MME6701: Lecture 02 The Structure of Thermodynamics A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Topics to discuss q Thermodynamic Systems Classification of thermodynamic systems q Thermodynamic Variables State functions vs. process variables Extensive vs. intensive variables 1
The Structure of Thermodynamics The science of thermodynamics is rooted with logics and reasons. At its foundation there are a very few, very general, and therefore very powerful principles: The Laws of Thermodynamics. The structure of thermodynamics can be visualised as an inverted pyramid. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 3 Surroundings System Temperature, T Pressure, P Volume, V Composition, X k..... Boundary The subset of the universe in focus for a particular application Identify the part of universe that encompasses the problem (known as the system) separates the problem using a enclosure (known as the boundary) from the rest of the universe (known as the surroundings), close enough to the system to have some perceptible effect on the system. Specify the conditions of the system at the point of investigation in terms of thermodynamic properties. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 4 2
If the system undergoes a process, use thermodynamic relations to compute the changes of these properties. T A, P A, V A Process T B, P B, V B State A State B A process is a change in the condition or state of the system Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 5 Strategy in Studying Thermodynamic Structure Thermodynamic systems Thermodynamic properties Thermodynamic processes Thermodynamic relations Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 6 3
Thermodynamic Systems Certain portion of the universe that encompasses the whole problem at hand; the boundary separates the system from its surroundings. Be explicit about the nature of the contents of the system, and the specific location and character of its boundary. Across the boundary of a system, heat flows, work appears or disappears, and sometimes even matter moves. The system and its surroundings are considered to be isolated. Water Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 7 Classifications of Thermodynamic Systems u Unary vs. multi-component Unary system (single component) Aluminium can Quartz (SiO 2 ) Water (H 2 O) (when undecomposed) Multi-component system (more than one component) Steel bar (containing Fe, C, Si, etc.) Water (H, O) Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 8 4
v Homogeneous vs. heterogeneous Homogeneous system (single phase) Ice (solid phase) Water (liquid phase) Heterogeneous system (more than one phase) Steel (containing ferrite and cementite) Ice water (solid and liquid phases) Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 9 w Closed vs. open Closed system (energy but mass transfer across boundary) A piece of paper Open system (mass and energy transfer across boundary) A cup of tea Isolated system (neither mass nor energy transfer across boundary) Hot milk in thermos flask Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 10 5
x Non-reacting vs. reacting Non-reacting system (no chemical reaction within) Sugar-water solution in a glass A piece of copper rod Reacting system (involving chemical reaction) Liquid steel in a crucible A piece of aluminium in sodium hydroxide solution Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 11 y Otherwise simple vs. complex Otherwise simple system No force field other than mechanical force is acting upon the system Complex system Force field other than mechanical such as magnetic, electrical, rotational, etc. is acting upon the system. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 12 6
Self Assessment Question #2.1 Classify the following thermodynamic systems: (a) a solid bar of copper (b) a glass of ice water (c) a yttria stabilised zirconia furnace tube (d) a styrofoam coffee cup (e) a eutectic alloy turbine blade rotating at 20000 rpm. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 13 Thermodynamic Variables Identifiable characteristics of matter whose are observable and can be measured either directly or indirectly are called variables, functions or, properties. Examples: pressure, temperature, volume, mass, velocity, work, etc. The physical properties of thermodynamics are distinct in two respects: u they can be expressed quantitatively in terms of dimensions and units, and v the measured value at any particular point of time is unique. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 14 7
Thermodynamic State It is the internal condition of a system as defined by the values of all its properties. It gives a complete description of the system. Properties describe and specify the state of the system in such a way that identical states have identical properties. If in any operation, one or more properties of a system change, the system changes its state. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 15 Classifications of Thermodynamic Variables u Microscopic state and macroscopic state v Independent properties and dependent properties w State functions and process variables x Intensive, extensive, and specific properties Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 16 8
Microscopic state and macroscopic state In microscopic sense, any thermodynamic system is not continuous. If the masses, velocities, positions and all modes of motions of all the particles in any particular instance is known, then this would describe the microscopic state or condition of the system and would, in turn, determine all the properties of the system. In macroscopic sense, the system is continuous and we determine the properties of the system as a whole. The state of the system described this way is known as the macroscopic state of the system Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 17 Independent and Dependent Properties It is not necessary to quantify all of the properties to define completely the state of system. It is found that when a very small number of properties have been measured at any instance of time, all other thermodynamic properties are fixed automatically. Thus, only a few numbers of independent properties are measured experimentally and the remaining multitude of dependent properties is calculated using those independent properties. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 18 9
State Functions or Thermodynamic Variables Depends on the current condition or state of the system, not on how the system is arrived at that condition. Rafiq weighs 72 kg and is 1.75 m tall. We are not concerned how he got to that stage. We are not interested what he ate!!. The temperature today is 500 K. We do not indicate whether the day is heated up to that temperature or cooled down to it. Example of state functions: Pressure, Temperature, Volume, energy, etc. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 19 If a variable Z depends only on the current values of the variables X and Y, then all three variables are state functions. The functional relationship among these variables, Z = Z (X, Y), is represented by a surface in (X, Y, Z) space. Z Z 1 Z = Z (X, Y) Y For any given values (X A,Y A ) in state A, there is a corresponding value of Z A. X (X 1,Y 1 ) Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 20 10
