Thermodynamics [ENGR 251] [Lyes KADEM 2007]

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1 hermodynamics [ENGR 25] [yes KADEM 2007] II. Carnot Cycle he Carnot cycle was first proposed 824, by Sadi Carnot. he terest the cycle is largely theoretical, as no practical Carnot cycle enge has yet been built. Nevertheless, it can be shown to be the most efficient cycle possible, so that considerable attention has been given at discoverg ways of makg the more practical cycles look, as much as possible, like the Carnot. Energy Energy Insulation Insulation Const Const Process -2 Process 2-3 Process 3-4 Process 4- (Process -2) A constant temperature heat addition. (Process 2-3) An adiabatic expansion (Process 3-4) A constant temperature heat rejection. (Process 4-) An adiabatic compression P v Second aw of hermodynamics 7

2 hermodynamics [ENGR 25] [yes KADEM 2007] II.. Carnot Cycle Efficiency ike other heat enges, the Carnot cycle efficiency can be attaed from the relationship: η W net out out W W out II... Carnot cycle prciples. he efficiency of an irreversible heat enge is always less than the efficiency of a reversible one operatg between the same two reservoirs. 2. he efficiencies of all reversible heat enges operatg between the same two reservoirs are the same. igh emperature Energy Reservoir, A A Reversible eat Enge A W A W C B B Reversible eat Enge C W C Reversible eat Enge B W B C C ow emperature Energy Reservoir, C Second aw of hermodynamics 72

3 hermodynamics [ENGR 25] [yes KADEM 2007] If we consider the Carnot cycle above, sce a control volume could be drawn about enges A & B together, they may be considered as a sgle reversible enge. he efficiency of Enge A&B must be the same as that of Enge C sce both are reversible. Also W A + W B W C Sce energy reservoirs are characterized by their temperatures, the thermal efficiency of reversible heat enges is a function of the reservoir temperatures only. hat is, f (, ) Applyg this idea to the three enges separately, A / C f( A, C ), A / B B f(a, BB), B / B C f( BB, C ) For the efficiency of A&B to be equal to that of C f( A, C ) f( A, B ) B f(bb, C ) A careful examation of this equation reveals that the left hand side is a function of A and C, and therefore the right hand side must also be a function of A and C only and not, B. B his condition will be satisfied only if the function has the followg form: Φ( A )/ Φ( C ) [Φ( A )/ Φ( B )] [Φ( B BB)/ Φ( C )] From this relationship Kelv proposed a temperature scale which Φ(), such that: II..2. Applications of the Carnot Cycle a. Carnot Cycle Enge η igh emperature region Carnot Cycle & & W & From the first law of thermodynamics: + W& ow emperature region Second aw of hermodynamics 73

4 hermodynamics [ENGR 25] [yes KADEM 2007] From the defition of efficiency, we fd for the Carnot enge: Usg the thermodynamic temperature scale: η b. Carnot Cycle Refrigerator η igh emperature region Carnot Cycle & & W & From the first law of thermodynamics: + W& ow emperature region From the defition of Coefficient of Performance (COP), we fd for the Carnot refrigeration cycle: COP W& Usg the thermodynamic temperature scale: COP Second aw of hermodynamics 74

5 hermodynamics [ENGR 25] [yes KADEM 2007] C. Carnot Cycle eat Pump igh emperature region Carnot Cycle & & W & From the first law of thermodynamics: + W& ow emperature region From the defition of Coefficient of Performance (COP), we fd for the Carnot refrigeration cycle: COP W& Usg the thermodynamic temperature scale: COP II.2. Applications Example An ventor claims to have developed a power cycle capable of deliverg a net work output of 40 kj for an energy put by heat transfer of 000 kj. he system undergog the cycle receives the heat transfer from hot gases at a temperature of 500 K and discharges energy by heat transfer to the atmosphere at 300 K. Evaluate this claim. Example 2 When a fridge stands, a room at 20 C, the motor has to extract 500 W of heat from the cabet at 4 C to compensate for less than perfect sulation. ow much power must be supplied to the motor if its efficiency is 80% of the maximum efficiency? Second aw of hermodynamics 75

6 hermodynamics [ENGR 25] [yes KADEM 2007] Example 3 An ideal or Carnot heat pump is used to heat a house to 294 K, how much work must be done by the pump to deliver 3350 J of heat to the house when the outdoor temperature is 273 K and 252 K. Example 4 A Carnot power cycle usg air as a workg fluid has a thermal efficiency of 40%. At the begng of isothermal expansion, the pressure is 620 kpa, and the specific volume is 0. m 3 /kg. If the heat put for the cycle is 50 kj/kg, determe: - he highest and the lowest temperature for the cycle. - he work and heat for each process of the cycle. Assume air to be an ideal gas with constant specific heats. Second aw of hermodynamics 76

η th W = Q Gas Power Cycles: Working fluid remains in the gaseous state through the cycle.

η th W = Q Gas Power Cycles: Working fluid remains in the gaseous state through the cycle. Gas Power Cycles: Gas Power Cycles: Working fluid remains in the gaseous state through the cycle. Sometimes useful to study an idealised cycle in which internal irreversibilities and complexities are