Spontaneous ( Irreversible ) Processes: The 2 nd Law of Thermodynamics

1. Spontaneous (Irreversible) Processes: The 2nd Lawof Thermodynamics

2. From Statistical Arguments we’ve • Quantitatively Defined • Entropy:S kBln() • kB Boltzmann’s constant •  (E) Number of Microstates at a Given Energy

3. We’ve also discussed • the fact that • Entropy • is a measure of • the amount of • Disorder • in a system.

4. Spontaneous Processes Processes that can proceed with no outside intervention. Entropycan be viewed as ameasure of randomness or disorderin the atoms & molecules in a system. Spontaneous Processes & Entropy • The 2nd Law of Thermodynamics  • Total Entropy: • Always increases in a spontaneous process! • So, Microscopic Disorder also • Always increases in a spontaneous process!

5. Entropy, S A Measure of Disorder Ssolid Sliquid  Sgas

6. Increasing Entropy Ssolid Sliquid  Sgas

7. Spontaneous Processes • Processes that can proceed with no outside intervention. Example in the figure: • Due to the 2nd Law of Thermodynamics, when the valve is opened, the gas in container B will spontaneously diffuse into container A. • But, once it is in both containers, it will neverspontaneously diffuse back into container B.

8. Spontaneous Processes

9. The 2nd Law of Thermodynamics • Processes that are spontaneous in one directionaren’t spontaneous in the reverse direction. • Example in the figure: Due to the 2nd Law of Thermodynamics the shiny nail at the top will, over a long time, rust & eventually look as at the bottom. But (obviously), if the nail is rusty, it will not ever spontaneously become shiny again!!

10. Processes that are spontaneous at one temperature may be non-spontaneous at other temperatures. Example in the figure: • For T > 0C the ice will melt spontaneously. • For T < 0C, the reverse process is spontaneous.

11. Irreversible Processes Irreversible Processes • Processes that cannot be undone by exactly reversing the process. • All Spontaneous Processesare Irreversible. • AllRealprocesses areIrreversible.

12. Spontaneous Processes: • Always occur on their own, without outside intervention. • Always have a definite direction. • The reverse process is never spontaneous. • Temperature can have an impact on spontaneity. • Example: Ice melting or forming • Example: Hot metal cooling at room temperature.

13. Whenever a chemical system is in equilibrium, a reaction can go reversibly to reactants or products. (Example: water  water vapor at 100 º C). • In a Spontaneous Process, the path between reactants and products is irreversible.

14. Whenever a chemical system is in equilibrium, a reaction can go reversibly to reactants or products. (Example: water  water vapor at 100 º C). • In a Spontaneous Process, the path between reactants and products is irreversible. • The reverse of a spontaneous process is not spontaneous. “Scrambled eggs don’t unscramble!”

15. Spontaneous, Irreversible Processes: More Examples 1. Due to frictional effects, mechanical work changes into heat automatically. 2. Gas inflates toward vacuum. 3. Heat transfers from a high temperature object to a low temperature object. 4. Two solutions of different concentrations are put together and mixed uniformly. • Note!! The 2nd Law of Thermodynamicssays that the opposite processes of these cannot proceed automatically. In order to take a system back to it’s initial state, External work must be done on it.

16. Spontaneous Processes(Changes): • Once such a process begins, it proceeds automatically without the need to do work on the system. • The opposite of every Spontaneous Process is a Non-Spontaneous Process that can only proceed if external work is done on the system.

17. Reversible Processes (Idealizations!) • In aReversible Process, the system undergoes changes such that the system plus it’s surroundings can be put back in their original states by exactly reversing the process. • In aReversible Process, changes proceed ininfinitesimally smallsteps, so that the system is infinitesimally close to equilibrium at every step. This is clearly an idealization & can never happen in a real system!

18. Other Statements of the2nd Law of Thermodynamics • “The entropy of the universedoes not change for Reversible Processes” and also: • “The entropy of the universeincreasesfor • Spontaneous Processes” (“You can’t break even”). • For Reversible(ideal)Processes: • For Irreversible(real, spontaneous) Processes:

19. Still Other Statements of the2nd Law of Thermodynamics “In any spontaneous process, there is always an increase in the entropy of the universe.”

20. Still Other Statements of the2nd Law of Thermodynamics “In any spontaneous process, there is always an increase in the entropy of the universe.” Or “The Total EntropySof the Universehas the property that, for any spontaneous process” ∆S ≥ 0.

