Thermodynamics notes[1]


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Thermodynamics notes[1]

  1. 1. MACROSCOPIC AND MICROSCOPIC VIEWPOINT OF THERMODYNAMICS<br />The behaviour of a matter can be studied at two levels: a) Macroscopic. b) Microscopic.<br />Macroscopic ( or classical thermodynamics): <br /><ul><li>In this approach, a certain quantity of matter is considered, without taking into account the events occurring at the molecular level.
  2. 2. This macroscopic approach to the study of thermodynamics that does not require knowledge of the behaviour of individual particles.
  3. 3. Macroscopic thermodynamics is only concerned with the effects of the action of many molecules, and these effects can be perceived by human senses.
  4. 4. The macroscopic observations are completely independent of the assumptions regarding the nature of matter.
  5. 5. Example: A moving car, a falling stone from a cliff, etc.</li></ul>Microscopic ( or statistical thermodynamics):<br /><ul><li>From the microscopic viewpoint, matter is composed of a large number of small molecules and atoms.
  6. 6. This microscopic approach to the study of thermodynamics that require knowledge of the behaviour of individual particles.
  7. 7. Microscopic thermodynamics is concerned with the effects of the action of many molecules, and these effects cannot be perceived by human senses.
  8. 8. The microscopic observations are completely dependent on the assumptions regarding the nature of matter.
  9. 9. Example: Individual molecules present in air, etc.</li></ul>ZEROTH LAW OF THERMODYNAMICS<br /> When a body A is in thermal equilibrium with a body B, and also separately with a body C, then B and C will be in thermal equilibrium with each other. This is the zeroth law of thermodynamics.<br />Importance of zeroth law of thermodynamics:<br /> It is the basis of temperature measurement. In order to obtain a quantitative measure of temperature, a reference body is used, and a certain physical characteristic of this body which changes with temperature is selected. The change in the selected characteristic may be taken as an indication of change in temperature. The selected characteristic is called the thermometric property, and the reference body which is used in the determination of temperature is called the thermometer. A very common thermometer consists of a small amount of mercury in an evacuated capillary tube. In this case, the extension of the mercury in the tube is used as the thermometric property.<br />Reference Points<br /> Temperature scales enable us to use a common basis for temperature measurements. All temperature scales are based on some easily reproducible states such as the freezing and boiling points of water, which are also called the ice point and the steam point, respectively. A mixture of ice and water that is in equilibrium with air saturated with vapor at 1 atm pressure is said to be at the ice point, and a mixture of liquid water and water vapor (with no air) in equilibrium at 1 atm pressure is said to be at the steam point. These points are also called as the reference points.<br /> A temperature scale may of two reference points (steam and ice point) like the Celsius scale or of a single reference point (273K, i.e, the ice point) like the Kelvin scale.<br /> The ice point and steam points have the following disadvantages:<br /><ul><li>The difficulty of achieving equilibrium between the pure ice and air-saturated water (since when ice melts, it surrounds itself only with pure water and prevents intimate contact with air-saturated water), and
  10. 10. Extreme sensitiveness of the steam point to the change in pressure.</li></ul> To overcome this difficulty, triple point of water is chosen as the reference point, at which ice, liquid water and water vapour coexist. Triple point of water is also known as the standard fixed point of thermometry.<br /> <br />SYSTEMS AND CONTROL VOLUMES<br />A system is defined as a quantity of matter or a region in space chosen for study. The mass or region outside the system is called the surroundings.<br />The real or imaginary surface that separates the system from its surroundings is called the boundary. <br />The boundary of a system can be fixed or movable. <br />The boundary is the contact surface shared by both the system and the surroundings.<br />The boundary has zero thickness, and thus it can neither contain any mass nor occupy any volume in space.<br /> <br />Open & Closed Systems<br />Systems may be considered to be closed or open, depending on whether a fixed mass or a fixed volume in space is chosen for study. <br />A closed system (also known as a control mass) consists of a fixed amount of mass, and no mass can cross its boundary. That is, no mass can enter or leave a closed system. But energy, in the form of heat or work, can cross the boundary; and the volume of a closed system does not have to be fixed.<br /> If, as a special case, even energy is not allowed to cross the boundary, that system is called an isolated system. <br />An open system, or a control volume, as it is often called, is a properly selected region in space. It usually encloses a device that involves mass flow such as a compressor, turbine, or nozzle.<br />Flow through these devices is best studied by selecting the region within the device as the control volume. Both mass and energy can cross the boundary of a control volume.<br />A large number of engineering problems involve mass flow in and out of a system and, therefore, are modeled as control volumes. <br />A car radiator, a turbine, and a compressor all involve mass flow and should be analyzed as control volumes (open systems) instead of as control masses (closed systems). <br />In general, any arbitrary region in space can be selected as a control volume. <br />The boundaries of a control volume are called a control surface, and they can be real or imaginary. In the case of a nozzle, the inner surface of the nozzle forms the real part of the boundary, and the entrance and exit areas form the imaginary part, since there are no physical surfaces there. <br />Example of Open system<br />PROPERTIES OF A SYSTEM<br />Any characteristic of a system by which it’s physical condition may be described is called a property.