The Second Law of Thermodynamics. (Second Law of Thermodynamics)

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he Second aw of hermodynamics For the free exansion, we have >. It is an irreversible rocess in a closed system. For the reversible isothermal rocess, for the gas > for exansion and < for comression.

1 he Second aw of hermodynamics For the free exansion, we have >. It is an irreversible rocess in a closed system. For the reversible isothermal rocess, for the gas > for exansion and < for comression. owever, the gas itself is not a closed system. It is only a closed system if we include both the gas and the reservoir. during exansion: So: total gas and S res (Second aw of hermodynamics) If a rocess occurs in a closed system, the entroy of the system increases for irreversible rocesses and remains constant for reversible rocesses. It never decreases. Calculate for the reversible isothermal rocess. since constant: 1 f Sf Si d i In isothermal exansion, >, therefore > that means > for free exansion For a rocess that is small comared to : S f S i avg

2 Entroy in real world: Engines et s exlore how entroy affects energy flow in devices -- (i.e., engines). heat engine is a device that: absorbs heat from a hot reservoir (1) does work on something (2) then exels heat to a cold reservoir (3) to return to the engine s starting conditions. his constitutes one cycle (and the rocess reeats itself). In an ideal engine, all rocesses are reversible Entroy in real world: Engines heat engine is a device that extracts heat from its environment and does useful work. Consider a - diagram with an ideal gas as the working substance for our engine. he cycle starts at and must return to at the end of the cycle. he area enclosed by the cycle is the net work the engine does.

3 Engines So..., hat cycle will roduce the maximum work () for the minimum cost ( ) and the minimum waste ( )? Note that and are fixed by external conditions such as the tye of fuel used, surrounding environment, etc. est Problem Stirling Cycle Carnot Cycle Engines So..., hat cycle will roduce the maximum work () for the minimum cost ( ) and the minimum waste ( )? Note that and are fixed by external conditions such as the tye of fuel used, surrounding environment, etc. (Internal combustion engine) Otto Cycle Diesel Cycle

4 nswer: he Carnot Cycle Carnot Engine: he most efficient heat engine. he Carnot cycle consists of four rocesses: a-b: isothermal exansion, working substance gets heat from the high-temerature reservoir b-c: adiabatic exansion. c-d: isothermal comression, working substance gives heat to the low temerature reservoir d-a: adiabatic comression. he work done by the gas: a-b-c: ositive work c-d-a: negative work Net work done in one cycle: area enclosed by cycle abcda. For a comlete cycle, E int (since E int is a state function) that is:, since herefore: For a comlete cycle, ( since S is a state function.)

1 energy we ay for out get energy we ε 1 ε > > ) (1 ε < For real engine: since the rocess is irreversible, > For Carnot engine: since the rocess is reversible, for the

5 1 energy we ay for out get energy we ε 1 ε > > ) (1 ε < For real engine: since the rocess is irreversible, > For Carnot engine: since the rocess is reversible, for the closed system (high- reservoir work substance low- reservoir), ( 2nd law of thermodynamics) hermal efficiency of an engine: emerature - Entroy Grah for the Carnot Engine

Is there a erfect engine, which converts all to work so that and ε 1, ossible? he entroy change for the closed system: ε 1 < his violates the 2nd law of thermodynamics!

6 Is there a erfect engine, which converts all to work so that and ε 1, ossible? he entroy change for the closed system: ε 1 < his violates the 2nd law of thermodynamics! lso, for ε 1, we need or to be infinity, either of which is imossible. Conclusion: Peretual motion machines are imossible!! Daily uiz, December 3, 24 n inventor claims to have invented an engine that oerates between constant temerature reservoirs of 6K and 3K. he data er cycle of the engines are listed. hich (if any) are ossible engines? (1) 2J, 1J, 5J (2) 4J, 1J, 3J (3) 4J, 2J, 2J (4) ll three engines are not ossible.

7 Daily uiz, December 3, 24 1st aw of hermodynamics: Engine 1 violates this law, but 2 & 3 obey it. 2nd aw of hermodynamics: ε max / 1 / 1 / 1 3/6 1/2 n inventor claims to have invented an engine that oerates between constant temerature reservoirs of 6K and 3K. he data er cycle of the engines are listed. hich (if any) are ossible engines? (1) 2J, 1J, 5J (2) 4J, 1J, 3J (3) 4J, 2J, 2J (4) ll three engines are not ossible. ε 2 / 3/4 ε 3 / 2/4 1/2

Lecture 13. Heat Engines. Thermodynamic processes and entropy Thermodynamic cycles Extracting work from heat

Lecture 13. Heat Engines. Thermodynamic processes and entropy Thermodynamic cycles Extracting work from heat Lecture 3 Heat Engines hermodynamic rocesses and entroy hermodynamic cycles Extracting work from heat - How do we define engine efficiency? - Carnot cycle: the best ossible efficiency Reading for this