The Story of Spontaneity and Energy Dispersal You

The Story of Spontaneity and Energy Dispersal You never get what you want: 100% return on investment

Spontaneity l Spontaneous process are those that occur naturally. ¡Hot body cools ¡A gas expands to fill the available volume l A spontaneous direction of change is where the direction of change does not require work to bring it about.

Spontaneity l The reverse of a spontaneous process is a nonspontaneous process ¡Confining a gas in a smaller volume ¡Cooling an already cool object l Nonspontaneous processes require energy in order to realize them.

Spontaneity l Note: ¡Spontaneity is often interpreted as a natural tendency of a process to take place, but it does not necessarily mean that it can be realized in practice. l Some spontaneous processes have rates sooo slow that the tendency is never realized in practice, while some are painfully obvious.

Spontaneity l The conversion of diamond to graphite is spontaneous, but it is joyfully slow. l The expansion of gas into a vacuum is spontaneous and also instantaneous.

2 ND LAW OF THERMODYNAMICS

Physical Statements of the 2 nd Law of Thermodynamics l Kelvin Statements l “No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work”

l “It is impossible for a system to undergo a cyclic process whose sole effects are the flow of an amount of heat from the surroundings to the system and the performance of an equal amount of work on the surroundings. ” l “It is impossible for a system to undergo a cyclic process that turns heat completely into work done on the surroundings. ”

l Clausius statement l It is impossible for a process to occur that has the sole effect of removing a quantity of heat from an object at a lower temperature and transferring this quantity of heat to an object at a higher temperature. l Heat cannot flow spontaneously from a cooler to a hotter object if nothing else happens

The 2 nd Law of Thermodynamics l The 2 nd Law of Thermodynamics recognizes the two classes of processes, the spontaneous and nonspontaneous processes.

Implications of the 2 nd Law l No heat engine can have an efficiency as great as unity l No macroscopic process can decrease the entropy of the universe

Are you kidding me? Thermodynamic Cat

Hot Reservoir Heat Cold Reservoir Engine Heat Work I approve!

What determines the direction of spontaneous change? l The total internal energy of a system does NOT determine whether a process is spontaneous or not. l Per the First Law, energy is conserved in any process involving an isolated system.

What determines the direction of spontaneous change? l Instead, it is important to note that the direction of change is related to the distribution of energy. l Spontaneous changes are always accompanied by a dispersal of energy.

Energy Dispersal l Superheroes with energy blasts and similar powers as well as the Super Saiyans are impossible characters. l They seem to violate the Second Law of Thermodynamics!

Power Genki dama

Energy Dispersal l A ball on a warm floor can never be observed to spontaneously bounce as a result of the energy from the warm floor

Energy Dispersal l In order for this to happen, thermal energy represented by the random motion and vibrations of the floor atoms would have to be spontaneously diverted to accumulate into the ball.

Energy Dispersal l It will also require the random thermal motion to be redirected to move in a single direction in order for the ball to jump upwards. l This redirection or localization of random, disorderly thermal motion into a concerted, ordered motion is so unlikely as to be virtually impossible.

Energy Dispersal and Spontaneity l Spontaneous change can now be interpreted as the direction of change that leads to the dispersal of the total energy of an isolated system! INDEED!

Entropy l A state function, denoted by S. l While the First Law can be associated with U, the Second Law may be expressed in terms of the S

Entropy and the Second Law l The Second Law can be expressed in terms of the entropy: The entropy of an isolated system increases over the course of a spontaneous change: ΔStot > 0 l Where Stot is the total entropy of the system and its surroundings.

Entropy: A molecular look l

Entropy l A simple definition of entropy is that it is a measure of the energy dispersed in a process. l For thermodynamic definition, it is based on the expression:

Entropy l For a measurable change between two states, l In order to calculate the difference in entropy between two states, we find a reversible pathway between them and integrate the energy supplied as heat at each stage, divided by the temperature.

Example

Change in entropy of the surroundings: ΔSsur l

Change in entropy of the surroundings: ΔSsur l For adiabatic change, qsur = 0, so DSsur = 0

Entropy as a State Function l To prove entropy is a state function we must show that ∫d. S is path independent ¡ Sufficient to show that the integral around a cycle is zero or l Sadi Carnot (1824) devised cycle to represent idealized engine Hot Th Reservoir Step 1: Isothermal reversible expansion @ Th qh w 3 -w 1 Step 2: Adiabatic expansion Th to Tc -w 2 Step 3: Isothermal reversible compression @ Tc (sign of q negative) Engine w 4 qc Cold Tc Reservoir Step 4: Adiabatic compression Tc to Th

Carnot Engine How is that possible?

