Physics 1501: Lecture 37, Pg 1 Physics 1501: Lecture 37 Today’s Agenda l Announcements çHomework #12 (Dec. 9): 2 lowest dropped çMidterm 2 … in class Wednesday çFriday: review session … bring your questions l Today’s topics çChap.18: Heat and Work »Zeroth Law of thermodynamics »First Law of thermodynamics and applications »Work and heat engines çChap.19: Second law of thermodynamics »Efficiency »Entropy

Physics 1501: Lecture 37, Pg 2 Chap. 18: Work & 1 st Law The Laws of Thermodynamics 0) If two objects are in thermal equilibrium with a third, they are in equilibrium with each other. 1) There is a quantity known as internal energy that in an isolated system always remains the same. 2) There is a quantity known as entropy that in a closed system always remains the same (reversible) or increases (irreversible).

Physics 1501: Lecture 37, Pg 3 Zeroth Law of Thermodynamics l Thermal equilibrium: when objects in thermal contact cease heat transfer çsame temperature T1T1 T2T2 U1U1 U2U2 = If objects A and B are separately in thermal equilibrium with a third object C, then objects A and B are in thermal equilibrium with each other. A C B

Physics 1501: Lecture 37, Pg 4 First Law of Thermodynamics l First Law of Thermodynamics  U = Q + W variation of internal energy heat flow “in” (+) or “out” (-) work done “on” the system çIndependent of path in PV-diagram çDepends only on state of the system (P,V,T, …) çEnergy conservation statement  only U changes

Physics 1501: Lecture 37, Pg 5 Heat Engines l We now try to do more than just raise the temperature of an object by adding heat. We want to add heat to get some work done! l Heat engines: çPurpose: Convert heat into work using a cyclic process çExample: Cycle a piston of gas between hot and cold reservoirs * (Stirling cycle) 1) hold volume fixed, raise temperature by adding heat 2) hold temperature fixed, do work by expansion 3) hold volume fixed, lower temperature by draining heat 4) hold temperature fixed, compress back to original V

Physics 1501: Lecture 37, Pg 6 Heat Engines l Example: the Stirling cycle Gas T=T H Gas T=T H Gas T=T C Gas T=T C V P TCTC THTH VaVa VbVb We can represent this cycle on a P-V diagram: * reservoir: large body whose temperature does not change when it absorbs or gives up heat

Physics 1501: Lecture 37, Pg 7 l Identify whether çHeat is ADDED or REMOVED from the gas çWork is done BY or ON the gas for each step of the Stirling cycle: V P TCTC THTH VaVa VbVb ADDED REMOVED BY ON 1 HEAT WORK step ADDED REMOVED BY ON 2 ADDED REMOVED BY ON 3 ADDED REMOVED BY ON 4 Heat Engines  U = Q + W

Physics 1501: Lecture 37, Pg 8 Realistic Stirling Engines çbeta-type: joined chambers From Wikipedia l 2 types çAlpha-type: 2 separate chambers

Physics 1501: Lecture 37, Pg 9 Realistic Stirling Engines l Alpha-type Most of the working gas is in contact with the hot cylinder walls, it has been heated and expansion has pushed the hot piston to the bottom of its travel in the cylinder. The expansion continues in the cold cylinder, which is 90° behind the hot piston. Maximum volume: the hot cylinder piston begins to move most of the gas into the cold cylinder, where it cools and the pressure drops. Most pf the gas is in the cold cylinder and cooling continues. The cold piston, powered by flywheel momentum compresses the remaining part of the gas. Minimum volume: gas will now expand in the hot cylinder, be heated once more, driving the hot piston in its power stroke.

Physics 1501: Lecture 37, Pg 10 Realistic Stirling Engines l Beta-type: Power piston (dark grey) has compressed the gas, the displacer piston (light grey) has moved so that most of the gas is adjacent to the hot heat exchanger. The heated gas increases in pressure and pushes the power piston to the farthest limit of the power stroke. The displacer piston now moves, shunting the gas to the cold end of the cylinder. The cooled gas is now compressed by the flywheel momentum. This takes less energy, since when it is cooled its pressure drops.

Physics 1501: Lecture 37, Pg 11 Another look at beta-type l “real” one

Physics 1501: Lecture 37, Pg 12 Chap. 19: Heat Engines and the 2 nd Law of Thermodynamics l A schematic representation of a heat engine. The engine receives energy Q h from the hot reservoir, expels energy Q c to the cold reservoir, and does work W. l If working substance is a gas Hot reservoir Cold reservoir Engine QhQh QcQc W eng V P Area = W eng Engine

Physics 1501: Lecture 37, Pg 13 Heat Engines and the 2 nd Law of Thermodynamics l A heat engine goes through a cycle ç1st Law gives  U = Q + W =0 l So Q net =|Q h | - |Q c | = -W = W eng Hot reservoir Cold reservoir Engine QhQh QcQc W eng Engine

Physics 1501: Lecture 37, Pg 14 Efficiency of a Heat Engine l How can we define a “figure of merit” for a heat engine? Define the efficiency  as: It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work

Physics 1501: Lecture 37, Pg 15 Heat Engines and the Second law of Thermodynamics Reservoir Engine QhQh W eng It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work Engine

Physics 1501: Lecture 37, Pg 16 l Consider two heat engines: çEngine I: »Requires Q in = 100 J of heat added to system to get W=10 J of work çEngine II: »To get W=10 J of work, Q out = 100 J of heat is exhausted to the environment Compare  I, the efficiency of engine I, to  II, the efficiency of engine II. A)  I <  II B)  I >  II C) Not enough data to determine Lecture 37: Act 1 Efficiency

Physics 1501: Lecture 37, Pg 17 Reversible/irreversible processes l Reversible process: çEvery state along some path is an equilibrium state çThe system can be returned to its initial conditions along the same path l Irreversible process; çProcess which is not reversible ! l Most real physical processes are irreversible çE.g., energy is lost through friction and the initial conditions cannot be reached along the same path çHowever, some processes are almost reversible »If they occur slowly enough (so that system is almost in equilibrium)

Physics 1501: Lecture 37, Pg 18 The Carnot Engine l No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs. A.A  B, the gas expands isothermally while in contact with a reservoir at T h B.B  C, the gas expands adiabatically (Q=0) C.C  D, the gas is compressed isothermally while in contact with a reservoir at T c D.D  A, the gas compressed adiabatically (Q=0) V P A B C D W eng

Physics 1501: Lecture 37, Pg 19 The Carnot Engine l All real engines are less efficient than the Carnot engine because they operate irreversibly due to friction as they complete a cycle in a brief time period. l Carnot showed that the thermal efficiency of a Carnot engine is:

Physics 1501: Lecture 37, Pg 20 Entropy and the 2 nd Law Consider a reversible process between two equilibrium states The change in entropy  S between the two states is given by the energy Q r transferred along the reversible path divided by the absolute temperature T of the system in this interval. l The Second Law of Thermodynamics “There is a quantity known as entropy that in a closed system always remains the same (reversible) or increases (irreversible).” l Entropy is a measure of disorder in a system.

Physics 1501: Lecture 37, Pg 21 Entropy and the 2 nd Law l What about the following situation çAtoms all located in half the room çAlthough possible, it is quite improbable l Disorderly arrangements are much more probable than orderly ones l Isolated systems tend toward greater disorder çEntropy is a measure of that disorder çEntropy increases in all natural processes no atomsall atoms