ERT 108 Physical Chemistry The Second Law of Thermodynamics by Rohazita Bahari

Outline The Second Law of Thermodynamics Heat Engines Entropy Calculation of entropy changes Entropy, Reversibility and Irreversibility The thermodynamics temperature scale What is entropy? Outline

The laws of thermodynamic describe the basic properties of energy The first law of thermodynamics (also called law of conservation of energy): the total amount of energy (E) within a given system remains constant. Energy can change form, such as from chemical E  heat E The second law of thermodynamics: E is converted from one form to another, the amount of useful E decreases. All spontaneous changes result in a more uniform distribution of E, reducing the E differences that are essential for doing work; E is spontaneously converted from more useful into less useful forms.

Direction of spontaneous change A spontaneous process is one that occurs without ongoing outside intervention (such as the performance of work by some external force. A spontaneous reaction occurs naturally and favors the formation of products at the specified conditions. Direction of spontaneous change Chemical potential

A nonspontaneous reaction is a reaction that does not favor the formation of products at the specified conditions. Photosynthesis is a nonspontaneous reaction that requires an input of energy.

The recognition of two classes of process, spontaneous and non-spontaneous is summarized by the Second Law Thermodynamic. This Law can be expressed in a variety of equivalent ways. One statement was formulated by Kelvin: “No process is possible in which the sole result is absorption of heat from a reservoir and its complete conversion into work” The Kelvin statement of the Second Law denies that possibility of the process illustrated here, in which heat is changed completely into work, there being no further change. The process is not in conflict with the First Law because energy is conserved. Example: Heats Engine

Kelvin-Plack formulation of the second law of thermodynamics: It is impossible for a system to undergo cyclic process whose sole effects are the flow of heat into the system from a heat reservoir and the performance of an equivalent amount of work by the system on the surroundings.

How to understand the role of distribution of energy? Inelastic losses in the materials of the ball and floor. Kinetic energy →energy of the thermal motion The direction of spontaneous change for a ball bouncing on a floor. On each bounce some of its energy is degraded into the thermal motion of the atoms of the floor, and that energy disperses. The reverse has never been observed to take place on microscopic scale.

The molecular interpretation of the reversibility expressed by the Second Law. (a) A ball resting on a warm surface are undergoing thermal motion (vibration, in this instance), as indicated by the arrows (b) For the ball to fly upwards, some of the random vibrational motion would have to change into coordinated, direction motion. Such as conversion is highly improbable.

The Second Law of Thermodynamics It is impossible to build a cyclic machine that converts 100% heat into work.

The Second Law of Thermodynamics Any heat engine must eject heat into the cold reservoir

Heat engine: a device that operates in a thermodynamic cycle and does a certain amount of net positive work as a result of heat transfer from a high-temperature body to a low-temperature body. (eg: the internal-combustion engine and the gas turbine) Heat Engines

Hot reservoir The efficiency of heat engine: The efficiency value is less than 1, qC has a negative value and qH has a positive value. Cold reservoir Work output per cycle Energy input per cycle Heat Engines

Definition; It is an ideal heat-engine cycle in which the working substance goes through four (4) successive operations of: Isothermal expansion Adiabatic expansion Isothermal Compression Adiabatic Compression back to its initial state. Carnot Cycle

Heat Engines The cycle for a reversible heat engine (Carnot cycle):

Heat, Work and ΔU for Reversible Carnot Cycle

Work flow in Carnot cycle

Carnot cycle For a complete cycle (assuming perfect gas); Dividing by T and integrating over Carnot cycle; First Law

Carnot cycle Thus; Differential of state function; independent of the path taken to reach final state. Thus;

Carnot cycle Since bc and da are adiabatic; dq=0; Thus;

Carnot cycle For Carnot cycle the efficiency can be also written as; Where is the maximum possible efficiency for the conversion of heat to work. Work output per cycle Energy input per cycle Because

Calculate the maximum work that can be done by reversible heat engine operating between 500 and 200 K if 1000 J is absorbed at 500 K Exercise 1

Solution Calculate the maximum work that can be done by reversible heat engine operating between 500 and 200 K if 1000 J is absorbed at 500 K

The Thermodynamic Definition of Entropy The thermodynamic of entropy concentrates on the change in entropy, dS that occurs as a result of a physical or chemical change (in general, as a result of a ‘process’). The thermodynamic definition of entripy is based on the expression: Definition of entropy change Eqn 3.1 Where qrev is the heat supplied reversibly. For measureable change between two states i and f this expression integrates to: Eqn 3.2 That is, to calculate the difference in entropy between any two states of a system, we find a reversible path between them, and integrate the energy supplied as heat at each stage of the path divided by the temperature at which heating occurs. The Thermodynamic Definition of Entropy

Entropy, S Closed sys, rev. process

System proceed to equilibrium What is entropy? Entropy is a measure of the probability, p of the thermodynamic state a a a a b a b b a b b b b b a a a a b b b a b a Partition removed System proceed to equilibrium Irreversible mixing of perfect gas at constant T & P The probability that all a molecules will be in the left half & all b molecules in right half is extremely small. The most probable distribution has a and b molecules equally distributed.

