Sustainable Energy 10/7/2010

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1 Toolbox 8: Thermodynamics and Efficiency alculations Sustainable Energy 10/7/2010 Sustainable Energy - Fall Thermodynamics

2 First law: conservation of heat plus work eat () and work (W) are forms of energy. Energy can neither be created or destroyed. E = + W Applies to energy (J, BTU, kw-hr, ) or power (W, J/s, hp) Work comes in several forms: PdV, electrical, mgh, kinetic, Photo by Ian Dunster on Wikimedia ommons. onservation of Energy discovered in 1847 (elmholtz, Joule, von Mayer)

3 Energy, mass balances. ontrol Volume onservation of energy: in in out out n k k ΔE = +W + E k n k E k k Image removed due to copyright restrictions. Please see Fig. 4.6 in Tester, Jefferson W., and M. Modell. Thermodynamics and its Applications. 3rd ed. Englewood liffs, NJ: Prentice all, hemical species conservation: Δn = n in n out + k k k k r dv dt r k is chemical rate of formation of kth species reactions don t change total mass or energy.

4 onverting heat and work In theory various forms of work can be interconverted with high efficiency (i.e. without making a lot of heat): Kinetic, mgh, electricity In practice it is difficult to efficiently convert some types of work: chemical/nuclear/light tend to make a lot of heat during conversions. Work can easily be converted to heat with high efficiency: Electrical resistance heaters, friction, exothermic reactions (e.g. combustion, nuclear reactions) Impossible to convert eat to Work with high efficiency: oal plants (~35%), nuclear plants (~35%), natural gas plants (~50%), automobiles (~20%)

5 Entropy (S) and the second law of thermodynamics Entropy: a measure of disorder Entropy of the universe is always increasing Moves to more statistically probable state Entropy is a state function d S δ T rev ΔS universe 0 2 nd Law discovered by Rudolf lausius in 1865

6 eat to work conversions Image removed due to copyright restrictions. Please see Fig in Tester, Jefferson W., and M. Modell. Thermodynamics and its Applications. 3rd ed. Englewood liffs, NJ: Prentice all, 1996.

7 eat to work conversions in W in W out out

8 A simple heat engine Energy balance: 0 (steady state) 0 (first law) 0 (first law) Accumulation = In Out + Generation onsumption W 0 = W W = 0 (steady state) Entropy balance: S 0 (2nd law) S gen Accumulation = In Out + Generation onsumption 0 = + S gen S = < 0 T gen T Violation of the 2 nd Law! Not possible. eat engine must reject heat, cannot convert all heat to work (since that would reduce entropy of the universe).

9 A possible heat engine Energy balance: W 0 (steady state) 0 (first law) 0 (first law) Accumulation = In Out + Generation onsumption 0 = W W = 0 (steady state) Entropy balance: S gen 0 (2nd law) Accumulation = In Out + Generation onsumption 0 = + S gen S gen = T T T T No obvious violation of the second law.

10 Maximum efficiency of heat engine W 0 gen = = S work heat W η To maximize efficiency: T = 0 gen = = T T S T = Algebra: work,max heat 1 T T T T W = = = η

11 arnot efficiency W max T ηarnot = 1 T Sets upper limit on work produced from a process that has a hot and cold reservoir Examples: coal power plant, gas power plant, nuclear power plant, internal combustion engine, geothermal power plant, solar thermal power plant Note: All temperatures must be expressed in Kelvin (or Rankine)! T c usually cannot be below environmental T. T usually limited by materials (melting, softening, oxidizing) or by need to avoid burning N 2 in air to pollutant NO.

12 Free Energy and Exergy: Measures of ow Much hemical Energy is potentially available to do work Usual measure of ability to do work: Free energy G = TS = U + PV - TS We have some minimum temperature in our system (usually T cooling, ~300 K), and a min pressure (e.g. P min = 1 atm) annot reduce entropy, so T S and P V not available. cooling min m n all G-T cooling S P min V the exergy : how much chemical energy going in to a device is available to do work. Should also consider the lowest-chemical-energy products (e.g. 2 O and O 2 ), not ordinary standard states of enthalpy (2, O2, graphite). A ton of room temperature air has quite a lot of thermal energy, but none of that energy can be converted into work.

