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# A Tutorial on Thermodynamics - University of Illinois at Urbana ...

A Tutorial on Thermodynamics - University of Illinois at Urbana ...

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Second Law of ThermodynamicsSourceT hSinkT cHeat QEntropy Q/T hQW WT Tc hElectrical energy WHeatengineQ-WEntropy (Q-W)/T cMark A. Shannon http://watercampws.uiuc.edu3

Second Law of ThermodynamicsQW Q Tc W 1TcTh ThQ In typical steam cycles (coal, nuclear) heatflow into cold heat sink is approximately thesame as electrical power (Q-W) ≈ W (andcomparable to heat lost to exhaust) Need to dissipate W of heat at as low of atemperature as possible.Mark A. Shannon http://watercampws.uiuc.edu4

Cooling requirements inpower generation Most effective way to do this iswith water, either by a heatinga large volume by a smallamount and then discharge toenvironment, or byevaporation. Discharge is warm andincreases evaporation sooverall consumption of water issimilar in both cases.Mark A. Shannon http://watercampws.uiuc.edu5

Cooling requirements in powergeneration Heat of vaporization of water is 2 J/mm 3 or 2GJ/m 3 In other words, need to evaporate 0.5 m 3 ofwater per second for a 1 GW nuclear powerplant. Order of magnitude the same as thehousehold water use (in the US) of a smallcity of 100,000 (e.g., Champaign-Urbana,IL)Mark A. Shannon http://watercampws.uiuc.edu6

Why not use more air cooling? Volume of air involved is huge. Heat capacity per molecule is (7/2)k B Heat capacity per unit volume is(7/2)(P/T)≈1kJ/m 3 -K at ambient conditions With ∆T=10 K, requires nearly 10 5 morevolume of air than evaporating water. Enormous heat exchangers, fans, high capitalcosts.Mark A. Shannon http://watercampws.uiuc.edu7

Why not use more air cooling? Efficiency suffers: 0.1% per degree C. Air temperature is not always as cold asavailable water. Worse in hot/climates wheremore air-conditioning is needed. Additional thermal resistance because heattransfer is not as effective: basic property ofeffusivity (square root of the product ofthermal conductivity and heat capacity perunit volume) is smaller by a factor of 100. Trade-off: do you want to reduce use ofH 2 O or CO 2 emission?Mark A. Shannon http://watercampws.uiuc.edu8

Why not use more air cooling? Combined cycle (natural gas powered)saves water and reduces CO 2 relative tocoal.cogenertion.netMark A. Shannon http://watercampws.uiuc.edu9

Thermodynamics of water purificationPureWaterBest we can do isW=∆μNPumpElectrical energy WSaltWaterChemical work = ∆μN,∆μ = change in chemical potentialN = number of water molecules10Mark A. Shannon http://watercampws.uiuc.edu

Thermodynamics of water purification Lowest possible energy is for a reversibleprocess.Semi-permeable membranePurewaterSaltwaterPiston applies pressure = osmotic pressure11Mark A. Shannon http://watercampws.uiuc.edu

Thermodynamics of water purification For ideal solution of n ions per unit volume nk TB Differential work done in moving volumedVdW ( dV ) Integrate from initial to final osmotic pressure(assume 50% recovery)(1/2) V0VW k T n0dVB VV012Mark A. Shannon http://watercampws.uiuc.edu

Thermodynamics of water purification For 50% recovery, ideal solution, 3.5% bymass NaCl (V 0 = 2 m 3 to recover 1 m 3 purewater)WWnV k T ln(2)0 B3.8 MJ 1 kWh No process can do better than this at 50%recovery. (For 0% recovery, no ln(2) term.) State-of-the-art RO is only a factor of 2 higherthan this limit.13Mark A. Shannon http://watercampws.uiuc.edu

Is 1 kWh = 3.6 MJ a lot of energy? Electrical power cost is about \$0.10 Heat 10 L of water to boiling point Light a CF light bulb for a few days Run a refrigerator for ½ day Do 3600 google searches One google search consumes as muchenergy as state-of-the-art RO uses to purify asmall cup of water.14Mark A. Shannon http://watercampws.uiuc.edu

Thermodynamic limits for a distillationprocess are the same For a reversible process, we have to makethe vapor pressures equal (almost) but thatmeans the temperature of the salt water ishigherSaltWaterPureWaterT h T c TcApproximate heat input: 1∆H=enthalpy of vaporizationper unit volumedQ H dV Th15Mark A. Shannon http://watercampws.uiuc.edu

Thermodynamic limits for distillation Real-world distillation processes (multi-stage)work far from the thermodynamic limit. T cdW H 1dV Th Even for ∆T=10 K, this is 15 times worse thanthe thermodynamic limit.16Mark A. Shannon http://watercampws.uiuc.edu

But maybe sometimes heat is free, i.e.,“waste heat”? Low-grade (low temperature) heat sourcethat is not feasible to use in electrical powergeneration might be used to purify water. But keep in mind that high efficiency powergeneration uses low temperature heat sinks.Not much of the heat is “wasted”17Mark A. Shannon http://watercampws.uiuc.edu