Chemistry 163B Winter 2013 Clausius Inequality and ΔS ideal gas

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Georgia Hensley
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1 Chemistry 163B q rev, Clausius Inequality and calculating ΔS for ideal gas,, changes (HW#5) Challenged enmanship Notes 1 statements of the Second Law of hermodynamics 1. Macroscopic properties of an isolated system eventually assume constant values (e.g. pressure in two bulbs of gas becomes constant; two block of metal reach same ) [Andrews. p37]. It is impossible to construct a device that operates in cycles and that converts heat into work without producing some other change in the surroundings. Kelvin s Statement [Raff p 157]; Carnot Cycle 3. It is impossible to have a natural process which produces no other effect than absorption of heat from a colder body and discharge of heat to a warmer body. Clausius s Statement, refrigerator 4. In the neighborhood of any prescribed initial state there are states which cannot be reached by any adiabatic process ~ Caratheodory s statement [Andrews p. 58] 1

2 four steps to exactitude wtotal L ql I. CARNO [ ideal gas] 1 1 q q U U U II. ANY REERSIBLE ' WO EMERAURE ' MACHINE CARNO [ ideal gas] or else violation of nd Law III. 0 eqn 5.11 E & R; demonstrated for ideal gas Carnot; cycle I. cycle dq rev general proof for two temperature reversible cycle; see "a REALLY BIG RESUL" last lecture (Dickerson p. 155; Raff p ) 0 for any reversible cyclic process figure 5.4 E & R (Dickerson pp , Raff pp ) 3 entropy dq rev ds is an exact differential S is a state function 4

3 goals of lecture 1. Relate ΔS and q. Calculate ΔS for,, changes of ideal gas (HW#5) a. using REERSIBLE path (q rev ) [even for ersible processes] b. using partial derivatives of S with respect to,, (look ahead) 5 entropy and heat for actual (ersible processes): q a ersible (actual) cyclic engine ε coupled with a Carnot refrigerator of ε C will not violate nd Law if ε < ε C (viz HO#3 SL 0-6) ΔU cyclic =0 -w total =q U +q L for both rev and ql L qu U q q L BU what about q with ε < ε C?? w total qu q q L L L 1 1 qu qu qu U L U 0 U qu rev ql rev Scyclic ( ) engine 0 ( ) ( ) reversible or ersible U L S cyclic engine ( reversible or ersible ) reversible dq dq ds ds ds 6 3

4 nd Law of hermodynamics in terms of entropy S is a SAE FUNCION x S rev dq E&R eqn 5.33 Clausius inequality 7 Lecture 3: ressure-olume work reversible isothermal expansion; ext = int = int 1atm) =10 atm isothermal 1atm 9atm expansion 9atm 1atm 1mole 300K 10 atm 1 w - ext d ext = int nr = initial w - nr 1 d = - nr d= - nr ln 1 initial 1 300K R (1mol) 300K R (1mol) 1 1 atm 10 atm 10 atm w= K-mol R ln 1 atm w= J= kj (more work done ON surroundings by reversible than ersible; w =-.44 kj) 1mole 300K 1 atm q rev =-w = kj 8 4

5 Lecture 3: Isothermal expansion: ext = const ideal gas (ersible) =10 atm isothermal D=0 =1 atm 1atm expansion Δ 1atm 9atm 9atm 1mole 300K 10 atm 1 w d =nr initial ext 1mole 300K 1 atm w 1atm K R (1mol) 300K R (1mol) 1 1 atm 10 atm 1 1 w= K-mol R 1 atm 10 atm w= -44 J= -.44 kj (- sign implies net work done ON surrounding) q =-w=+.44 kj 9 EXAMLE from early lectures: isothermal expansion ( 1=10 atm, 1=300K, 1) ( =1 atm, =300K, ) initial ö same initial and ext = int ; q = 5743 J rev ext = const 1 atm; q dq q for isothermal process = 44 J q q J K 748. J K -1-1 S 19.14? J K ? J K -1 S initial some reversible path dq to calculate S must use reversible path initial rv e 10 5

6 S universe 0 soon : S S 0 S system surroundings universe disorder increases 11 calculating entropy (see summary on review handout) 1 6

7 look ahead - ΔS for changes in,; (always S ) also: S (, ): S S ds d d initial coming soon S ncv S so: nc ds d d ideal gas always (no w other, closed system) nc nr nc nr ds d d S d d rev const path rev const path S ncv ln nrln E&R eqn 5.18 initial initial q rev vary const path q rev vary const path 13 look ahead- ΔS for changes in,; (always S ) also: S (, ): S S ds d d coming soon initial S nc S so: nc ds d d ideal gas always (no w other, closed system) nc nr nc nr ds d d S d d rev const path rev const path S nc ln nrln E&R eqn 5.19 initial initial q rev vary const path q rev vary const path 14 7

8 End of Lecture 15 8

Chemistry 163B. q rev, Clausius Inequality and calculating ΔS for ideal gas P,V,T changes (HW#6) Challenged Penmanship Notes

Chemistry 163B. q rev, Clausius Inequality and calculating ΔS for ideal gas P,V,T changes (HW#6) Challenged Penmanship Notes Chemistry 163B q rev, Clausius Inequality and calculating ΔS for ideal gas P,V, changes (HW#6) Challenged Penmanship Notes 1 statements of the Second Law of hermodynamics 1. Macroscopic properties of an