# Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator

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1 Lecture. Real eat Engines and refrigerators (Ch. ) Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator

2 Carnot Cycle - is not very practical (too slow), but operates at the maximum efficiency allowed by the Second Law. absorbs heat isothermal expansion (in contact with ) isentropic expansion to C isothermal compression (in contact with C ) isentropic compression to (isentropic adiabatic+quasistatic) rejects heat C Efficiency of Carnot cycle for an ideal gas: (r..5) e max = C S entropy contained in gas C On the S-diagram, the work done is the area of the loop: du 0 = ds = d he heat consumed at ( ) is the area surrounded by the broken line: ( S S ) S - entropy = C contained in gas

3 Stirling heat engine Stirling engine a simple, practical heat engine using a gas as working substance. It s more practical than Carnot, though its efficiency is pretty close to the Carnot maximum efficiency. he Stirling engine contains a fixed amount of gas which is transferred back and forth between a "cold" and and a "hot" end of a long cylinder. he "displacer piston" moves the gas between the two ends and the "power piston" changes the internal volume as the gas expands and contracts. age, r..

4 Stirling heat engine he gases used inside a Stirling engine never leave the engine. here are no exhaust valves that vent high-pressure gasses, as in a gasoline or diesel engine, and there are no explosions taking place. Because of this, Stirling engines are very quiet. he Stirling cycle uses an external heat source, which could be anything from gasoline to solar energy to the heat produced by decaying plants. oday, Stirling engines are used in some very specialized applications, like in submarines or auxiliary power generators, where quiet operation is important.

5 Efficiency of Stirling Engine In the Stirling heat engine, a working substance, which may be assumed to be an ideal monatomic gas, at initial volume and temperature takesin heat at constant volume until its temperature is, and then expands isothermally until its volume is. It gives out heat at constant volume until its temperature is again and then returns to its initial state by isothermal contraction. Calculate the efficiency and compare with a Carnot engine operating between the same two temperatures. = e W d = d = nr = nr ln > = C = nr < 0 W d = d = nr = nr ln < - = C ( ) = nr( ) > 0 W 0 = ( ) ( ) 0 = = W - 0 ( ) + ln( / ) = = = + > + ( ) ln( / ) ln( / ) emax = W

6 Internal Combustion Engines (Otto cycle) - engines where the fuel is burned inside the engine cylinder as opposed to that where the fuel is burned outside the cylinder (e.g., the Stirling engine). More economical than ideal-gas engines because a small engine can generate a considerable power. atm ignition 0 intake/exhaust Otto cycle. Working substance a mixture of air and vaporized gasoline. No hot reservoir thermal energy is produced by burning fuel. exhaust 0 intake (fuel+air is pulled into the cylinder by the retreating piston) isentropic compression isochoric heating isentropic expansion 0 exhaust

7 Otto cycle (cont.) he efficiency: (r..8) e γ = = - maximum cylinder volume - minimum cylinder volume - the compression ratio γ = +/f - the adiabatic exponent atm ignition 0 For typical numbers / ~8, γ ~ 7/5 e = 0.56, (in reality, e = 0. 0.) (even an ideal efficiency is smaller than the second law limit - / ) S intake/exhaust exhaust S S = 0 = 0 C

8 e δ = δ Diesel engine c h (r..0) : adiabatic, = γ γ f + : isobaric, δ = nr ( ) h : adiabatic, = γ γ f : isochoric, =, δ = nr ( ) c e γ = γ ( ) γ

9 Steam engine (Rankine cycle) ump hot reservoir, Boiler heat heat Condenser C cold reservoir, C urbine work ump water Boiler Water+steam condense urbine NO an ideal gas! steam ( δ ) ( ) ( ) = U +, = Δ : isothermal adiabatic : isobaric, δ = : adiabatic : isobaric, δ = h h processes at = const, δ=d Sadi Carnot

10 Steam engine (Rankine cycle) ump hot reservoir, Boiler heat heat Condenser C cold reservoir, C urbine work ump ere water Boiler Water+steam condense ( ) urbine steam e = ( ) S = S S = x S + x S processes at = const, δ=d Sadi Carnot gas gas liquid = x + x gas liquid (.), water is almost incompressible.

11 Kitchen Refrigerator A liquid with suitable characteristics (e.g., Freon) circulates through the system. he compressor pushes the liquid through the condenser coil at a high pressure (~ 0 atm). he liquid sprays through a throttling valve into the evaporation coil which is maintained by the compressor at a low pressure (~ atm). cold reservoir (fridge interior) =5 0 C throttling valve liquid condenser liquid+gas evaporator compressor gas processes at = const, δ=d C CO = = = C ( ) hot reservoir (fridge exterior) =5 0 C he enthalpies i can be found in tables. (, ) ( ) =, = x + x liquid liquid gas S = S

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