Physics 1501 Lecture 37

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1 Physics 1501: Lecture 37 Todays Agenda Announcements Homework #12 (Dec. 9): 2 lowest dropped Midterm 2 in class Wednesday Friday: review session bring your questions Todays topics Chap.18: Heat and Work» Zeroth Law of thermodynamics» First Law of thermodynamics and applications» Work and heat engines Chap.19: Second law of thermodynamics» Efficiency» Entropy Physics 1501: Lecture 37, Pg 1 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 2 Page 1

2 Zeroth Law of Thermodynamics Thermal equilibrium: when objects in thermal contact cease heat transfer same temperature T 1 = T 2 U 1 U 2 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 3 First Law of Thermodynamics First Law of Thermodynamics ΔU = Q + W work done on the system heat flow in (+) or out (-) variation of internal energy Independent of path in PV-diagram Depends only on state of the system (P,V,T, ) Energy conservation statement only U changes Physics 1501: Lecture 37, Pg 4 Page 2

3 Heat Engines 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! Heat engines: Purpose: Convert heat into work using a cyclic process Example: 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 5 Heat Engines Example: the Stirling cycle We can represent this cycle on a P-V diagram: 1 Gas 2 1 T=T H P 1 2 Gas T=T C Gas T=T H V a 4 V b 3 V T C T H 4 Gas T=T C 3 * reservoir: large body whose temperature does not change when it absorbs or gives up heat Physics 1501: Lecture 37, Pg 6 Page 3

U = 0 " W = #Q 3 ADDED REMOVED BY ON W = 0 " #U = Q 4 ADDED REMOVED BY ON!

4 Heat Engines Identify whether Heat is ADDED or REMOVED from the gas Work is done BY or ON the gas for each step of the Stirling cycle: P T C T H V a V b V step HEAT WORK ΔU = Q + W 1 ADDED REMOVED BY ON W = 0 " #U = Q 2 ADDED REMOVED BY ON!U = 0 " W = #Q 3 ADDED REMOVED BY ON W = 0 " #U = Q 4 ADDED REMOVED BY ON!U = 0 " W = #Q Physics 1501: Lecture 37, Pg 7 Realistic Stirling Engines 2 types Alpha-type: 2 separate chambers beta-type: joined chambers From Wikipedia Physics 1501: Lecture 37, Pg 8 Page 4

Realistic Stirling Engines 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

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.

5 Realistic Stirling Engines 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. 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. Maximum volume: the hot cylinder piston begins to move most of the gas into the cold cylinder, where it cools and the pressure drops. 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 9 Beta-type: Realistic Stirling Engines 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 10 Page 5

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

reservoir Engine W eng A schematic representation of a heat engine.

6 Another look at beta-type real one Physics 1501: Lecture 37, Pg 11 Chap. 19: Heat Engines and the 2 nd Law of Thermodynamics Hot reservoir Engine W eng A schematic representation of a heat engine. The engine receives energy from the hot reservoir, expels energy Q c to the cold reservoir, and does work W. If working substance is a gas P Q c Area = W eng Cold reservoir V Physics 1501: Lecture 37, Pg 12 Page 6

7 Heat Engines and the 2 nd Law of Thermodynamics Hot reservoir A heat engine goes through a cycle 1st Law gives ΔU = Q + W =0 W eng So Q net = - Q c = -W = W eng Engine Q c Cold reservoir Physics 1501: Lecture 37, Pg 13 Efficiency of a Heat Engine How can we define a figure of merit for a heat engine? Define the efficiency ε as: " = W eng = # Q c =1# Q c 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 14 Page 7

8 Heat Engines and the Second law of Thermodynamics Reservoir Engine 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 Physics 1501: Lecture 37, Pg 15 Lecture 37: Act 1 Efficiency Consider two heat engines: Engine I:» Requires Q in = 100 J of heat added to system to get W=10 J of work Engine II:» To get W=10 J of work, Q out = 100 J of heat is exhausted to the environment Compare ε I, the efficiency of engine I, to ε II, the efficiency of engine II. A) ε I < ε II B) ε I > ε II C) Not enough data to determine Physics 1501: Lecture 37, Pg 16 Page 8

9 Reversible/irreversible processes Reversible process: Every state along some path is an equilibrium state The system can be returned to its initial conditions along the same path Irreversible process; Process which is not reversible! Most real physical processes are irreversible E.g., energy is lost through friction and the initial conditions cannot be reached along the same path However, some processes are almost reversible» If they occur slowly enough (so that system is almost in equilibrium) Physics 1501: Lecture 37, Pg 17 The Carnot Engine 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 Th P B. B C, the gas expands adiabatically (Q=0) A B C. C D, the gas is compressed isothermally while in contact with a reservoir at Tc D. D A, the gas compressed adiabatically (Q=0) D W eng C V Physics 1501: Lecture 37, Pg 18 Page 9

10 The Carnot Engine Carnot showed that the thermal efficiency of a Carnot engine is: e c =1" T c T h 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. Physics 1501: Lecture 37, Pg 19 Entropy and the 2 nd Law Consider a reversible process between two equilibrium states The change in entropy ΔS 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. "S = Q r T 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). Entropy is a measure of disorder in a system. Physics 1501: Lecture 37, Pg 20 Page 10

11 Entropy and the 2 nd Law What about the following situation Atoms all located in half the room Although possible, it is quite improbable Disorderly arrangements are much more probable than orderly ones all atoms no atoms Isolated systems tend toward greater disorder Entropy is a measure of that disorder Entropy increases in all natural processes Physics 1501: Lecture 37, Pg 21 Page 11

The laws of Thermodynamics. Work in thermodynamic processes

The laws of Thermodynamics. Work in thermodynamic processes The laws of Thermodynamics ork in thermodynamic processes The work done on a gas in a cylinder is directly proportional to the force and the displacement. = F y = PA y It can be also expressed in terms