Z Z = Z (X, Y) Processes Δ Z Z A (X A, Y A ) a b c Z B Y Any change in a state function depends only the initial and final state of the system, not on the path followed. (X B, Y B ) ΔZ = Z B - Z A X Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 21 Process Variables Only have meaning for changing systems Examples: Heat (Q) and Work (W). Change is inherent to the very concept of these quantities. The values of process variables at rest are zero. Depends explicitly upon the path, that is, the specific sequence of states the system takes while moving from state A to state B. A system can have some energy, but the system contain no work. Thus, energy is a property of system, work is not. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 22 11
Intensive, Extensive, and Specific Properties Intensive properties Values are independent of the size/extent of system Vary from place to place within the system at any moment The fundamental or derived properties of system are always intensive Examples: Temperature, Pressure Extensive properties Values depends on the size/extent of system Only have a value for the system as a whole The total properties the system are always extensive Examples: Volume, Mass, Energy Specific properties Extensive variables per unit mass or volume All specific properties are intensive properties Examples: Density, specific volume, specific energy Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 23 MME6701: Lecture 02 (Contd..) The Structure of Thermodynamics 12
Topics to discuss q Thermodynamic Processes q Thermodynamic Relations q Problem Solving Thermodynamic Processes A process suggests u change in system from one state to another v some operations by which the change is achieved A path represents a sequence of situations a system passes through during a change in the state of the system. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 26 13
Process A B System changes from state A to state B; But does not indicate any particular operation or the path it followed A a b c B Three different paths a, b, c for the process A B A process is often specified with certain constraints imposed on the system and/or its surroundings. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 27 Adiabatic Process No heat transfer occurs across the boundary between the system and its surroundings q If the temperature gradient, ΔT = 0, no heat will transfer q If ΔT 0, heat will transfer (which is a rate process) so for a short period of time, the process can be assumed to be adiabatic (e.g., compression of air and gasoline in internal combustion engine) How to recognise an adiabatic process? q Process is carried out quickly q Well insulated boundary Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 28 14
Isothermal Process Temperature is uniform at every point throughout the system and remains constant during the entire process q If ΔT = 0, Transfer of heat = 0. q If ΔT 0, Transfer of heat/work will occur until ΔT = 0. If the process produces heat q Transfer of heat and/or work across the boundary is mandatory q Process should occur for a prolonged period of time to encourage heat transfer How to recognise an isothermal process? q Process is carried out very slowly (close to infinity) q Permeable boundary Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 29 Isobaric Process Pressure remained constant throughout the system. Isochoric Process Volume remained constant throughout the system. Impermeable and rigid container/boundary Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 30 15
Cyclic Process The initial and final states of the system are the same. The overall changes in all state variables are zero. If the cyclic change in a state of a system results a ZERO change in a property, that property is a state function dz = 0 Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 31 Table 2.1: Characteristics of different thermodynamic processes Process Constraints imposed Quantity exchanged Isobaric Isothermal Isochoric Adiabatic Pressure remains constant (ΔP=0) Temperature remains constant (ΔT=0) Volume remains constant (ΔV=0) System remains insulated (Q=0) Heat and work may be exchanged Heat and work may be exchanged Only heat is exchanged Only work is exchanged Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 32 16
Thermodynamic Relations 1. Laws of Thermodynamics These fundamental equations form the basis of all thermodynamic relations. Generally describes the connection between the different forms of energy and state variables. 2. Definitions There are quite a few number of thermodynamic properties that are defined in terms of previously formulated quantities. They describe a particular class of system or process. In this category, there are some energy function and some experimental variables. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 33 3. Coefficient Relations Z = Z (X, Y ) " Z % dz = $ ' # X & Y dx + " Z % $ ' # Y & X dy dz = MdX + NdY " M = Z % $ ' # X & Y " and N = Z % $ ' # Y & These equations are known as the coefficient relations. X Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 34 17
4. Maxwell Relations dz = MdX + NdY " M = Z % $ ' # X & Y and " N = Z % $ ' # Y & X " $ # M Y % ' & " N % $ ' # X & Y X = = ( " Z % * $ ' ) Y # X & Y X + -, ( " Z % + * $ ' - ) X # Y &, X Y = = 2 Z X. Y 2 Z Y. X " $ # M Y % ' & X = " N % $ ' # X & Y Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 35 " $ # M Y % ' & X = " N % $ ' # X & Y This equation is known as the Maxwell relation. If a function Z = Z (X, Y) obeys the Maxwell relation, the function will be a state variable. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 36 18
5. Condition for Equilibrium When an external force is acted upon a system, the system undergoes changes until it has exhausted all of its capacity for change. When the system attains this final resting place, we indicate that the system is in equilibrium with its surroundings. The conditions for equilibrium are a set of equations that describe the relationships between state functions that must exist within the system when it attains the equilibrium (or stable) state. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 37 Problem Solving Example 2.1 z Is the function 9x 2 y 2 dx + 6x 3 y dy an exact differential? Z A Z B ΔZ = ΔZ CA + ΔZ BC = 381 y ΔZ = ΔZ DA + ΔZ BD = 381 A(1,1) C (1,4) ΔZ = ΔZ BCA = ΔZ BDA x D (2,1) B(2,4) Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 38 19
Problem 2.15: Write total differential equation of the function z = 17 x 4 y + 22 xy 5 and then, using Maxwell relation, prove that z is a state function. dz = [ 17 (4x 3 ) y + 22 y 5 ] dx + [ 17 x 4 + 22 x (5y 4 ) ] dy M = 68 x 3 y + 22 y 5 N = 17 x 4 + 110 xy 4 ( M/ y) x = 68 x 3 + 110 y 4 ( N/ x) y = 68 x 3 + 110 y 4 So M/ y) x = ( N/ x) y Thus, z is a state function. Rashid, DMME, BUET, OCT 2012 SEMESTER MME6701, Lec 02 P 39 Next Class Lecture 03 The Laws of Thermodynamics 20