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

From Statistical Arguments we’ve seen that a Quantitative Definition of Entropy is S  k B ln(  ) k B  Boltzmann’s constant    (E)  Number of Microstates at a Given Energy

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

Spontaneous Processes & Entropy Spontaneous Processes  Processes that can proceed with no outside intervention. Entropy Entropy can be viewed as a measure of randomness or disorder in the atoms & molecules in a system. The 2 nd Law of Thermodynamics  Total Entropy always increases in a spontaneous process! Microscopic Disorder also increases in a spontaneous process!

Entropy, S A Measure of Disorder S solid  S liquid  S gas

S solid  S liquid  S gas

Spontaneous Processes Spontaneous Processes  Processes that can proceed with no outside intervention. Example in the figure: Due to the 2 nd Law of Thermodynamics, the gas in container B will spontaneously diffuse into container A. But, once it is in both containers, it will never spontaneously diffuse back into container B.

Spontaneous Processes

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

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.

Irreversible Processes Irreversible Processes  Processes that cannot be undone by exactly reversing the process. All Spontaneous Processes are Irreversible. All Real processes are Irreversible.

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

Whenever a chemical system is in equilibrium, a reaction can go reversibly to reactants or products (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!”

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 2 nd Law of Thermodynamics says 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. Spontaneous, Irreversible Processes: More Examples

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.

Reversible Processes In a Reversible 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 a Reversible Process, changes proceed in infinitesimally small steps, so that the system is infinitesimally close to equilibrium at every step. This is clearly an idealization & can never happen in a real system!

Other Statements of the 2 nd Law of Thermodynamics “The entropy of the universe does not change for Reversible Processes” and also: “The entropy of the universe increases for Spontaneous Processes”: “You can’t break even”. For Reversible (ideal) Processes: For Irreversible (real, spontaneous) Processes:

Still Another Statement of the 2 nd Law of Thermodynamics “In any spontaneous process, there is always an increase in the entropy of the universe.” The Total Entropy S of the Universe has the property that, for any spontaneous process, ∆S ≥ 0.

Example: Entropy of the Universe Increases 1200 J of heat flows spontaneously through a copper rod from a hot reservoir at T H = 650 K to a cold reservoir at T C = 350 K. Calculate the amount by which this irreversible process changes the entropy of the universe, (assuming no other changes occur).

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

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 Vacuum Gas More Examples of Spontaneous Processes

The Entropy Increases!! After some time, there is a new Equilibrium After the valve is opened, for some time, it is no longer an equilibrium situation. The 2 nd 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. Gas Valve Opened Gas

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

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

Just before hitting the ground, E = KE = (½)mv 2 Mechanical Energy E is conserved! Mechanical Energy to Internal Energy Conversion Consider a ball of mass m. It’s Mechanical Energy is: 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. h Initially, E = PE = mgh Conservation of Mechanical Energy tells us that mgh = (½)mv 2

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)mv 2 = mgh In reality, The Collision will be Inelastic. So, the initial upward kinetic energy, KE', will be less than KE just before it hit. Just before hitting the ground, KE = (½)mv 2. The collision is Inelastic, so right after it bounces, its kinetic energy is KE' < KE. 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!!

The ball’s collision with 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 Ch. 4, we’ll show 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 dĒ = mc V dT m ≡ ball’s mass c V ≡ specific heat at constant volume KE = (½)mv 2 KE' < KE The change in the ball’s internal energy is dĒ = mc V dT

With Multiple Bounces of the ball, there will be Multiple Inelastic Collisions with the ground. When it finally comes to rest after several bounces, the ball may be MUCH WARMER than 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!!

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 up the incline of its own accord. The conversion of mechanical energy to thermal energy by friction as it slides is irreversible.

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

More Examples of Spontaneous Processes Example Disolving a Solid in a Liquid Example: 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. Spontaneous processes occur in a system left to itself. No action from outside the system is necessary to bring the change about.

More Examples of Spontaneous Processes Question: Water put into a freezer spontaneously turns to ice. 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. Spontaneous processes occur in a system left to itself. No action from outside the system is necessary to bring the change about.

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.

Brief Discussion of “Impossible Processes” Impossible Processes are processes which are Allowed by the 1 st Law of Thermo but which Cannot Occur Naturally because they would violate the 2 nd Law of Thermo. Any process which would take a system from an equilibrium state to a non-equilibrium state without work being done on the system Would violate the 2 nd Law of Thermo & thus Would be an Impossible Process!

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

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

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) mv 2 & it cools down! Warm The Entropy Decreases!

Impossible Processes Cannot occur without the input of work đW

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