Dept. of Energy System Engineering 제 6 장. 열역학제 법칙 (he Second aw of ) Chon, Mun Soo Dept. of Energy System Engineering Korea National University of ransportation el. 04-84-59 Email: mschon@ut.ac.kr
열역학제 법칙 열역학제 법칙 (the second law of thermodynamics) 열역학제 법칙 : 에너지는보존되는물리량으로어떠한과정도열역학제 법칙을위반하지않으나, 열역학제 법칙을만족하더라도실제과정이일어난다고말할수없음 열역학제 법칙 : 모든과정은정해진방향으로만일어나며, 따라서과정이완전하게일어날수있는지를확인하기위해열역학제 법칙이라는일반적인법칙의적용이필요함 모든과정은열역학제 법칙과제 법칙을만족하여야진행될수있음. 열역학제 법칙은과정의방향성을결정하는것이외에에너지는양 (quantity) 뿐만아니라질 (quality) 도가지고있음을의미함 A cup of hot coffee does not get hotter in a cooler room ransferring heat to a wire will not generate electricity ransferring heat to a paddle wheel will not cause it to rotate
열에너지저장조 열에너지저장조 (thermal energy reservoirs) 열을공급하거나흡수하여도온도변화가없는매우큰열용량 (mass specific heat) 의가상물체 일반적으로열에너지의저장능력이큰대기, 호수, 강바다등을열에너지저장조로모델링할수있으며, 일정한온도에서열을흡수하거나방출하는 상계 (two-phase system), 등온을유지하면서많은열에너지를공급하는산업용노 (industrial furnace) 등을열에너지저장조로간주할수있음 열의형태로에너지를공급하는열저장조를열원 (heat source), 열의형태로에너지를흡수하는열저장조를열침 (heat sink) 이라함 Bodies with relatively large thermal masses can be modeled as thermal energy reservoirs A source supplies energy in the form of heat, and a sink absorbs it
열기관 열기관 (heat engines) 열 (heat) 을일 (work) 로변환시키는장치. ( 일은열로직접적인변환이가능함 ). 높은열원 ( 태양에너지, 연소, 핵반응등 ) 으로부터열에너지를공급받음. 받은열의일부를일 ( 보통축일 ) 로변환함. 저온의열침 ( 대기, 강등 ) 에남은폐기열을방출함 4. 사이클로작동됨 작동유체 (working fluid) : 열기관이나기타사이클로작동하는장치에서열을흡수하고방출하는유체 ero s steam engine Steam power plant 4
열기관 증기원동소 (steam power plant) in : 고온의열원 (furnace) 으로부터보일러내부의증기에공급된열량 out : 응축기내부의증기로부터저온의열침 ( 대기, 강등 ) 으로방출된열량 W out : 팽창된증기가터빈에전달한일량 W in : 펌프를통해물 ( 응축된증기 ) 을보일러까지공급하는데필요한일량 W net W out W in W turbine W pump W net in out 5
열기관 열효율 (thermal efficiency) 열기관의성능을나타내는척도로공급된열에너지가일에너지로변환된비율 열기관으로부터방출된열에너지 ( out ) 은영이아니므로열기관의정미출력일은언제나공급된열에너지보다적으며, 열효율은항상 보다작음 열기관, 냉동기, 열펌프와같은사이클장치는온도가 인고온의매체 ( 열저장조 ) 와온도가 인저온의매체 ( 열저장조 ) 사이에서작동함 hermal efficiency Net work output otal heat input th W net in out in th W net 6
열기관 Can we save out? Can we not just take the condenser out of the plant and save all that waste energy? he answer is, unfortunately, a firm No for the simple reason that without a heat rejection process in a condenser, the cycle cannot be completed. Every heat engine must waste some energy by transferring it to a low-temperature reservoir in order to complete the cycle, even under idealized conditions. W net = 5 kj du = 85 kj X Reservoir at 00 C in = 00 kj out = 85 kj Reservoir at 0 C out = 85 kj Reservoir at 00 C 7