Carnot Cycle

Carnot Cycle Step 1: ΔU=0 Step 2: ΔU=w Step 3: ΔU=0 Step 4: ΔU=-w

Carnot Cycle - Thermodynamic Temperature Scale l The efficiency of a heat engine is the ratio of the work performed to the heat of the hot reservoir e=|w|/qh ¡ The greater the work the greater the efficiency ¡ Work is the difference between the heat supplied to the engine and the heat returned to the cold reservoir w = qh -(-qc) = qh + qc l Therefore, e = |w|/qh = ( qh + qc)/qh = 1 + (qc/qh ) Hot Reservoir qh w Heat Engine Work Cold Reservoir Heat -qc

Efficiency of Heat Engines l

Carnot Cycle - Thermodynamic Temperature Scale Hot Ø William Thomson (Lord Kelvin) defined a substance-independent temperature scale based on the heat transferred between two Carnot cycles sharing an isotherm ¡ He defined a temperature scale such that qc/qh = Tc/Th e = 1 - (Tc/Th ) Zero point on the scale is that temperature where e = 1 Or as Tc approaches 0 e approaches 1 Efficiency can be used as a measure of temperature regardless of the working fluid § Applies directly to the power required to maintain a low temperature in refrigerators Reservoir qh w Heat Engine Work Cold Reservoir Heat -qc ØEfficiency is maximized ØGreater temperature difference between reservoirs ØThe lower Tc, the greater the efficiency

Refrigeration

Coefficient of performance (COP or β or c) l

Entropy changes: Expansion l

Isothermal Isochoric Isobaric Adiabatic 0 n. CvΔT q+w w q n. CvΔT n. CpΔT or –wirrev 0 wrev 0 =-n. CvΔT =-pextΔV ΔU wirrev -pextΔV 0 -pextΔV ΔH 0 (for ideal gas) ΔU =ΔU + pΔV =n. CpΔT ΔS 0

Entropy changes: Phase Transitions l

General equations for entropy during a heating process l

Measurement of Entropy (or molar entropy)

Measurement of Entropy (or molar entropy) l The terms in the previous equation can be calculated or determined experimentally l The difficult part is assessing heat capacities near T = 0. l Such heat capacities can be evaluated via the Debye extrapolation

Measurement of Entropy (or molar entropy) l

Third Law of Thermodynamics l At T = 0, all energy of thermal motion has been quenched, and in a perfect crystal all the atoms or ions are in a regular, uniform array. l The localization of matter and the absence of thermal motion suggest that such materials also have zero entropy. l This conclusion is consistent with the molecular interpretation of entropy, because S = 0 if there is only one way of arranging the molecules and only one microstate is accessible (the ground state).

Third Law of Thermodynamics The entropy of all perfect crystalline substances is zero at T = 0.

Nernst heat theorem l The entropy change accompanying any physical or chemical transformation approaches zero as the temperature approaches zero: ΔS 0 as T 0 provided all the substances involved are perfectly crystalline.

Third-Law entropies l These are entropies reported on the basis that S(0) = 0.

Exercises

HELMHOLTZ AND GIBBS ENERGIES

Clausius inequality l

Criteria for spontaneity l

Criteria for spontaneity l

Criteria for spontaneity l

Criteria for spontaneity l

Helmholtz and Gibbs energy l Helmholtz energy, A: A = U - TS l Gibbs energy, G: G = H - TS d. A = d. U – Td. S d. G = d. H – Td. S d. AT, V ≤ 0 d. GT, p ≤ 0

Helmholtz energy l A change in a system at constant temperature and volume is spontaneous if it corresponds to a decrease in the Helmholtz energy. l Aside from an indicator of spontaneity, the change in the Helmholtz function is equal to the maximum work accompanying a process.

Helmholtz energy

, useful

Variation of the Gibbs free energy with temperature

Variation of the Gibbs free energy with pressure

Variation of the Gibbs free energy with pressure

Homework 1. When 1. 000 mol C 6 H 12 O 6 (glucose) is oxidized to carbon dioxide and water at 25°C according to the equation C 6 H 12 O 6(s) + 6 O 2(g) 6 CO 2(g) + 6 H 2 O(l), calorimetric measurements give Δr. Hθ= -2808 k. J mol-1 and Δr. Sθ = +182. 4 J K-1 mol-1 at 25°C. How much of this energy change can be extracted as (a) heat at constant pressure, (b) work? 2. How much energy is available for sustaining muscular and nervous activity from the combustion of 1. 00 mol of glucose molecules under standard conditions at 37°C (blood temperature)? The standard entropy of reaction is +182. 4 J K-1 mol-1. 3. Calculate the standard reaction Gibbs energies of the following reactions given the Gibbs energies of formation of their components a) Zn(s) + Cu 2+(aq) Zn 2+(aq) + Cu(s) b) C 12 H 22 O 11(s) + 12 O 2(g) 12 CO 2(s) + 11 H 2 O(l)

One for the road l Life requires the assembly of a large number of simple molecules into more complex but very ordered macromolecules. Does life violate the Second Law of Thermodynamics? Why or why not?