Real processes have a natural direction of change. Second and hird Laws of hermodynamics Chapter 5 Spontaneity of Changes For example heat flows from hotter bodies to colder bodies, and gases mix rather than separate. he state function that predicts the direction of spontaneous change of termed entropy, S. For an isolated system, S increases for a spontaneous change. For a system that interacts with its environment; the sum of the entropy of the system and that of the surroundings increases. he first law: in any process, the total energy of the universe remains constant. If several possible energy conserving processes can occur, first law cannot predict which one is more likely to occur. Some transformations/changes do not violate the first law of thermodynamics, however such changes (transformations) may not occur naturally. Natural transformations, termed as spontaneous processes are processes that are extremely likely to happen. hey would follow the first law. he concept of entropy has it s origin in studies to maximize the work output of heat engines. An idealized version of a heat engine has a working substance heat source at hot and a heat sink at cold he working substance is contained in a piston and cylinder assembly with diathermal walls. he expansion or contraction of the gas caused by changes in its temperature drives the piston in or out of the cylinder in a linear motion. he linear motion is converted to circular motion/rotary motion is employed to do work on the surroundings (heat to work!). Spontaneous processes has to satisfy the entropy reuirement as well. Spontaneity indicates nothing about the rate of occurrence of such transformations.
he P- diagram for a reversible heat engine is shown below. Carnot Cycle a d b U cycle wcycle 0 cycle c a b; rev. isothermal expansion - gas absorbs heat from the reservoir at high and does work on the surroundings. bc; gas expands adiabatically - work done on the surroundings, gas has cools to the temperature cold cd; an isothermal compression - surroundings do work on the system and heat is absorbed by the cold reservoir da; gas is compressed to its initial volume adiabatically - work is done on the system, temperature returns high its initial value. cycle ab cd U w w cycle cycle cycle cycle 0 () cycle ab cd () 0; ab cd ab cd ab cd :because cd 0 0 More heat absorbed from the hot source than lost to the surroundings. Efficiency of a reversible heat engine: w cycle in work-out energy-in
work-out energy-in Efficiency of a reversible heat engine, : w cycle in wcycle hot cold cold 1 1 ab hot hot Also, w cycle,irrev for an engine operating in an irreversible cycle is less than the w cycle,rev in a reversible cycle irrev. rev. 1 Entropy Starting from efficiency expression:. hot cold ab cd hot cold 1 1 ab hot hot cd cold 0 he uantity for the reversible cycle would be = 0. 0 S drev. drev. entropy ds S cd ab ab d rev
he sum of the uantity ( rev /) around the Carnot cycle is zero. his is true for any reversible cycle, because any reversible cycle is made up of many incremental Carnot cycles. Scycle 0 cycles S cycle 0 rev If so S is a state function!! Because S is a state function it is path independent. herefore S is the same reversible or not, so for any process/change S, easier calculation S Srev Sirrev d rev. d d ds S. Although d is not an exact differential; division of makes d an exact differential! S Calculations: ideal gases a Any two macroscopic variables,, and P defines the state of an ideal gas. 1. S for the reversible isothermal expansion or compression of an ideal gas. P b d c 2. S for an ideal gas that undergoes a reversible change in at constant. P
S (=S f S i ) for i i f f 3. S for an ideal gas that undergoes a reversible change in at constant P. P S for i i f f = (S 1 for i i f i ) + S 2 for ( f i f f ) S f f f i i f i S i S (=S f S i ) for P i i P f f S for P i i P f f = (S 1 for P i i P f i ) + S 2 for (P f i P f f ) S f P f f S Calculations: phase changes vapor liuid P i i S i P f i solid liuid