열기관 p.89, Ex. 6- : 자동차의연료소비율 출력이 65 hp 인자동차엔진의열효율이 4 % 이다. 연료의발열량 ( 연료 kg 이연소할때발생하는열에너지 ) 이 44,000 kj/kg 일때, 이자동차의연료소비율을구하여라. Assumption : he power output of the vehicle is constant Solve :. m fuel W net th 65hp 0. 7457 kw 0. 4 hp 0kW Combustion chamber m V 0kJ / s, 600 s m fuel 0. 00459kg / s 6. 5kg / h 44, 000kJ / kg h V Vehicle engine. W lnet = 65 hp Atmosphere 8
냉동기와열펌프 냉동기 (refrigerator) 낮은온도의물체에서높은온도의물체로열을전달하는장치 냉동기도열기관과같은사이클장치이며, 냉동사이클에사용되는작동유체를냉매 (refrigerant) 라함 증기압축식냉동사이클 (vapor-compression refrigeration cycle) 이가장많이사용됨 : 증발기내부저온저압의냉매가증발하면서냉각물체에서흡수한열량 W in : 냉매를증발압력에서응축압력으로압축하는데소요되는일량 : 응축기내부고온고압의냉매가응축하면서주위매체로방출한열량 팽창밸브 (expansion valve) : 교축과정을통해냉매의압력과온도를저하시킴 9
냉동기와열펌프 냉동기의성적계수 (coefficient of performance) 냉동기의효율또는성능은성적계수 (coefficient of performance, COP R ) 로나타냄 냉동기는냉각공간으로부터열 ( ) 을제거하기위한장치임 COP R Desired output Required input W net W net COP R / U U a PdV U U b PdV P W cycle b PdV a PdV W cycle V 0
냉동기와열펌프 열펌프 (heat pump) 낮은온도의물체에서높은온도의물체로열을전달하는또다른장치 냉동기와동일한사이클로작동하나높은온도의물체에열 ( ) 을방출하는것이열펌프의목적임 COP P Desired output Required input W net W net COP P / COP P W net Wnet W net COP R
냉동기와열펌프 p.9, Ex. 6- : 냉장고의열방출 한냉장고의냉장실은 60 kj/min 으로열이제거되어 4 C 로유지된다. 냉장고에필요한전력이 kw 일때 (a) 냉장 고의성적계수, (b) 냉장고가설치된방으로방출하는열량을계산하여라. Assumption : Operating conditions are steady state Solve : COP R W net, in 60kJ / min kw min 60 s Kitchen. 60 W net, in kw 60kJ / min 480kJ / min min R. W net, in = kw. = 60 kj/min
열역학제 법칙 he Kelvin Planck Statement It is impossible for any system to operate in a thermodynamic cycle and deliver a net amount of work to its surroundings receiving energy by heat transfer from a single thermal reservoir. 사이클로작동하는어떠한장치도하나의열저장조로부터만열을받아정미일을생산해내는것은불가능하다. ord Kelvin, 84-907 eat loss is inevitable. hermal efficiency of any cycle cannot be 00%. A heat engine that violates the Kelvin Planck statement of the second law. Max Karl Earnest udwig Planck 858-947
열역학제 법칙 he Clausius Statement It is impossible for any system to operate in such a way that the sole result would be an energy transfer from a cooler to a hotter body. 사이클로작동하면서낮은온도의물체로부터그보다높은온도의물체로열을전달하는것이외에주위에아무런영향을일으키지않는장치를만드는것은불가능하다. It requires other effect (e.g., work) to transfer heat from a cooler to a hotter body. Rudolph J. E. Clausius 8-888 A refrigerator that violates the Clausius statement of the second law. 4
열역학제 법칙 두서술의동등성 (equivalence of the Clausius and Kelvin-Planck statements) Kelvin-Planck 서술과 Clausius 서술은열역학제 법칙에대해서로동등한 (equivalent) 표현임 For heat engine that violates the Kelvin Planck statement. W net ( 0) For refrigerator out, refrigerat or W net For combined cycle that violates the Clausius statement. Any device that violates the Kelvin Planck statement also violates the Clausius statement, and vice versa. 5