<br />Pressure, temperature, volume, mass, viscosity, thermal conductivity, modulus of elasticity, thermal expansion coefficient, electric resistivity, velocity, elevation, etc.<br />Properties are considered to be either intensive or extensive. <br />Intensive properties are those that are independent of the mass of a system, such as temperature, pressure, and density. <br />Extensive properties are those whose values depend on the size—or extent—of the system. Total mass, total volume, and total momentum are some examples of extensive properties.<br />Extensive properties per unit mass are called specific properties. Some examples of specific properties are specific volume (v=V/m) and specific total energy (e =E/m). <br />STATE AND EQUILIBRIUM<br />Consider a system not undergoing any change. At this point, all the properties can be measured or calculated throughout the entire system, which gives us a set of properties that completely describes the condition, or the state, of the system. <br />At a given state, all the properties of a system have fixed values. If the value of even one property changes, the state will change to a different one. <br />A system at two different states<br />Thermodynamics deals with equilibrium states. The word equilibrium implies a state of balance. <br />In an equilibrium state there are no unbalanced potentials (or driving forces) within the system. <br />A system in equilibrium experiences no changes when it is isolated from its surroundings.<br />There are many types of equilibrium, and a system is not in thermodynamic equilibrium unless the conditions of all the three relevant types of equilibrium are satisfied:<br /><ul><li>Thermal equilibrium- Temperature should be same throughout the system. </li></ul>Mechanical equilibrium-Unbalanced forces should be absent, eg, change in pressure<br />Chemical equilibrium –No chemical reaction and mass transfer <br />PROCESSES AND CYCLES<br />Any change that a system undergoes from one equilibrium state to another is called a process, and the series of states through which a system passes during a process is called the path of the process.<br />To describe a process completely, one should specify the initial and final states of the process, as well as the path it follows, and the interactions with the surroundings. <br />When a process proceeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times, it is called a quasistatic, or quasi-equilibrium, process. <br />A quasi-equilibrium process can be viewed as a sufficiently slow process that allows the system to adjust itself internally so that properties in one part of the system do not change any faster than those at other parts. <br /><ul><li>The prefix iso- is often used to designate a process for which a particular property remains constant.
  11. 11. An isothermal process, for example, is a process during which the temperature T remains constant.
  12. 12. An isobaric process is a process during which the pressure P remains constant.
  13. 13. An isochoric (or isometric) process is a process during which the specific volume v remains constant.
  14. 14. Adiabatic process:
  15. 15. A process during which there is no heat transfer is called an adiabatic process .
  16. 16. The word adiabatic comes from the Greek word adiabatos, which means not to be passed.
  17. 17. For a adiabatic process, the system is well insulated so that no or only a negligible amount of heat can pass through the boundary.
  18. 18. A wall which is impermeable to the flow of heat is an adiabatic wall.
  19. 19. A wall which permits the flow of heat is a diathermic wall.
  20. 20. A system is said to have undergone a cycle if it returns to its initial state at the end of the process. That is, for a cycle the initial and final states are identical. </li></ul>The Steady-Flow Process<br />The term steady implies no change with time. The opposite of steady is unsteady, or transient.<br />During a steady-flow process, fluid properties within the control volume may change with position but not with time. <br />The Steady-Flow Process<br />Uniform-Flow Process<br />The term uniform, however, implies no change with location over a specified region. <br />Uniform-Flow Process<br />PATH & POINT FUNCTIONS<br />Path functions - their magnitudes depend on the path followed during a process as well as the end states. Eg: Heat and Work.<br />Point functions - they depend on the state only, and not on how a system reaches that state. Eg: Properties <br />WORK AND HEAT TRANSFER<br />A closed system can interact with its surroundings in two ways:<br /><ul><li>Work Transfer
  21. 21. Heat Transfer
  22. 22. Work Transfer</li></ul>The work is done by a force as it acts upon a body moving in the direction of the force.<br />Therefore, from definition Work Done = Force x Distance<br />Characteristics of Work<br /><ul><li>P.dv work or Displacement work or boundary work</li></ul>Consider the gas enclosed in the piston–cylinder device shown in Figure.<br />The initial pressure of the gas is P, the total volume is V, and the cross-sectional area of the piston is A. <br />If the piston is allowed to move a distance ds in a quasi-equilibrium manner, the differential work done during this process is<br /> δW = F.ds = P.A.ds = P.dV <br />Therefore, the Displacement work in the differential form is equal to the product of the absolute pressure P and the differential change in the volume dV of the system. This expression also explains why the Displacement work is sometimes called the P dV work.<br />The total boundary work done during the entire process as the piston moves is obtained by adding all the differential works from the initial state to the final state:<br /> W= V2V1 PdV , kJ <br />The area under the process curve on a P-V diagram represents the boundary work. <br /><ul><li>Since the magnitude of work done depends on the path followed during the process, therefore work is a path function.