13 Rankine cycle Image removed due to copyright restrictions. Please see Fig in Tester, Jefferson W., and M. Modell. Thermodynamics and its Applications. 3rd ed. Englewood liffs, NJ: Prentice all, 1996.

14 Which of these Six ases are not Feasible? Feasible Not Feasible. Violates Second Law W Not Feasible. Violates Second Law ot W old Feasible. Example: electric heater W Feasible. eat Engine W Feasible. eat Pump

15 ommon heat to work engines in practice Rankine cycle: (shown before) Brayton cycle: combustion gases are directly expanded across a turbine and exhausted; ombustion Turbine T gas plants ombined cycle (): Brayton cycle followed by a Rankine cycle on the turbine exhaust IG: applied to syngas produced from coal Internal combustion engine: combustion gases powering a piston

16 In most eat Engines, Work extracted as PdV Boiling a liquid under pressure: big volume change, lots of W = PdV Turbines, pistons extract mechanical work from the pressurized gas by a nearly adiabatic expansion: T V γ 1 = T V γ 1 P V γ = P V γ hi hi lo lo hi hi lo lo γ 1 nrt V γ 1 hi highp W = γ = / γ 1 1 p V VlowP Would like to arrange so that P lo ~ 1 atm, T lo ~ lowest feasible temperature Low T good for arnot efficiency If we exhaust the gas, don t want to waste enthalpy T, P both drop in expansion, but at different rates

17 Impractical to arrange ideal P hi, T hi Material limits on pressure, temperature Steam cycles confined to relatively low T hi Internal ombustion Engines, Turbines Exhaust tends to be too hot (T lo >> ambient) A lot of energy carried away as waste heat in the exhaust (LV, exergy analysis). So despite high T hi, these are usually much less efficient than arnot. Need to combine Topping and Bottoming cycles.

18 ombined heat and power (P) eat and power are often produced together to maximize the use of otherwise wasted heat. Topping cycles produce electricity from high T, and use the waste heat for other process needs (e.g., MIT cogen facility) Bottoming cycles are processes which use medium heat T heat to generate electricity. Topping Lowtemp. heat need W el Bottoming igh- temp. heat need M W el

19 eat pumps Move heat from cold to hot oefficient of performance (OP) ~25 OP w T = W T T ~10 eat pump W Practically, OPs are ~3 3x as much heat can be supplied as electricity supplied Limited by power generation efficiency

20 Select the More Efficient ome eating Option Burn NG with 90% efficiency furnace OR Use electricity to drive heat pump eat pump OP is 3 NG Power Plant ombined ycle with 50% efficiency Transmission and distribution losses are 10%

21 Air conditioning and refrigeration ~35 eat pump ~25 W Type of heat pump oefficient of performance (OP) OP s = W T T T

22 an convert heat to chemical energy but still run into arnot limit O + = O Δ rxn >0 and ΔS rxn>0 Need to supply heat at high T (to shift equilibrium to the right) Remove hot 2 from catalyst to freeze the equilibrium. When we cool hot 2 to room T, emit heat at lower T (makes additional entropy).

23 onclusions 1. eat plus work is conserved (from the First Law). 2. eat can t be converted to work with 100% efficiency (from the Second Law). 3. Real processes suffer from non-idealities which generally keep them from operating close to their thermodynamic limits (from real life, plus the Second Law). 4. hemical, nuclear energy in principle are work, but most practical devices convert them into heat, then use heat engines to extract PdV work: arnot limit 5. areful accounting for energy/exergy and the limits on what is possible is necessary for assessing new energy proposals. Relatively easy to do, and the results are much more solid and exact than other aspects of the problem like financing, economics, marketing, politics.

24 MIT OpenourseWare J / 2.650J / J / 1.818J / 2.65J / J / J / J / ESD.166J Introduction to Sustainable Energy Fall 2010 For information about citing these materials or our Terms of Use, visit:

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