영구운동기계 영구운동기계 (perpetual-motion machines) 열역학제 법칙또는열역학제 법칙을위반하는장치 열역학제 법칙과열역학제 법칙을모두만족하지않으면어떠한과정도일어나지않음 제 종영구운동기계 (perpetual-motion machine of the first kind, PMM) : 열역학제 법칙을위반하는장치 제 종영구운동기계 (perpetual-motion machine of the second kind, PMM) : 열역학제 법칙을위반하는장치.. in = W net, out.. in = W net, out PMM (by energy creating) PMM ( th = 00 %) 6
가역과정과비가역과정 가역과정과비가역과정 가역과정 (reversible processes) : 주위에어떠한흔적도남기지않고역으로진행될수있는이론적이상 (ideal) 과정. 가역과정에가까운시스템일수록열효율 (W out ) 또는성적계수 (W in ) 가커지며해석이용이함 비가역과정 (irreversible processes) : 가역과정이아닌과정으로실제자연현상에서는일어나는과정으로비가역과정은주위가계에대해일을해야하므로초기상태로회복할수없음 W o = W R W o W R Insulated Gas P 0, 0 Initial state Gas P, Original process Gas P 0, 0 Reverse process Friction loss Gas P, Original process loss Gas P 0, 0 Reverse process Reversible : W net = 0, net = 0 Irreversible : W net 0, net 0 7
가역과정과비가역과정 비가역성 (irreversibility) 마찰 (friction) : 운동하는물체와관련된가장흔한비가역성의형태로접촉면에서운동방향과반대방향으로마찰력이작용하고이를이겨내기위한마찰일이필요하며, 마찰과정중공급된일에너지는열에너지로변환되어마찰면의온도가증가함마찰은접촉되어있는고체사이에만존재하는것이아니며, 유체와고체, 속도분포를갖는유체층에도존재함 (ex. 달리는자동차의표면과주위유체 마찰손실로주위유체의내부에너지가증가 ) 가스의자유팽창 (unrestrained expansion of a gas) 열전달 (heat transfer) 8
가역과정과비가역과정 내적가역과정과외적가역과정 내적가역과정 (internally reversible processes) : 과정동안계의경계내에서비가역성이일어나지않는과정. 가역과정동안계내부의물리량은평형상태를유지하며, 역과정도동일한동일한평형상태와동일한경로를유지함 ( 준평형과정, quasi-equilibrium process) 외적가역과정 (externally reversible processes) : 과정동안계경계의외부에서비가역성이일어나지않는과정. 계의외부경계면의온도와외부열저장조의온도가동일한경우 완전가역과정 (totally reversible processes) : 계내부와그주위사이에비가역성이없는과정. 완전가역과정에는열전달, 비준평형과정, 마찰, 소산효과 (dissipation effect) 등이없음 Reversible process internally reversible 9 otally reversible
카르노사이클 카르노사이클 (Carnot cycle) 가역과정으로이루어진사이클로등온팽창 (isothermal expansion), 단열팽창 (adiabatic expansion), 등온압축 (isothermal compression), 단열압축 (adiabatic compression) 과정으로구성되며, 84년프랑스엔지니어 Sadi Carnot가제안함 Reversible isothermal expansion Reversible isothermal compression Reversible adiabatic expansion Reversible adibatic compression 0
카르노사이클 카르노열기관 (Carnot heat engine) 카르노사이클로작동하는최대효율을갖는이론적인열기관 Carnot R ln( V R ln( V / V4 ) / V ), 4 : adiabatic process V V k 4 V V 4 k Carnot V V V V 4 th th th Carnot Carnot Carnot : irreversible heat engine : reversible heat engine : impossible heat engine
카르노사이클 역카르노사이클 (reversed Carnot cycle) 역으로진행되는카르노사이클로냉동기또는열펌프의열역학적이상사이클 카르노냉동기와열펌프 (Carnot refrigerator and heat pump) : 역카르노사이클로작동하는최대성능을갖는이론적인냉동기와열펌프 : Adiabatic expansion : Isothermal expansion 4 : Adiabatic compression 4 : Isothermal compression - For refrigerator : - For heat pump : COP COP R P W net, in W net, in COP R COP R COP R COP COP COP R, Carnot R, Carnot R, Carnot : irreversible refrigerator : reversible refrigerator : impossible refrigerator
