A HEAT ENGINE: PRODUCES WORK FROM HEAT BY WASTING A FRACTION OF HEAT INPUT TO A LOW TEMPERATURE RESERVOIR

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1 RANKINE POWER GENERAION CYCE A EA ENGINE: PRODUCES WORK FROM EA BY WASING A FRACION OF EA INPU O A OW EMPERAURE RESERVOIR o C CARACERISICS s (kj/kg-k. Rankine cycle is a eat engine comprised of four internally reversible processes. Significance: area enclosed by process lines euals te net eat transfer by Clausius Principle for internally reversible processes: for a cycle: d ds net ds and by te First aw for a cycle: net W net W turbine + W pump + were W turbine is positive, W pump is negative, is positive, is negative, > and W turbine > W pump.

2 . Process analysis using te First aw: Process Pases adiabatic and reversible (isentropic compression input: w pump Saturated iuid Compressed liuid isobaric expansion eat input from ig temp reservoir iuid Supereated (usually vapor adiabatic and reversible (isentropic expansion output: w turbine >> w pump Supereated vapor iuid-vapor mixture (usually isotermal and isobaric compression eat rejected to low temp reservoir iuid-vapor mixture Saturated liuid. Device st aw expression pump w pump v(p P boiler turbine w turbine condenser Note from te st aw expressions tat in te two processes tat are adiabatic and reversible (isentropic, te pump and te turbine, te only energy interaction wit surroundings is work. For te two isobaric eat excange processes, te devices are passive and tere is no work, only eat transfer.

3 . eat transfer in te ideal Rankine Cycle relies on pase cange, a very efficient way to store and release energy. e working fluid is usually water/steam. During te cycle, te properties of te working fluid cange as below wit associated eat/work excanges. (kj/kg Small increase P + v(p P P (kpa arge P >> P ( o C Negligible cange s (kj/kg-k s s P s s or w (kj/kg W pump < 0 w pump > arge (P, x fg + (P, P P arge P < P > arge s (P, s s x (s -s f /s fg > 0 > W turbine > 0 w turbine arge < P P P, arge s < s < < 0 <. Analysis: Efficiency: W net η w net [ ] Also, te mass flow rate can be calculated using tese relations: W net m η REMINDER: FOR CACUAING η, USE ABSOUE VAUES FOR EA AND WORK ERMS.

4 5. ENROPY GENERAION IN RANKINE CYCES For te cycle: Δs 0 ten s gen k k R R R R kj kg K and S gen ms gen kw K were > 0, < 0, and altoug <, R >> R assuring tat (positive > (negative and s R gen > 0, making Rankine Cycle R possible.

5 VAPOR-COMPRESSION REFRIGERAION (VCR CYCE FOR REFRIGERAORS AND EA PUMPS VCR RANSFERS EA FROM A OW EMPERAURE RESERVOIR O A IG EMPERAURE RESERVOIR WI WORK INPU. o C s (kj/kg-k CARACERISICS. VCR cycle is comprised of tree internally reversible processes. One process is actually irreversible; owever, te area enclosed by te process lines can be considered to approximately indicate te net eat transfer, and te First aw for a cycle applies: net W + were W is negative, is negative, is positive, and >. 5

6 . Process analysis using te First aw: Process Pases adiabatic and reversible (isentropic compression input: w compressor Saturated Vapor Supereated Vapor isobaric compression eat rejected to ig temp reservoir Supereated vapor saturated liuid adiabatic expansion (not isentropic: s s Saturated iuid iuid-vapor mixture isotermal and isobaric expansion eat input from low temp reservoir iuid-vapor mixture Saturated vapor Device st aw expression compressor w compressor condenser trottling valve evaporator Note from te st aw expressions tat in te one process tat is adiabatic and reversible (isentropic, te compressor, te only energy interaction wit surroundings is work. For te two isobaric eat excange processes, te devices are passive and tere is no work, only eat transfer. e adiabatic trottling valve is isentalpic, NO isentropic, as can be seen from te -s diagram. 6

7 . eat transfer in te ideal VCR Cycle relies on pase cange, a very efficient way to store and release energy. e working fluid is usually refrigerant (e.g. R-a, a compound tat boils (evaporates at very low temperatures at near-atmosperic pressures. During te cycle, te properties of te working fluid cange as below wit associated eat/work excanges. (kj/kg (P, P (kpa arge P >> P ( o (P, s s (kj/kg-k s s P s s or w (kj/kg W compressor < 0 w compressor arge decrease P x - f / P P arge P < P > s s (P, > < 0 < s x (s fg + s Bot 0 P arge increase > P P P, arge increase s > s > 0 >. Analysis: In general, te measure of VCR cycle performance is: Coefficient of Performance (COP Desired eat transfer Re uired work input 7

8 For a refrigerator (air conditioner desired eat transfer is cooling - transfer of eat to te evaporator from te low temperature reservoir. w W COP in in R For a eat pump desired eat transfer is eating - transfer of eat from te condenser to te ig temperature reservoir. w W COP in in P COP P COP R + and terefore, > Also te mass flow rate in te VCR cycle can be calculated using te relations: COP COP m P R REMINDER: FOR CACUAING COP R AND COP P, USE ABSOUE VAUES FOR EA AND WORK ERMS. 8

9 ENROPY GENERAION IN VCR CYCES For te cycle: Δs 0 ten s gen k k R R R R kj kg K and S gen ms gen kw K were < 0, > 0, and <. Also, R is close to R assuring tat (positive > (negative and s R gen > 0, making VCR cycle R possible. 9

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