay, having a total water content 6 to 8 percent. The clay and water furnish the bond for green sand. It is fine, soft, light, and porous. Being damp when squeezed in the hand, it retains the shape, the impression given to it under pressure. Moulds prepared in this sand are known as green sand moulds.


           DRY SAND- Green sand that has been dried or baked after the mould is made is called dry sand. They are suitable for larger castings. Moulds prepared in this sand are known as dry sand.


            LOAM SAND- Loam Sand is high in clay, as much as 50 percent  or so, and dries hard. This is particularly employed for laom moulding usually for large castings.


            FACING SAND- Facing sand forms the face of the mould. It is used directly next to the surface of the pattern and it comes into contact with the molten metal when the mould is poured. Consequently, it is subjected to the the severest conditions and therefore, must possess, high strength and ls with refractoriness. It is made of silica sand and clay, without the addition of used sand. Different forms of carbon are uscd to prevent the metal from burning into the sand. They are sometimes mixed with 6 to 15 times as much fine moulding sand to make facings.


          BACKING SAND- Backing sand or floor sand or floor sand is used to back up the facing sand and to fill the whole volume of the flask. Old, repeatedly used moulding sand is mainly employed for this purpose.
     The backing sand is sometimes called black sand because of the fact that old, repeatedly used moulding sand is black in colour due to the addition of coal dust and burning on coming in contact with molten metal.


           SYSTEM SAND-In mechanical preparation and handling unit, no facing sand is used. The used sand is cleaned and reactivated by the addition binder in of water binders and special additives. This is known as system sand, In etimes mechanical foundries, where machine moulding is employed so called system sand is used to fill the whole flask. Since the whole mould is made of this system sand therefore, strength, permeability and refractoriness of this sand must be higher than those of backing sand.


              PARTING SAND-Parting sand is used to prevent the green sand from sticking to the pattern and also to allow the sand on the parting surface of the cope and drag to separate without clinging. This is clean clay-free silica sand which serves the same purpose as parting dust


              CORE SAND- Sand used for making cores is called core sand sometimes called oil sand. This is silica oil sand. This is silica sand mixed with core oil which is composed of linseed oil, resin, light mineral oil and other binding materials. Pitch or flours and water may be used in larger cores for the sake of economy.

Types of SAND in civil Engineering

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Stress and strain. Hook's Law

DEFINE STRESS AND STRAIN:-

Stress-
             When some external forces are applied to a body, it offers resistance to these forces. The magnitude of this resisting force is numerically equal to the applied forces. This internal resisting force per unit area is called stress. Therefore, stress can be defined as the intensity of internal forces resisting change in the shape of the body. It is calculated by simply dividing on an area divided by the a: ea. It is measured in N/m2 o: kg the force acting cm2. There are three types of stresses namely, tension, compression and shear. Mathematically,
                                                               Stress, a = P/A
                                   where,             P= Force applied
                                                          A=Cross-sectional area.
[जब कुछ बाहरी बलों को एक निकाय पर लागू किया जाता है, तो यह इन बलों के लिए प्रतिरोध प्रदान करता है। इस प्रतिरोध बल का परिमाण संख्यात्मक रूप से लागू बलों के बराबर होता है। प्रति इकाई क्षेत्र के इस आंतरिक प्रतिरोध बल को तनाव कहा जाता है। इसलिए, तनाव को शरीर के आकार में परिवर्तन का विरोध करने वाली आंतरिक शक्तियों की तीव्रता के रूप में परिभाषित किया जा सकता है। इसकी गणना केवल a: ea द्वारा विभाजित क्षेत्र पर विभाजित करके की जाती है। यह एन / एम 2 ओ में मापा जाता है: बल एक्टिंग सेमी 2 किग्रा। तनाव, संपीड़न और कतरनी जैसे तीन प्रकार के तनाव हैं.]


Types of Stresses;-
                                 The various types of stresses may be classified as follows-

(1) Simple or direct stress 
(a) Tension               (b) Compression         (3) shear

(2) Indirect stress
(a) Bending              (2) Torsion

(3) Combined stress



Strain-
              Strain is defined as the deformation or change produced in the dimensions of a body due to the effect of stress on it. It is a ratio of the change in dimension to the original dimension. Mathematically
                                   
                               
                                             Strain,                                                                                                                                         

                where, 


 

  


          Strain is a dimensionless quantity. Depending upon the type of stress, it where, can be of three types, namely tensile, compressive and shearing strain.



Types of Strain ;-
                           The various types of strains may be classified as follows-

(1) Tensile strain
(2) Compressive strain
(3) Shear strain
(4) Volumetric strain.


Hook's Law;-

Define:

                      According to Hook's law, when a material is loaded within its elastic limit, the stress is proportional to strain, or in other words, within elastic limits the ratio of stress in a material to the strain produced remains. Mathematical


                                                           

                                                                     


                 Where,
                               E is a constant of proportionality, which is called as a modulus of elasticity, or young's modulus. It has unit as the stress, i. e. or






Poisson's ratio;-
                                       Whenever body is stressed within elastic limits, it is subjected to both longitudinal and lateral deformation. The ratio of the lateral strain to longitudinal strain is a constant quantity for a material and this ratio is known as Poisson's ratio. This ratio is designated by 1/m or u. Mathematically,

Poisson's ratio, 1/m or





Thus,  
           

The limitation of Poisson's ratio is that it can be applied only when material is stressed within the elastic limits

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