카르노사이클 p.08, Ex. 6-5 : 카르노열기관해석 카르노열기관이 65 C 인고온의열원으로부터사이클당 500 kj 의열을받고 0 C 인저온의열침에열을방출할 때 (a) 카르노열기관의열효율, (b) 사이클당저온열침에방출하는열량을구하여라. Solve : ( 0 7) th, Carnot 0. 67 ( 67. %) ( 65 7) igh-temp. reservoir at = 65 C. = 500 kj/min ( 0 7) 500kJ 6. 8kJ ( 65 7) Carnot heat engine. W net, out. ow-temp. reservoir at = 0 C
카르노사이클 에너지의품질 (quality of energy) 열원의온도가높을수록열기관의이론열효율은증가함 따라서, 에너지는양뿐만아니라품질 (quality) 이있으며, 온도가높을수록열에너지의품질이높음 Carnot 4
카르노사이클 p., Ex. 6-6 : 포화액체-증기혼합영역에서작동하는카르노냉동사이클카르노냉동사이클이 0.8 kg의 R-4a를작동유체로액체-증기혼합영역에서밀폐계로작동하며, 사이클의최고온도와최저온도는각각 0 C와 -8 C 이다. 열방출과정끝에서냉매는포화액체상태이며, 사이클중 5 kj의정미일이공급된다. 열흡수과정중증발한냉매의질량비율을구하고열방출과정을마칠때의냉매압력을구하여라. Solve : COP 65 9 65 R, Carnot. 9 464 (C ) COP W 9. 464 5 kj 4kJ eva R, Carnot fg 8C net, in m h @ ( able A) h @ 04. 5kJ kg fg 8C / 0 4 mass m 4kJ 0 694kg 04. 5kJ / kg eva. hfg @ 8C m fraction m eva total 0. 694kg 0. 868 ( 86. 8%) 0. 8kg -8 v (m /kg) P4 P Psat, @ 0C 57. 07 kpa ( able A) 5
카르노사이클 p., Ex. 6-7 : 카르노열펌프를이용한주택난방 겨울철에집을난방하기위하여열펌프를사용하고있다. 외기온도가 -5 C 인경우, 집은 5000 kj/h 의열손실이 있으며, 집내부온도는항상 C 로유지할때이열펌프를구동하는데필요한최소일을구하여라. Solve : h loss, house 5, 000kJ / h 7. 5kW, 600 s W COP 94 94 68 P, Carnot. COP 7. 5kW. net, in. P, Carnot kw ouse = C P.. W net, in 전열기를사용하는경우 : 7.5 kw 의전력소비가필요함 그러나, 열펌프는단지. kw 를소비하는냉동사이클로 4.8 kw (7.5 kw. kw) 의 외부에너지를내부로옮길수있음. Cold outside air = -5 C 6
카르노원리 카르노원리 (Carnot principles) 두개의열저장조사이에서작동하는비가역열기관의효율은동일한두열저장조사이에서작동하는가역열기관의효율보다항상낮다. 동일한두개의열저장조사이에서작동하는모든가역열기관의효율은같다. igh-temperature reservoir at If (W irrev. W rev. > 0 ) : Violation of Kelvin-Planck statement Irrev. E W irrev Rev. E (or R) W rev Combined E + R W irrev - W rev If (W irrev. W rev. = 0 ) : Irrev. E becomes a Rev. E. If (W irrev. W rev. < 0 ), irrev. <, rev. (assumed) ow-temperature reservoir at, rev. -, irrev. ow-temperature reservoir at W rev. Wrev. Crrnot actual rev. rev. 7
카르노원리 카르노원리 (Carnot principles) 두개의열저장조사이에서작동하는비가역열기관의효율은동일한두열저장조사이에서작동하는가역열기관의효율보다항상낮다. 동일한두개의열저장조사이에서작동하는모든가역열기관의효율은같다. igh-temperature reservoir at If (W rev. W rev. > 0 ) : Violation of Kelvin-Planck statement If (W rev. W rev. < 0 ) Rev. E W rev Rev. E (or R) W rev Combined E + R W rev - W rev : Violation of Kelvin-Planck statement If (W irrev. W rev. = 0 ), rev <, rev (assumed) ow-temperature reservoir at, rev -, rev ow-temperature reservoir at W rev. Wrev. rev. rev. 8
9 열역학적온도눈금 (thermodynamic temperature scale) 온도척도 (temperature scale) : 온도계물질 ( 예, 수은 ) 의상태량에의해정의 열역학적온도눈금 : 온도계물질의상태량과무관한온도눈금으로 Kelvin 눈금 (Kelvin scale) 이라하며, 이눈금에의한온도를절대온도 (absolute temperature) 라함열역학적온도눈금 - From Carnot principle : rev th f f,,,., f f f,,,,, f f f,,,, ) ( ) ( ) ( ) (, f
열역학적온도눈금 Kelvin scale 의정의 열역학적온도눈금은절대온도의비로주어짐 954 년국제도량회의에서물의 중점 (P, triple point) 을 7.5 K 로결정함 ( ) ( ) f, rev. P, P P P 7. 6 ( K) P 0