1、SecondLaw of Thermodynamics (Chapter18) 热 热 热 力 力 力 学 学 学 第 第 第 二 二 二 定 定 定 律 律 律contents 1 SecondLaw ofThermodynamics 2 Reversible andIrreversibleProcesses 3 Entropy andThePrinciple ofMaximumEntropy 4 MicroscopicInterpretation ofEntropyS 1 Second Law of Thermodynamics 1.1Kelvinstatement Kelvin stat
2、ement for second law of thermodynamics No device is possible whose sole eect is to transform a given amount of heat completely into work. It must be pointed out It is possible that heat transforms into work completely. Isothermal expansion is an example. It is impossible that heat transforms into wo
3、rk com- pletely without other eects. Another way of Kelvin statement: No heat engine is possible whose eciency is equal to 100%.S 1 Second Law of Thermodynamics 1.2Clausiusstatement Clausius statement for second law of thermodynamics Heat ows naturally from a hot object to a cold object; Heat will n
4、ot ow spontaneously from a cold object to a hot one. It must be pointed out It is possible that heat ows from a cold object to a hot one. Refrigerators are the examples. It is impossible that heat ows spontaneously from a cold object to a hot one.S 1 Second Law of Thermodynamics 1.3Equivalenceofthet
5、wostatements 1， If Kelvin statement holds, Clausius statement must hold Q Q W Q+ W W W Suppose Clausius statement were not true, the above gure shows that: it is possible the sole eect is to transform a given amount of heat completely into work, i.e., the Kelvin statement is incorrect.S 1 Second Law
6、 of Thermodynamics 2, If Clausius statement holds, Kelvin statement must hold W Q Q W Q+ W Q Q Suppose Kelvin statement were not true, the above gure shows that: heat can ow spontaneously from a cold place to a hot one, i.e., the Clausius statement is incorrect.S 1 Second Law of Thermodynamics Concl
7、usion | Direction of thermodynamic process The second law of thermodynamics states that there are directions in which a truly thermodynamic process proceeds spontaneously. Truly processes will proceed spontaneously in one direction but not the other.S 2 Reversible and Irreversible Processes 2.1Rever
8、sibleandirreversibleprocesses Denition A reversible process is one that all the changes of both the system and its environments can be canceled out by a pro- cess simultaneously. If not, the process is called irreversible process. The second law of thermodynamics states that The heat ow from hot to
9、cold are irreversible processes The conversion of work to heat are irreversible pro- cesses Conclusion All the realistic thermodynamic processes are irreversible processes.S 2 Reversible and Irreversible Processes 2.2Reason Reason The reason why truly process are irreversible processes comes from no
10、n-equilibrium. If a process which can be considered as a series of equilibrium states, it must be re- versible process! So Quasistatic processes are reversible processes Any curve in pV diagram is reversible process Reversible processes can be approached arbitrarily closely by carrying out truly pro
11、cesses innitely slowly.S 3 Entropy and The Principle of Maximum Entropy 3.1Carnotstheorem Carnots theorem All reversible engines operating between the same two constant temperatures T 1 and T 2 have the same e- ciency. Any irreversible engine operating between the same two xed temperatures will have
12、 an eciency less than this. 3.2Entropy Utilizing Carnots theorem, we get dQ T = 0 holdsforallreversiblecyclesS 3 Entropy and The Principle of Maximum Entropy 1 | Q out | | Q in | = 1 T 2 T 1 | Q in | T 1 | Q out | T 2 = 0 | Q in | T 1 + | Q out | T 2 = 0 Q 1 T 1 + Q 2 T 2 = 0 T 1 and T 2 areconstant
13、s C B dQ T + A D dQ dT = 0 AB and CD are adiabatic processes B A dQ T + C B dQ T + D C dQ T + A D dQ dT = dQ T = 0S 3 Entropy and The Principle of Maximum Entropy So, integration b a dQ dT alonganyreversiblepath depends only on the starting and ending states a, b, not on the details of how the proce
14、ss takes place. Denition We dene entropy S as S b S a = b a dQ T for any nite reversible process dS = dQ T for any innitesimal reversible processS 3 Entropy and The Principle of Maximum Entropy 3.3Entropyinirreversibleprocesses From Carnots theorem, for any irreversible process we get 1 T 2 T 1 1 |
15、Q 2 | | Q 1 | | Q 1 | T 1 | Q 2 | T 20 and Q 2 0 so Q 1 T 1 + Q 2 T 2 0S 3 Entropy and The Principle of Maximum Entropy in general, we get dQ T abc dQ T foranyirreversibleporcessS 3 Entropy and The Principle of Maximum Entropy S b S a = b a dQ T foranyreversibleporcess b a dQ T foranyirreversiblepor
16、cess 3.4Entropyandthesecondlawofthermodynamics The principle of maximum entropy The entropy of an isolated system never decreases. It either stays constant (for reversible processes) or in- creases (for irreversible process).S 4 Microscopic Interpretation of Entropy 4.2Statisticalinterpretationofent
17、ropy Conclusion Entropy of macroscopic state of a system presents the number of corresponding microscopic states. Entropy of macroscopic state of a system presents its disorder Conclusion Natural processes tend to move toward a macroscopic state with greater disorder or greater entropy1, Container A
18、 holds an ideal gas at a pressure of 5:0 10 5 Pa and a temperature of 300K. It is connected by a thin tube (and a closed valve) to container B, with four times the volume of A. Container B holds the same ideal gas at a pressure of 1:0 10 5 Pa and a temperature of 400K. The valve is opened to allow t
19、he pressures to equalize, but the temperature of each container is maintained. What then is the pressure? A B2, In a certain particle accelerator, protons travel around a circular path of diameter23:0m in an evacuated chamber, whose residual gas is at295K and the molecular diameter is 2:00 10 8 cm,
20、(a) What is the mean free path of the gas molecules, (b) estimate the pressure needed.3, A capstan is a rotating drum or cylinder over which a rope or cord slides in order to provide a great ampli- cation of the ropes tension while keeping both ends free. Since the added tension in the rope is due t
21、o fric- tion, the capstan generates thermal energy. (a) If the dierence in tension between the two ends of the rope is 520:0N and the capstan has a diameter of 10:0cm and turns once in 0:900s, nd the rate at which thermal en- ergy is generated.(b) If the capstan is made of iron and has mass 6:00kg,
22、at what rate does its temperature rise? Assume that the temperature in the capstan is uniform and that all the thermal energy generated ows into it. (c = 470J=kg K)4, The molar heat capacity of a certain substance varies with temperature according to the empirical equation C = 29:5J=mol K+(8:20 10 3 J=mol K 2 )T How much heat is necessary to change the temperature of 3:00mol of this substance from 27 C to 227 C