21. Example:Entropy of the Universe Increases • 1200 J of heat flows • spontaneouslythrough a • copper rod from a hot • reservoir at TH = 650 K to a • cold reservoir at TC = 350 K. • Calculatethe amount by • which this irreversible • process changes the entropy • of the universe. (Assuming no • other changes occur).

22. Solution • The 2nd Lawfor a system interacting with a • heat reservoir is: + + Any irreversible process increases the entropy of the universe.

23. More Examples of Spontaneous Processes Free Expansion of a Gas • The container on the right is filled with gas. The container on the left is vacuum. The valve between them is closed. Now, imagine that the valve is opened. Valve Closed Gas Vacuum

24. After the valve is opened, for some time, it is no longer an equilibrium situation. The 2nd Law says the molecules on the right will flow to the left. After a sufficient time, a new equilibrium is reached & the molecules are uniformly distributed between the 2 containers. The Entropy Increases!! After some time, there is a new Equilibrium Valve Opened Gas Gas

25. đQ Cold Hot Thermal Conduction • A hot object (red) is brought into thermal contact with a colder object (blue). The 2nd Law says that heat đQ will flow from the hot object to the colder object.

26. After the objects are brought into thermal contact, for some time, by the 2nd Law, heat đQ flows from the hot object to the colder object. During that time, it isn’t an equilibrium situation. After a sufficient time, a new equilibrium is reached & the 2 objects are at the same temperature.  The Entropy Increases!! Warm After some time, there is a new Equilibrium

27. Mechanical Energy toInternal Energy Conversion • Consider a ball of mass m. It’s Mechanical Energyis: E  KE + PE.KE = Kinetic Energy, PE = Potential Energy. • For conservative forces, E is conserved (a constant). • Drop the ball from rest at a height h above the ground. Initially, E = PE = mgh Conservation of Mechanical Energy tells us that mgh = (½)mv2 h Just before hitting the ground, E = KE = (½)mv2 Mechanical Energy E is conserved!

28. At the bottom of it’s fall, the ball collides with the ground & bounces upward. If it has an Elastic Collision with the ground, by definition, right after it has started up, its mechanical & kinetic energies would be the same as just before it hit: E = (½)mv2 = mgh • In reality, The Collision will be Inelastic.So, the initial upward kinetic energy from the bounce,KE',will be less thanKEjust before it hit. The collision is Inelastic, so right after it bounces, its kinetic energy is KE' < KE. Just before hitting the ground, KE = (½)mv2. • Where did the “lost” KE go? It is converted to heat, • which changes the internal energy Ē of the ball. • As a result, the ball heats up!!

29. The ball’s collisionwith the ground is inelastic, so it loses some kinetic energy: KE' < KE. The lost kinetic energy is converted to heat, which changes the ball’s internal energy Ē. So, the ball gets warmer!! • In your undergrad course you should have been shown that, for an infinitesimal, quasi-static process in which an object heats up, changing its temperature by an amount dT, it’s internal energy change is (m ≡ball’s mass cV≡ specific heatat constant volume) dĒ = mcVdT KE = (½)mv2 KE' < KE The change in the ball’s internal energy is dĒ = mcVdT

30. With Multiple Bouncesof the ball, there will be Multiple • Inelastic Collisionswith the ground. • When it finally comes to rest after several bounces, the • ball may be MUCH warmerthan when it was dropped! The ball loses more KE on each bounce & it eventually stops on the ground. Thus, after sufficient time, It tends towards Equilibrium The more bounces the ball has, the warmer it gets! The Ball’s Entropy Increases!!

31. Irreversible (Spontaneous) Processes • A block of ice can slide down an incline plane if the frictional force is overcome. But the ice cannot spontaneously move upthe incline of its own accord. • The conversion of mechanical energy to thermal energy by friction as it slides is irreversible.

32. More Examples of Spontaneous Processes • Spontaneous processesoccur in a system left to itself. • No action from outside the system is necessary to bring • the change about.

33. More Examples of Spontaneous Processes • Spontaneous processesoccur in a system left to • itself. No action from outside the system is necessary • to bring the change about. • Example • Disolving a Solid in a Liquid • (like salt in water) • Ions have more entropy (more states) than the water, • But,some water molecules have less entropy (they are grouped around ions). Usually, there is an overall increase in entropy.

