Examples. Fire Piston (demo) Example (Comparison of processes)

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1 Examples Fire Piston (demo) Fire Piston istory Example (Comparison of processes) Fire piston calculations Example calculations Given initial state P1, V1 final V 2 3 diff ways: a) Isothermal isotherms b) Adiabatic c) Isobaric

U < 0 also implies T < 0 (temperature drops!

2 Adiabatic Expansion (reversible & nonrevesible) Reversible adiabatic expansion (quasi-static) : Expanding gas push piston up work is done by gas W > 0 U < 0 (energy flows out of gas) For an Ideal Gas, U is a function of T only, So, U < 0 also implies T < 0 (temperature drops!) insulation Adiabatic free expansion (non-quasi-static /nonreversible): Gas expands into vacuum no work done W=0 Adiabatic Q = 0 1 st law gives U = 0 U remains unchanged and T is a constant!

3 Physics 262/266 George Mason University Prof. Paul So

Efficiency The 2 nd Law of Thermodynamics The Carnot

4 Chapter 20: The 2 nd Law of Thermodynamics Preferential Direction in Thermodynamic Processes eat Engine and Efficiency The 2 nd Law of Thermodynamics The Carnot Cycle (the most efficient heat engine) Entropy Entropy and Disorder

5 Preferred Direction of Natural Processes Processes not observed in nature: Example 1: Ball absorbing heat energy from surrounding Then, converts it into mechanical energy and starts to bounce and roll Note: energy is conserved (1 st Law is NOT violated): heat mechanical eng. BUT, we don t observe this process in nature while the reverse occurs!

Preferred Direction of Natural Processes Example 2: cold Q hot Two objects are in thermal contact and heat flows from the cold object to the hot object.

6 Preferred Direction of Natural Processes Example 2: cold Q hot Two objects are in thermal contact and heat flows from the cold object to the hot object. Again, energy is conserved (1 st Law is NOT violated): Q ( absorbed) Q ( release) 0 hot BUT, we don t observe this process in nature while the reverse occurs! cold

7 Disorder and Thermodynamic Processes The 2 nd Law of Thermodynamics is the physical principle which will delineate the preferred direction of natural processes. We will later see that The preferred direction of natural processes The degree of randomness (disorder) of the resulting state All natural processes in isolation will tend toward a state with a larger degree of disorder!

8 The 2 nd Law of Thermodynamics istorically, there are more than one but equivalent way to state the 2 nd Law: To address the condition in example #2, here is the Clausius Statement on the 2 nd Law: cold Q hot It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter body.

9 The 2 nd Law of Thermodynamics There is also the Kelvin-Planck s Statement: It is impossible for any system to undergo a cyclic process in which it absorbs heat from a reservoir at a given temperature and converts the heat completely into mechanical work. This implies that all heat engines have limited efficiency! (efficiency of real mechanical engines ~ 15 to 40%) To understand this form of the 2 nd Law, we need to look at a toy model: heat engine

10 eat Engines Definition: A device that converts a given amount of heat into mechanical energy. All heat engines carry some working substance thru a cyclic process: Engine absorbs heat from hot reservoir at T Mechanical work is done by engine Engine releases residual heat to cold reservoir at T C D stering

11 Work Done by an eat Engine The heat engine works in a cyclic process, U 1 st Law gives, U Q W 0 0 net Qnet W where, Qnet Q QC Q QC explicit signs for heats

12 Efficiency for a eat Engine Thermal Efficiency e is defined as the ratio of the mechanical energy output to the heat energy input, e W Q what you get out what you put in Substituting W Q Q, we have W Q Q QC 1 1 Q Q Q e C C Q Q using explicit signs here C

13 A perfect (100% efficient) heat engine Q A perfect heat engine means 100% efficiency (e=1). This means that QC e1 1 means QC 0 Q All heat absorbed from reservoir T is converted into mechanical work W. No residual heat is released back. eperfect 1 The Kelvin-Planck s statement of the 2 nd Law does not allow this! e 1 D drinking bird realistic

14 Refrigerators Refrigerators are basically heat engine running in reverse. eat from inside the refrigerator (cold T reservoir) is absorbed and released into the room (high T reservoir) with the input of mechanical work.

15 Refrigerators From 1 st Law, Ucycle 0 QC Q W Q Q W C explicit signs (Note: we have put in the explicit signs according to our sign convention.) Q C (absorbed) positive Q (released) negative W (work is done on working substance by motor) negative Coefficient of Performance for a Refrigerator K what you get QC QC what you put in W Q Q C

16 A perfect Refrigerator K QC QC W Q Q C A perfect refrigerator means ( ). This means that Q Q or W C No mechanical work W is needed to transfer heat from the cold reservoir to the hot reservoir. The Clausius s statement of the 2 nd Law does not allow this! Krealistic 0 K

17 2 nd Law, Disorder, & Available Energy Two Forms of Energy in any Thermal Process: Internal Energy In the Kinetic-Molecular Model, this consists of the KE and PE associated with all the randomly moving microscopic molecules. (One typically cannot control the individual random motions of all these molecules.) Macroscopic Mechanical Energy The piston s motion in an automobile engine results from the coordinated macroscopic motion of the molecules. (Energy associated with this coordinated [ordered] motion can be used for useful work.)

18 2 nd Law, Disorder, & Available Energy In a natural process (a block sliding to a stop), e.g. f v stopped slightly warmer due to friction before after The coordinated motion of the block is converted into the KE & PE of the slightly more agitated random motions of the molecules in the block/table. Macroscopic Mechanical Energy (KE of the block) is converted into Internal Energy through heat as a result of friction.

19 2 nd Law, Disorder, & Available Energy Now consider the reverse situation it is unlikely that one can coordinate ALL the randomly moving molecules in a concerted fashion. In other words, one typically cannot completely convert the internal energy of a system back into macroscopic mechanical energy. owever, this does not mean that internal energy is not accessible. An eat Engine is exactly the machine that can perform this conversion but only partially. The 2nd Law of Thermodynamics is basically a statement limiting the availability of internal energy for useful mechanical work.

20 The Carnot Cycle (Most Efficient eat Engine) A reversible cycle described by Sadi Carnot in The Carnot Theorem gives the theoretical limit to the thermal efficiency of any heat engine. The Carnot cycle consists of: A cycle operating between two temperatures: 2 reversible isothermal processes in which 2 reversible adiabatic processes in which An Ideal Gas as its working substance T T Q T and C T C

21 Steps of the Carnot Cycle animation

22 Steps of the Carnot Cycle animation

12 The Laws of Thermodynamics

June 14, 1998 12 The Laws of Thermodynamics Using Thermal Energy to do Work Understanding the laws of thermodynamics allows us to use thermal energy in a practical way. The first law of thermodynamics