Exergy. What s it all about? Thermodynamics and Exergy

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3 Exergy What s it all about? Thermodynamics and Exergy

4 Quality of Energy General recognition that some forms of energy are more useful than others Electricity can be used for light, heat, cooling, mechanical power, electrolysis.. Chemical fuels can be used to power vehicles or other engine-driven devices, make batteries (sometimes) Heat can be used to make power (if at high temperature)

5 Quality of Energy What decides which forms are useful, and which not? What happens when a fuel is used up? Conservation of Energy is a well-known principle. It s still there all of it. Just what is lost?

7 Thermodynamics Zeroth Law If two systems are in equilibrium with each other, and a third is in equilibrium with one of them, then it is also in equilibrium with the other.

8 Thermodynamics First Law Energy can be transformed from one form to another, but not created or destroyed.

9 Forms of Energy Mechanical work Heat Chemical Nuclear Electrical Kinetic Gravitational

10 Gas Internal Energy All kinetic in this case Speeds not all the same Redistribution of energy by collision Pressure collisions with walls Temperature Internal Energy s thermodynamic symbol is E

11 Enthalpy Defined as E + PV Internal energy + energy required to make space with volume V in an environment with pressure P Symbol is H

12 Enthalpy Taken as zero for elements at standard conditions (298K and 1 atm pressure) To get H for other conditions, measure the energy addition required. The route does not matter consequence of 1 st Law Work done on the environment if expansion occurs is included in the PV term.

13 Enthalpy of Reaction T C + ½ O 2 CO Elements at standard conditions Product also at standard conditions Heat given out measured as kj/mol ΔH for the reaction is kj/mol Standard Enthalpy for CO is kj/mol Reaction Process

14 Hess Law CO ½O 2 ΔH = kj/mol ½O2 ΔH =? C ΔH = kj/mol CO 2 O 2

15 Enthalpy of Reaction Standard Enthalpy for CO 2 is kj/mol C + O 2 CO 2 ΔH of reaction is kj/mol We can infer that the ΔH of reaction for oxidation of CO to CO 2 is the difference between kj/mol and kj/mol, i.e., kj/mol CO + ½O 2 CO 2 ΔH is kj/mol

16 Hess Law another use ΔH =? C + O 2 CO K C + O 2 CO 2 ΔH = kj/mol 298 K

17 Another Example C + 2H 2 CH 4 ΔH kj/mol C + O 2 CO 2 ΔH kj/mol H 2 + ½O 2 H 2 O (l) ΔH kj/mol Combine: CH 4 + 2O 2 2H 2 O + CO 2 ΔH kj/mol

18 Energy We know very well how to measure or calculate the energy in a system. We know the exchange rates between different forms of energy. These are fixed. We can predict very well the energy that will be given off or used by a process or chemical reaction.

19 Entropy Hot things cool down. The process is irreversible. Things mix irreversibly. Organised motion becomes disorganised friction leading to production of heat. What is going on here?

20 The Usefulness of Energy High Kinetic Electrical Gravitational potential Medium Fuel combustion High temperature heat Low Low temperature heat

21 Temperature Property of matter Comparison can be made by measuring heat transfer Equilibrium situation Energy shared by different parts of the system

Entropy The origin of the idea of entropy comes from the study of heat engine efficiencies Heat q, at temperature T, has entropy q/t. The symbol for entropy is S. The units are Joules per degree.

22 Entropy The origin of the idea of entropy comes from the study of heat engine efficiencies Heat q, at temperature T, has entropy q/t. The symbol for entropy is S. The units are Joules per degree. From this starting point, one can get to the statistical interpretation, where a change in S is shown to be proportional to the logarithm of the relative probabilities of the two states. William Thomson ( ) For the same total energy, disordered states have greater probability than ordered ones, and higher entropy.

23 Entropy and the Third Law 3 rd Law At absolute zero, no entropy changes are possible Stronger interpretation at absolute zero, entropies of all pure substances are zero To get entropy at any other conditions, measure the heat required to get there from absolute zero, and integrate dq/t from zero to those conditions

24 Entropies of Substances As with Enthalpy, Entropy is a State Function i.e., not dependent on how you got there. As with Enthalpy, Entropy numbers are published in tables. In chemical thermodynamic tables, these are absolute numbers, unlike Enthalpies. For both, you actually use differences, calculating the change in Enthalpy or Entropy when a process occurs.