What is entropy? Entropy is a measure of molecular disorder of a state. Eg: In mixing two gases, the disordered (mixed state) is far more probable than the ordered (unmixed) state.

What is entropy? Entropy is related to the distribution or spread of energy among the available molecular energy levels. The greater the number of energy levels, the larger the entropy is. Increasing the system’s energy (eg:by heating) will increase its entropy because it allows higher energy levels to be significantly occupied Increasing the volume of a system at constant energy also allows more energy level to be occupied.

Calculation of Entropy Changes Cyclic process; Reversible adiabatic process; Reversible phase change at constant T & P at constant P, , thus Rev. adiab. proc. Rev. phase change at const. T & P

Calculation of Entropy Changes Reversible isothermal process Constant-pressure heating with no phase change If is constant over the temperature range, then Rev, isothermal proc. Const. P, no phase change

Calculation of Entropy Changes 6. Reversible change of state of a perfect gas; Perfect gas

Calculation of Entropy Changes 7. Irreversible change of state of a perfect gas; 8. Mixing of different inert perfect gases at constant T & P Perfect gas

Exercise 2 One mole of a perfect gas at 300 K is reversibly and isothermally compressed from a volume of 25.0 L to a volume of 10.0 L. Because the water bath in the surroundings is very large, T remains essentially constant at 300 K during the process. Calculate ΔS of the system.

Exercise 2-Solution One mole of a perfect gas at 300 K is reversibly and isothermally compressed from a volume of 25.0 L to a volume of 10.0 L. Because the water bath in the surroundings is very large, T remains essentially constant at 300 K during the process. Calculate ΔS. This is an isothermal process, ΔT=0, thus ΔU=0 (for perfect gas, U depends only on T. ( )

Exercise 3 Calculate ΔS for the melting of 5.0 g of ice (heat of fusion= 79.7 cal/g) at 0°C and 1 atm. Estimate ΔS for the reverse process

Exercise 3- Solution Calculate ΔS for the melting of 5.0 g of ice (heat of fusion= 79.7 cal/g) at 0°C and 1 atm. Estimate ΔS for the reverse process. Identify type of process: Phase change at constant T & P At constant P, q= ΔH Thus, Calculate ΔS;

Exercise 3- Solution Calculate ΔS for the melting of 5.0 g of ice (heat of fusion= 79.7 cal/g) at 0°C and 1 atm. Estimate ΔS for the reverse process. ΔS for reverse process (freezing of 5g liquid water );

Exercise 4 The specific heat capacity cP of water is nearly constant at 100 cal/g K in the temperature range of 25°C to 50°C at 1 atm. Calculate ΔS when 100 g of water is reversibly heated from 25°C to 50°C at 1 atm. Without doing a calculation, state whether ΔS for heating 100g of water from 50°C to 75°C at 1 atm will be greater, equal to or less than ΔS for the 25°C to 50°C heating.

Exercise 4- Solution The specific heat capacity cP of water is nearly constant at 100 cal/g K in the temperature range of 25°C to 50°C at 1 atm. Calculate ΔS when 100 g of water is reversibly heated from 25°C to 50°C at 1 atm.

Exercise 4 - Solution The specific heat capacity cP of water is nearly constant at 100 cal/g K in the temperature range of 25°C to 50°C at 1 atm. Without doing a calculation, state whether ΔS for heating 100g of water from 50°C to 75°C at 1 atm will be greater, equal to or less than ΔS for the 25°C to 50°C heating. Thus, ↑T, ↓ΔS ΔS for heating 100g of water from 50°C to 75°C at 1 atm will be smaller than ΔS for the 25°C to 50°C heating.

Entropy, Reversibility and Irreversibility Reversible Process, ΔSuniv = 0 In reversible process, any heat flow between system & surroundings must occur with no finite temperature difference

Entropy, Reversibility and Irreversibility Irreversible Process, ΔSuniv > 0 Recall first law; rearranging More work is done when a change is reversible than when it is irreversible; When energy leaves the system as work, rearranging

Entropy, Reversibility and Irreversibility Irreversible Process, ΔSuniv > 0 Substituting into Dividing by T; Clausius inequality

Entropy, Reversibility and Irreversibility Irreversible Process, ΔSuniv > 0 Suppose that the system is isolated from its surroundings, thus dq=0

Entropy, Reversibility and Irreversibility Entropy & Equilibrium S Equilibrium reach S=Smax Time Thermodynamic equilibrium in an isolated system is reached when the system’s entropy is maximized.

The thermodynamics temperature scale -a scale that is independent of the choice of a particular thermometric substance. rearranging This expression enabled Kelvin to define thermodynamic temperature scale Kelvin scale is defined by using water at its triple point as the notional of hot source and defining that temperature as 273.16 K If it is found that the efficiency of heat engine equal to 0.2, then the temperature of cold sink is (0.8) x 273.16 K =220 K, regardless of the working substance of the engine.

Boltzmann made link between distribution of molecules over energy levels and the entropy; Where k= 1.381 x 10-23 JK-1 W= probability/ways in which the molecules of a system can be arranged while keeping the energy constant What is entropy?