Engineering Physics - 1 PDF

ENGINEERING PHYSICS – 1 Subject Code: 303192101 UNIT 1 (Properties of Materials) Dr. Samrat Sarkar (Assistant Professor) Applied Sciences and Humanities, PIET  CHAPTER-1A Elastic Properties of Materials Introduction  Elasticity ❖ We have use...

ENGINEERING PHYSICS – 1 Subject Code: 303192101 UNIT 1 (Properties of Materials) Dr. Samrat Sarkar (Assistant Professor) Applied Sciences and Humanities, PIET  CHAPTER-1A Elastic Properties of Materials Introduction  Elasticity ❖ We have used the concept of a rigid body in which the distance between any two particles is always fixed. ❖ But in the real scenario, when external forces are applied, a body may get deformed. ❖ When the body is under deformation, internal forces are developed which try to regain the original shape of the body. The extent, to which the shape of a body is restored when the its deforming forces are removed, varies from material to material. ❖ The property to restore the natural shape is called Elasticity. If a body completely gains its natural 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 perfectly plastic body. ❖ Quite often the deforming forces are removed, the body partially regains its original shape. Such bodies are partially elastic.  Elasticity REASON FOR ELASTICITY ❖ A solid body is composed of great many molecules or atoms arranged in a particular fashion. ❖ Each molecule is acted upon by the forces (coulombic forces) due to the neighboring molecules. The solid takes 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 distance change and restoring forces start acting on the molecules which drive them back to their original positions and the body takes its natural shape.  Some definitions Elasticity: The inherent property of a body due to which the body tries to restore its normal shape is known as elasticity.  Some definitions Deforming force: A force when applied to a body, changes the shape of the body is called deforming force. The deformations are of three types, length, volume and shape.  Some definitions Restoring Force: When deforming force is applied to a body, it tries to deform the body. At the same time due to internal property of material a force is produced in the body which opposes the deformation. When the deforming force is removed, restoring force reduces to nullify the deformation. In static equilibrium restoring force is equal to deforming force i.e. external force.  Some definitions Elastic body: If a body can completely regain its original shape after removable of the deforming force, it is called a perfect elastic body.  Some definitions Plastic body: If a body remains in deformed state and does not even partially regain its original shape after the removal of deforming shape, it is called a plastic body. Stress  Stress Stress: For a rod, length is more with comparison to thickness (cross-sectional area). When external force is applied to a rod, it causes increase in the length resulting stress is called tensile stress. If due to application of external forces, length of the rod decreases the resulting stress is compressive stress. Types of Stress: (1) Longitudinal Stress (Tensile and Compressive) (2) Volume Stress (Hydraulic Stress) (3) Shearing Stress (Tangential Stress) Strain  Stress versus Pressure Difference between Stress and Pressure STRESSStress PRESSURE Pressure Stress can be defined as the internal Pressure can be defined as the amount of resistive force to the deformation per unit Stress can be defined as the internal resistive area. Pressure force canunit applied per bearea. defined as the amount of force to the deformation per unit area. force applied per unit area. Due to stress, the pressure will not be Due to pressure, stress will be developed. developed. Due to stress, the pressure will not be Due to pressure, stress will be developed. developed. Stress can be either a positive or a negative The pressure is always a positive force force Stress can be either Stress a positive is developed or a negative internally Pressure is exerted externally The pressure is always a positive force force Stress may be tensile, compressive and Pressure is always compressive shear Stress is developed internally Pressure is exerted externally Stress may be tensile, compressive and shear Pressure is always compressive Elastic Moduli Hooke’s Law Model of Elastic Behaviour Stress strain curve has different regions and points. These regions and points are: 1. Proportional limit 2. Elastic limit 3. Yield point 4. Ultimate stress point 5. Fracture or breaking point  Model of Elastic Behaviour: Proportional Limit Hooke’s law: Strain in a material will stay constant over a range of strain rates. Proportional limit: The stress within an elastic limit is directly proportional to the strain produced in the material. The proportionality constant is Elastic modulus. Elasticity: Measure of stretchiness of a material. The elastic limit is the point on the graph where the material gradually returns to its original size. Beyond this limit: Plastic deformation. Model of Elastic Behaviour : Elastic limit (Yield point)  Model of Elastic Behaviour : Yield Point The Yield point: Material starts to deform plastically. Beyond this limit: Permanent deformation develops in the material, which can't be undone. There are two yield points: upper yielding point, lower yielding point. Tensile strength: The region at which a material fails is known as its “tensile strength.” This strength is determined by the amount of stress the material can withstand before it breaks. The material can handle the maximum load at its maximum strength point. Beyond this point, failure will occur. The graph shows the stress points at which a material or structure tends to break is the most critical, as it represents the point of ultimate stress. Fracture point: The fracture point is the point at which the material breaks. The fracture or breaking of material takes place at this point due to the force of the impact. The point at which the graph breaks is called point E. Some Terminologies Some Terminologies Some Terminologies Some Terminologies  CHAPTER-1B Thermal Properties of Materials  Modes of Heat Transfer CONDUCTION OF HEAT ❖ Heat conduction is a process in which heat is transferred from the hotter part to the colder part in a body without involving any actual movement of the molecules of the body. ❖ Heat transfer takes place from one molecule to another molecule as a result of the vibratory motion of the molecules. ❖ It generally takes place in solids. Substances can be classified as thermal conductors and insulators. Substances that conduct heat easily are known as conductors and those that do not conduct heat are known as insulators. ❖ Example: Frying vegetables in a pan.  