34. More Examples of Spontaneous Processes • Spontaneous processesoccur in a system left to itself. • No action from outside the system is necessary to bring • the change about. • Question: Water put into a freezer spontaneously turns to ice.(So, the water entropy decreases!) • Entropy always increases, so, how can we account for this? • Answers • The compressor does work on the ice + freezer. • This causes evaporation & condensation of the refrigerant. • This also causes warming of the air around the container • As a result of these effects, the entropy of the universe will increase.

35. Some Processes That Lead to an Increase in Entropy (Spontaneous Processes) 1. Melting of a solid. 2. Dissolving of a solid in a solution. 3. A solid or a liquid becomes a gas. 4. The temperature of a substance increases. 5. A chemical reaction produces more molecules.

36. FYI: Brief Discussion “Impossible Processes” • Impossible Processes are those which would be Allowed by the 1st Lawof Thermo but which Can’t Occur Naturallybecause they would violate the 2nd Lawof Thermo. • Any process which would take a system from an equilibrium state to a non-equilibrium state without work being doneon the system Would violate the 2nd Law & thus Would be an “Impossible Process”!

37. Examples of Impossible Processes Initially, the valve is open& gas molecules are uniformly distributed in the 2 containers. • Example 1:“Free Compression”of a Gas! Valve Open After some time,all gas molecules are gathered in the right container & the left container is empty. Gas Gas The Entropy Decreases! Vacuum Gas Valve Open

38. Thermal Conduction Initially, An object is warm. Warm After some time, The left side is hot & the right side is cold!! Hot Cold So, the Entropy Decreases!!

39. Conversion of Internal Energy to Mechanical Energy Initially, a ball is on the ground & is hot. Hot After some time,the ball begins to move upward with kinetic energy KE = (½) mv2 & it cools down! Warm The Entropy Decreases!

40. “Impossible Processes”Cannot occur withoutthe input of work đW

41. In such a process, the System’s Entropy Decreases, but the Total Entropy of the System+ Environment Increases Decrease in Entropy Environment đW Increase in Entropy

42. FYI: Very BriefDiscussion: “Perpetual Motion” • We’ve said, “Impossible Processes” are processes which are Allowed by the 1st Lawof Thermobut which Can’t Occur Naturallybecause they would violate the 2nd Lawof Thermo. • Any process which takes a system from an equilibrium state to a non-equilibrium state without work being doneon the system Would violate the 2nd Law of Thermo & thus Would be an Impossible Process! • As examples which we sometimes hear about, the so-called “Perpetual Motion” or “Free Energy” machines rely on such “Impossible Processes” & thus are Always Bogus!

43. What is “Perpetual Motion”? • That term describes hypothetical machinesthat • operate or produce useful work indefinitely &, • more generally, hypothetical machines that produce • more work or energy than they consume, • whether they might operate indefinitely or not. • There is undisputed scientific consensus that • Perpetual motion would violateeitherthe 1st Laworthe 2nd Law of Thermodynamics,or both! • Such machines rely on “Impossible Processes” & thus are • Always Bogus!

44. “Perpetual Motion” • Describes a theoretical machine that, without any losses due to friction or other forms of dissipation of energy, would continue to operate indefinitely at the same rate without any external energy being applied to it. • Machines which comply with both the 1st & 2nd • Laws of Thermodynamics but access energy • from obscure sources are also sometimes referred • to as “Perpetual Motion” machines, although • they do not meet the standard criteria for the name.

45. Brief Overview: Classification of“Perpetual Motion” Machines! 1. “Perpetual Motion” Machine of the 1st Kind 2. “Perpetual Motion” Machine of the 2nd Kind 3. “Perpetual Motion” Machine of the 3rd Kind

46. The 1st Kind • A “perpetual motion” machine of the first kind produces work without the input of energy. It thus violates the 1st Law of Thermodynamics: the Law of Conservation of Energy. • The law of conservation of energy is an empirical law of physics. It states that the total amount of energy in an isolated system remains constant over. • A consequence of this law is that energy can neither be created nor destroyed: it can only be transformed from one state to another. So, It is clearly impossible for a machine to do work indefinitely without consuming energy.

47. The 2nd Kind • A “perpetual motion” machine of the 2nd kind is a machine which spontaneously convertsthermal energy into mechanical work. • When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy. However, it does violate the 2nd Law of Thermo! • The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.

48. The 3rd Kind • A “perpetual motion” machine of the 3rd kind is a machine which relies on the Complete Elimination of Friction & other dissipative forces, to maintain motion forever. • Technically, it is not so much an energy generating machine so much as an energy storage device. • It is not possible to move with zero friction, so although low friction devices are real, zero friction devices are not.