Thermodynamics – The science of energy and the properties of substances that bear a relationship to energy Energy – Ability to do work – OR – Ability to cause changes Thermedynamis (Heat)(Power) We try to convert heat to power or vice- versa Examples Heat to power – Engine Power to heat – Refrigerator, heat pump Power or heat to change properties – Heat water, fill a balloon

a.What are we going to study? b.How are we going to study it? c.At what level or depth are we going to study it? d.How are we going to describe what we are studying? System: A quantity of matter or a region in space chosen for study separated from the rest of the world by the system boundary Closed system: Across the system boundary, energy transfer can occur but mass transfer cannot occur Example: Can of soda

Isolated system: No energy transfer and no mass transfer Example: Universe, “Perfectly insulated” can of soda Open system: Mass and energy transfer can occur across the system boundary – also called control volume Control Volume – Region in space separated from the rest of the universe by a control surface Example: Room, IC engine To what level are we going to study? Macroscopic Two levels - Microscopic

Microscopic: Attempt to describe the motion of molecules in an average sense – Statistical thermodynamics Macroscopic – Attempt to describe the effects of molecular motion – Classical thermodynamics Difficulty in microscopic approach Each molecule has three coordinates and three directions of motion A room (15m x 5m x 3m) has approximately 6.23*10 27 molecules So the total number of equations is 6*6.23*10 27 = 3.7*10 28 equations IMPOSSIBLE TO SOLVE

Finally, how do we describe what we are studying? State: The position of the system in “thermodynamic space” Properties: Properties are the co-ordinates that fix the state of the system. Example: Pressure, temperature, density, volume Does the property of the system vary within the system? Equilibrium: The condition where there are no imbalances within the system

Thermal equilibrium: A condition where there is no heat transfer within the system – constant and uniform temperature Mechanical equilibrium: All the forces within the system are in balance – constant pressure Note that pressure is not uniform but the variation is generally small Chemical equilibrium: Condition where there is no change in chemical composition Phase equilibrium: No change in relative mass of each phase If all of the above are satisfied, the system is at “Thermodynamic equilibrium”

Properties are of two types Extensive properties: Properties dependant on the amount of matter considered Intensive properties: Properties independent of the amount of matter considered Fig. 1 Consider pressure, temperature and volume Which are the same between A and B? P A =P B – Intensive T A =T B – Intensive V A  V B – Extensive if A and B are systems at equilibrium

All systems we study will be at equilibrium Extensive properties can be converted to intensive properties by dividing by mass V/M = specific volume ( ) {m 3 /kg} M/V = density (  ) {kg/m 3 } How many properties do we need to fix a state? This depends on the number of ways in which the state can be changed. State can be changed by heat transfer or work transfer The work transfer has a number of mode – Electrical, pressure, magnetic, shaft etc

State Principle: The number of independent properties required to fix the state of a substance is equal to the number of reversible work modes + 1 In our case, the work modes we will consider are pressure (compression/expansion) and shaft of which pressure is the only reversible work mode Therefore, number of independent properties required = 2 Relationship between macroscopic and microscopic viewpoints All macroscopic properties are an effect of what is happening at a microscopic level Example: Pressure is the force exerted by molecular collisions on the wall per unit area

Let us try to see the relationship between pressure and the microscopic quantities Let us assume that the number of molecules per unit volume is n Let us also assume that the average speed of molecules is c The velocity of a molecule is given by V = u x i + u y j + u z k Keeping in mind that body forces are negligible for a molecule, u x = u y = u z |V| = c = (u x 2 +u y 2 +u z 2 ) 0.5 =u x *3 0.5

Force on the wall is due to collision and consequent change of momentum of molecules Pressure is force per unit area Force is rate of change of momentum If there are f number of collisions per second and each is associated with  M x change in x momentum, F x = f  M x P = F x /A

Fig. 2 In one second, a molecule at a distance u x from the wall has a chance of colliding with the wall All molecules within that distance may collide with the wall Consider a cuboid with sides u x, dy, dz V = u x *dy*dz N = n*u x *dy*dz Half these molecules are going away from the wall Therefore, f = 0.5N = 0.5*n*u x *dy*dz If the molecules bounce off with the same x component of velocity (elastic collisions),  M x = 2m*u x

F x = f  M x =0.5*n*u x *dy*dz*2*m*u x F x = n m u x 2 dy dz P = F x /A = n m u x 2 dy dz/(dy dz) = n m u x 2 u x = c/3 0.5 Therefore, P = 1/3*n m c 2 Similarly, the temperature is proportional to the molecule’s kinetic energy 3/2 kT = ½ mc 2 T = ½ mc 2 /k k = Boltzmann constant 1/3 mc 2 = kT = P/n P = nkT n = N/V N = n moles *A (A = Avogadro’s number) n = n moles A/V

P = n k T = n moles A k T/V PV = n moles A k T A k = R (Universal Gas Constant) PV = n moles R T Thermodynamics lingo – contd. Systems do change their state from time to time Process: A system changing from state 1 to state 2 is said to be undergoing a process Path: The locus of states through which the system passes during a process is the path But are all the intermediate state during the process also at equilibrium?

Quasi-equilibrium process: A process proceeding in such a manner that the system is close to equilibrium at all times This basically means that the process occurs slowly enough that the system can “keep up” with it. Actual processes may be near quasi- equilibrium Cycle: A series of processes that results in the final state of the system being the same as the initial state Example: Refrigerant in a refrigerator Since a state can be defined by two independent properties, processes and cycles are frequently plotted on charts Example: P-v diagram, T-v diagram etc.

Pure substance : A substance that has a fixed chemical composition throughout is called a pure substance. Some mixtures are also considered pure substances as long as the mixture is homogenous. Example: Air; Counterexample: Mixture of water and oil