Modes of Heat Transfer CONDUCTION Conduction is the transfer of thermal energy through direct contact. Occurs in solid materials.  Modes of Heat Transfer CONVECTION OF HEAT ❖ In this process, heat is transferred in liquids and gases from a region of higher temperature to a region of lower temperature. ❖ Convection heat transfer occurs partly due to the actual movement of molecules or due to the mass transfer. ❖ Example: Heating of milk in a pan, heating of atmosphere.  Modes of Heat Transfer CONVECTION Convection is the process of heat transfer by the bulk movement of molecules within fluids such as gases and liquids.  Modes of Heat Transfer RADIATION OF HEAT ❖ It is the process in which heat is transferred from one body to another body without involving the molecules of the medium. ❖ Radiation heat transfer does not depend on the medium. ❖ Example: Earth receives heat from Sun by radiation. In a microwave, the substances are heated directly without the need of any heating medium.  Modes of Heat Transfer RADIATION Radiation is a process where heat waves (EM waves) are emitted that may be absorbed, reflected, or transmitted through a colder body. Modes of Heat Transfer Electric Conductivity Electric Conductivity Electric Conductivity Thermal Conductivity Thermal Conductivity Thermal Conductivity Electrical versus Thermal Conductivity Wiedemann-Franz law  Thermoelectric Effect Turning temperature differences directly into electricity could be an efficient way of harnessing heat that is wasted in cars and power plants. The simple interpretation of the thermoelectric effect is the temperature difference or the temperature gradient within the material can induce electric current or electric voltage within it. This process is reversible. If there is potential difference between any two points of material, the temperature gradient is induced. Which means flowing current or potential difference can produce temperature difference or temperature gradient is material.  Thermoelectric Effect SEEBECK EFFECT- The Seebeck effect is the build up of an electric potential across a temperature gradient. A thermocouple measures the difference in potential across a hot and cold end for two dissimilar materials. This potential difference is proportional to the temperature difference between the hot and cold ends. First discovered in 1794 by Italian scientist Alessandro Volta, it is named after Thomas Johann Seebeck, who in 1821 independently rediscovered it. Thermoelectric Effect  Thermoelectric Effect PELTIER EFFECT - When an electric current is passed through a circuit of a thermocouple, heat is evolved at one junction and absorbed at the other junction. This is known as the Peltier Effect. The Peltier effect is the presence of heating or cooling at an electrified junction of two different conductors and is named after French physicist Jean Charles Peltier, who discovered it in 1834. When a current is made to flow through a junction between two conductors, A and B, heat may be generated or removed at the junction. The Peltier heat generated at the junction per unit time is, where πA and πB are the Peltier coefficients of conductors A and B, and I is the electric current (from A to B). The total heat generated is not determined by the Peltier effect alone; as it may also be influenced by Joule heating and thermal gradient effects.  Thermoelectric Effect THOMSON EFFECT - William Thomson discovered a 3rd thermoelectric effect which provides a link between Seebeck effect and Peltier effect. Thomson found that when a current is passed through an wire of single homogeneous material along which a temperature gradient exists, heat must be exchanged with the surrounding in order that the original temperature gradient may be maintained along the wire. Thomson effect may be understood by a simple picture. A conductor has free charge carriers. Consider a section of such a conductor whose one end is hotter than the other end. Charge carriers at the hot end, being more energetic, will diffuse towards the colder end. The charge separation sets up an electric field. Diffusion of carriers would stop when the attractive force on the carriers due to this field is strong enough to retard the motion of the carriers due to thermal effect. Thermoelectric Effect Reason of Thermoelectricity Applications of Thermoelectricity Applications of Thermoelectricity Phonons Phonons Specific Heats of Solids Specific Heats of Solids Specific Heats of Solids Quantum Theory Specific Heats of Solids Quantum Theory Specific Heats of Solids DEBYE MODEL EINSTEIN MODEL Specific Heats of Solids Statistical Distributions Statistical Distributions  Problems 1. An iron wire of length 1 m and radius 0.1 mm elongates by 0.32 mm when stretched by a force of 49 N. Calculate the elastic constant of iron. 2. Show that the Poisson's ratio, σ = 0.5 for a cylinder whose volume remains unchanged upon the application of a longitudinal stress. 3. A spring of force constant ‘k’ is cut into 4 equal parts perpendicular to the length. Find the force constant of each equal part. 4. The bulk modulus of a spherical object is ‘B’. If it is subjected to a uniform pressure ‘p’ then show that the fractional decrease in radius is p/3B. 5. A wire of length L and cross-sectional area A is made of a material of Young’s modulus Y. If the wire is stretched by an amount x, show that the work done is W = YAx2/2L. 6. Prove that the elastic potential energy stored in an elastic body per unit volume is given by, u = 1/2 x Stress x Strain. www.paruluniversity.ac.in