  23. 23. Work done depends on the mass, therefore work is extensive property.
  24. 24. Formal sign convention for work:
  25. 25. Work done by a system or work done due to expansion is positive;
  26. 26. Work done on a system or work done on due to compression is negative.
  27. 27. Heat Transfer</li></ul>Heat is defined as the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference . <br />That is, an energy interaction is heat only if it takes place because of a temperature difference. <br />Then it follows that there cannot be any heat transfer between two systems that are at the same temperature. <br />Characteristics of Heat<br /><ul><li>Heat Transfer is given by Q, in Joules
  28. 28. Q=m×c×∆T</li></ul>Where m= mass, kg<br />c= specific heat, J/kg-K<br />∆T= Change in temperature, K<br /><ul><li>Heat transfer occurs through three modes:
  29. 29. Convection- Interaction between solid surface and adjacent fluid system or between two fluid systems.
  30. 30. Conduction - Heat transfer when Two bodies are in direct contact.
  31. 31. Radiation – Due to the emission of electromagnetic waves.
  32. 32. Since the magnitude of heat depends on the path followed during the process, therefore heat is a path function.
  33. 33. Heat depends on the mass, therefore heat is extensive property.
  34. 34. Formal sign convention for Heat Transfer
  35. 35. Heat transfer to a system is positive;
  36. 36. Heat transfer from a system is negative.</li></ul>WORK DONE IN DIFFERENT PROCESSES<br /><ul><li>Isobaric process
  37. 37. Work done is given by</li></ul>W= V2V1 PdV , kJ<br />Where,<br /> P is pressure in pascal,<br />V is volume in m3<br />1 is initial and 2 is final state of system <br />Since, for isobaric process Pressure P is constant<br />W= P V2V1 dV , kJ<br />W= P(V2-V1), kJ<br /><ul><li>Isochoric Process
  38. 38. Work done is given by</li></ul>W= V2V1 PdV , kJ<br />Where,<br /> P is pressure in pascal,<br />V is volume in m3<br />1 is initial and 2 is final state of system <br />Since, for isochoric process Volume V is constant<br /><ul><li>Therefore, change in volume = dV = 0
  39. 39. Therefore, Work done = W = 0
  40. 40. Isothermal Process
  41. 41. Isothermal ProcessP1P2V2V1PVPV=CW1-2
  42. 42. Work done is given by</li></ul>W= V2V1 PdV , kJ<br />Where,<br /> P is pressure in pascal,<br />V is volume in m3<br />1 is initial and 2 is final state of system <br />Ideal Gas equation, PV=nRT<br /><ul><li>Since, for isothermal process Temperature T is constant
  43. 43. Therefore, PV=Constant=C=P1V1=P2V2
  44. 44. ->P=CV
  45. 45. Work done is given by</li></ul>W= V2V1 CV.dV <br /><ul><li>->W= C V2V1 1V.dV
  46. 46. -> W= C ln(V2 / V1)
  47. 47. -> W = PV ln(V2 / V1) = P1V1 ln(V2 / V1) = P2V2 ln(V2 / V1)
  48. 48. =nRTln(V2V1) =nRTln(P1P2) =P1V1ln(P1P2) =P2V2ln(P1P2)
  49. 49. Polytropic or adiabatic process
  50. 50. Polytropic ProcessPV12P V n =Cn= 0n= 1n= 2n= ∞
  51. 51. Work done is given by</li></ul>W= V2V1 PdV , kJ<br />Where,<br /> P is pressure in pascal,<br />V is volume in m3<br />1 is initial and 2 is final state of system <br />Heat Transfer is zero<br /><ul><li>Therefore, PVδ=Constant=C=P1V1δ=P2V2δ
  52. 52. ->P=CVδ=C× V-δ</li></ul>-> W= C.V-δ.dVv2v1-> W= C V-δ+1-δ+1v2v1-> W= C V2-δ+1 – V1-δ+1 - δ +1-> W = P2V2 – P1V11 - δ<br />Reversible Process<br />