S Calculations - General Case: arbitrary changes (solids, liuids and gases) A process occurring in an isolated system is spontaneous and the system entropy increases. 1 > 2 Heat moves from left to right irreversibly. 1 2 1 2 S irrev = S rev Rigid adiabatic system 1 P 2 For the system; 0 Q P 1 2 2 1 0 and 0 S system 0 For an irreversible process in an isolated system, U=0, = -w; there is a uniue direction of spontaneous change: S > 0 for the spontaneous process; S < 0 for the opposite or nonspontaneous direction of change. non-spontaneous Ideal gas contracting to half its volume. drev i / 2 S nr ln nr ln 2 0 i S irrev = S rev < 0 S > 0 is a criterion for spontaneous change for isolated systems; i.e. if the system does not exchange energy in the form of heat or work with its surroundings. A process occurring naturally in an isolated system is by definition spontaneous and results in an entropy increase. Whereas U can neither be created nor destroyed, S for an isolated system can be created S > 0, but not destroyed S < 0. Ideal gas expanding to double its volume. drev 2 i S nr ln nr ln 2 0 S irrev = S rev > 0 Irreversible process, spontaneous i
In a uasi-static reversible process, there is no direction of spontaneous change because the system is proceeding along a path, each step of which corresponds to an euilibrium state. Ideal gas expanding to double its volume. S irrev = S rev = 0 Entropy Change of System and Surroundings For most situations both the system and the surrounding undergo changes during a process/change therefore the criterion for spontaneity should include entropy change in both the system and the surroundings. system immediate surrounding he immediate surrounding is a large thermal reservoir at a temperature, say, and in internal euilibrium with heat transfer. Heat exchanges occur between the system and the surroundings. If surrounding has a constant volume surr = U surr and if surrounding has at a constant pressure surr = H surr. immediate surrounding system S For spontaneity: S S S 0 hat is, Suniv Ssys Ssurr 0 sys surr otal surr Process that occurs in the universe is by definition spontaneous and leads to an increase of S total. herefore S univ > 0 increases time increases, defining a uniue direction of change with time. surr Absolute Entropies and the hird Law hermodynamics: Matter exist in three different states of aggregation. Common behavior of matter is such that when solid phase temperature is increased to the melts, at constant temperature transitioning into the liuid phase. Further temperature increase further at constant temperature, liuid phase transitions into a gas phase at the boiling point. At each transition point there will be an absorption of heat (latent heat) with no change of temperature. he entropy of a pure, perfectly crystalline substance (element or compound) is zero at 0K; S m (0) = 0 kj/mol-k. he entropy of a pure substance increases with temperature, S m ().
hird Law hermodynamics: he entropy of a pure substance increases with temperature, S m (). Oxygen With relevant values of C Pm heats of transitions and transition temperatures one can calculate the molar entropy S m () at any (and at P = 1atm, conventionally) 1 2 3 5 4 5 3 4 C Pm often vary with temperature. 1 2 http://ts4.mm.bing.net/th?id=jn.r%2fur1nlz1nw%2faxkgpdmdq&pid=15.1&h=172&w=160 With relevant values of C Pm heats of transitions and transition temperatures the standard molar entropy S o m() at = 298.15 and P = 1bar. Redline S m S 0 m Entropy Changes in Chemical Reactions S R he entropy change in a chemical reaction is essential in determining the euilibrium concentration in a reaction mixture. Calculating S o R is similar to that of H o R and U o R for chemical reactions and is eual to the difference in the entropies of products and reactants. Further at an arbitrary temperature, S o R,
Usually large and negative entropy change is mainly because net number of gaseous species from the reaction is negative (more gas molecules consumed in the reaction than generated). Entropy change is large and positive because net number of gaseous species is positive (more gas molecules produced in the reaction than consumed). Dependence of S on and (s,l,g) Single Phase: S f (,) du ds Pd S S ds d d 1 P ds du d Expressing U as a f(,) U U du d d U C d d substituting for du; 1 U P ds C d d d C 1 U ds d P S S ds d d S C compare terms C 1 U ds d P d S 1 U P :because ds is an exact differential S 1 U also: P left S 1 U P C ds d right S C 1 U 1 U
1 U 1 U P P S 1 U Again; P S P S P P and Using; P P 1 :cyclic rule P 1 P P P and definition: isobaric expansion coefficient 1 P 1 and definition: isothermal compressibility coefficient P S P P P P P S S ds d d S C S Dependence of S on P and (s,l,g) Single Phase: p.117