25 There exists a huge database of properties (enthalpies, entropies and others) of chemical substances. This is the result of immense amounts of work by many people over the last two centuries

26 Reversibility and Irreversibility For an isolated system, entropy stays the same or increases. So for a reversible process, there can be no entropy change For irreversible processes, entropy increases

27 Reversible Processes No temperature gradients No friction No diffusion Infinitely slow

28 Irreversible Processes Anything real! Example 1000 Joules of heat at 100 C (373K) leaks to a room at 20 C (293K). Entropy loss of source = 1000/373 = 2.68 J/K Entropy gain of room = 1000/293 = 3.41 J/K Overall increase = 0.73 J/K

29 Irreversible Processes 1 L of air at 20 C and 2 atmospheres pressure leaks into another 1 L container How to calculate entropy increase?

30 Gas Expansion - Irreversible Leak P = 2 atm P = 0 T = 20 C

31 Gas Expansion - Reversible Piston P = 0 Heat in P = 2 atm Work out T = 20 C

32 Irreversible Processes 1 L of air at 20 C and 2 atmospheres pressure leaks in to another 1 L container How to calculate entropy increase? Reversible route work done = 139 J So heat in must be 139 J The entropy increase for the air in this case = 0.47 J/K

Statistical Connection That air contains 4.9 x 10 22 molecules What are the odds against all of them being in the starting vessel by chance?

33 Statistical Connection That air contains 4.9 x molecules What are the odds against all of them being in the starting vessel by chance? 1 in 2 to the 4.9 x power! Boltzmann s law: S = k ln(w) In this case ΔS = k ln(w 1 /W 2 ) Increase in entropy = 0.47 J/K Ludwig Eduard Boltzmann ( )

34 Maximum Work A process has a known ΔH and ΔS What is the maximum work we can get from it? Heat out = q Work out = w We know that q + w = - ΔH (1 st law) How does ΔS fit in?

35 Maximum Work Process ΔH p, ΔS p Work, w For total entropy constant: q/t0 = - ΔS p so: q = - T0*Δ S p but: q + w = - ΔH p Heat, q Environment temperature T0 w = - ΔH p + T 0 *ΔS p

36 Exergy This is the maximum work available when a system changes from its starting state to being in equilibrium with its environment. This includes, temperature, pressure, and, strictly, mixing.

37 Energy Quality A comparison of the exergy and enthalpy contents. Electricity: 100% Kinetic Energy of bulk matter: 100% Mechanical Power: 100% Heat: (T T 0 )/T Chemical: (-ΔH + T 0 ΔS)/(-ΔH)

Oxidation of Methane ΔH = -890.1 kj/mol ΔS = -242.8 J/(mol.

38 Oxidation of Methane ΔH = kj/mol ΔS = J/(mol.K) Exergy available = - ΔH + T 0.ΔS If T 0 = 298K, then: Exergy = kj/mol Energy quality = 92%

39 Heat at 1000 C 1 kj of heat at 1000 C (1273 K) Entropy = 1000/1273 = 0.79 J/K If reference temperature = 20 C (293 K) Exergy = *0.79 = 770 J Energy quality = 77%

40 Electrical Energy 1 kwh of electricity No entropy Exergy = Energy Energy quality = 100%

41 Reference Temperature Exergy results depend on the choice of reference temperature. The choice of temperature must be made carefully. The lower the reference temperature, the less the significance of the entropy term.

42 Summary 0 th and 1 st laws of thermodynamics are about the consistency of systems and conservation of energy 2 nd law concerns the increase in entropy 3 rd law lets us measure entropies Enthalpy and entropy changes let us calculate exergy

2013, 2011, 2009, 2008 AP

2013, 2011, 2009, 2008 AP Lecture 15 Thermodynamics I Heat vs. Temperature Enthalpy and Work Endothermic and Exothermic Reactions Average Bond Enthalpy Thermodynamics The relationship between chemical reactions and heat. What causes