homeworkA

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The Laws of Thermodynamics

Chapter 16: Giordano Chapter 15: Giambattista et. al Chapter 12: Serway and Faughn

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•  The internal energy of a system can be increased by adding energy through heat or by doing work

•  This is a special case of conservation of energy, applied to a thermodynamic system (e.g. gas and piston)

•  Mathematically: ΔU = Q + WGP OR ΔU = Q - WPG

First Law of Thermodynamics

+ -

ΔU internal energy increases (T increases)

internal energy decreases (T decreases)

Q heat flows into system heat flows out of system

W surroundings do work on gas gas does work on surroundings

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Work •  Recall: work W = •  W is positive if F and d are in the same direction (draw)

e.g. OR •  W is negative if F and d are in the opposite direction (draw)

e.g. OR •  W is zero if F and d are perpendicular or if d = 0 (draw)

•  Often we deal with a gas in a cylinder and a piston. d will be the distance the piston moves.

•  Since FPG = - FGP, that means WPG = -WGP •  Different books have different conventions

eg. in the lab W is WPG (work on the piston by the gas)

F d cos θ

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Lab 10: First Law of Thermodynamics •  Pre-lab •  Do p. 1- 2 of lab

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Thermodynamic Processes •  There are 5 special cases of the first law:

1.  Q = 0, no heat transfer, “adiabatic” 2.  W = 0, constant volume, d = 0 3.  ΔU = 0, constant temperature 4.  constant pressure 5.  cyclic (engines)

•  In lab we will investigate processes 1, 2, and 3

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Special Cases Case 1: Adiabatic •  Q = 0 à First Law à ΔU = W •  no heat is transferred, but temperature can

change and work is done •  can happen if system is insulated such that no

heat can get in or out •  can also happen if process is so fast that heat

doesn’t have time to go in or out o  e.g. stretch a rubber band several times quickly. it heats

up because of work done on it

Case 2: Constant Volume •  W = 0 à First Law à ΔU = Q •  piston does not move: d =0 •  therefore no work is done

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Special Cases Case 3: Constant Temperature •  aka “isothermal” •  can keep temp constant by keeping system in

contact with a reservoir (something with a large heat capacity)

•  for an ideal gas U depends on T, so if ΔT =0, then ΔU = 0 •  à First Law à Q = - WPG

o  i.e. work done on the gas = energy added by heat

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Special Cases Case 4: Constant Pressure •  aka “isobaric” •  ΔU, Q, and W all non-zero

Case 5: Cyclic •  we will discuss engines later

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PV Diagrams •  Plot of pressure vs. volume

•  Arrow on curve represents direction of process

•  Can be used to determine the work done on a system: work is the area under the curve on a PV diagram

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Clicker Question Sequence: Thermodynamics

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Which of the graphs below show an isobaric process?

Initial response(s) ü

Correct response

A

B

C

Graph A Graph B Graph C

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The graphs below show a piston undergoing either one or two processes. Rank the magnitudes of the work done in each of the cases from greatest to least.

Initial response(s) ü

Correct response

A

E

B

C D

1 A>B=D=E>C 2 A>D>B=E>C 3 A=B=C=D=E 4 B=D=E>A>C 5 C>A>B>D>E 6 none of the above

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Which of the following statements are always true?

Initial response(s) ü

Correct response

A. If heat is added to a system the temperature will increase. B. If a piston is locked in place the work done by the gas is zero. C. If ΔU = 0, the process is called an isothermal process. D.  In an adiabatic process the temperature remains constant. E.  A and B are both true. F.  B and C are true. G.  A, B, C, and D are all true.

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Draw PV Diagrams •  Constant pressure case:

•  Constant volume case:

•  Constant temperature case:

V

P

V

P

V

P

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Group Problem Sketch a PV diagram of the following processes:

a. A gas expands at constant pressure P1 from volume V1 to volume V2. It is then kept at constant volume while the pressure is reduced to P2.

b. A gas is reduced in pressure from P1 to P2 while its volume is held constant at V1. It is then expanded at constant pressure P2 to a final volume V2.

c. In which of the processes is more work done by the gas? Why?

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Sample Problem •  Gas is enclosed in a container with a piston of area 0.10 m2. The

pressure remains constant at 8000 Pa while 42 J of energy are added via heat. The piston is pushed in a distance of 4 cm.

•  What is the change in internal energy? •  Find:

•  Given:

•  Concept(s):

•  Solution:

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Sample Problem •  In a car engine, a hot high-pressure gas expands against a piston

in 10 ms, which is so fast that very little heat leaves the gas during the expansion.

•  If the cylinder contains 0.10 moles of gas and the temperature goes from 1200 K to 400K, how much work is done during the expansion?

•  Find:

•  Given:

•  Concept(s):

•  Solution:

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The First Law and Human Metabolism •  Animals do work and give off energy by heat •  Internal energy in humans transferred into

work: walking, lifting, etc. heat: warm body, cold surroundings

•  Energy transfer depends on intensity and duration of activity

•  Can re-write the first law à ΔU/Δt = Q/Δt + W/Δt heat flows out, work is done on surroundings

•  We add internal energy by eating and breathing •  Metabolic rate is ΔU/Δt •  Basal metabolic rate is 80 watts (sleeping) •  Body’s efficiency in delivering mechanical power:

e = |W/Δt| / |ΔU/Δt| depends on person and activity

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Lab 10: First Law of Thermodynamics •  Finish lab •  Discussion

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Reversible and Irreversible Processes

•  Have you ever wished you could make time go backward? Why can’t you?

•  A reversible process is one that doesn’t violate the laws of physics if played in reverse o  e.g. elastic collision of 2 billard balls w/o friction o  projectile on moon (no air resistance)

•  An irreversible process is one that does violate the laws of physics if played in reverse. Happens if energy is transferred to internal energy or by heat o  e.g. friction o  air resistance o  spontaneous heat flow, eg. ice cubes in lemonade

•  Most natural processes are irreversible

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Second Law of Thermodynamics •  Heat never flows spontaneously from a colder

body to a hotter body

•  Several other ways to state the second law as we will see

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Heat Engines •  An engine converts internal energy into useful

forms of energy like electrical or mechanical energy.

•  Examples: steam engine, internal combustion engine; used in power plants, cars, etc.

•  There’s a fundamental limit on how much useful work an engine can do because of the second law of thermodynamics.

•  A heat engine in reverse is an air conditioner or refrigerator. With a fridge, energy is extracted from food and delivered to the air.

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Power Plants •  Coal or other fuel is burned

•  That internal energy is used to turn water into steam

•  Steam turns the blades of a turbine

•  This drives an electric generator

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Steam Engines •  Water evaporates into steam in boiler

•  Steam expands against piston

•  Steam condenses into water, sent back to boiler

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Internal Combustion Engines •  Intake stroke: piston pulled out, drawing fuel and

air into cylinder

•  Compression stroke: piston pushed in, compressing fuel-air mixture; work is done on the gas

•  Ignition: spark ignites gases, T and P increase

•  Power stroke: pressure from ignition pushes piston out; work is done on piston plus some heat leaves

•  Exhaust stroke: valve opens and exhaust gas pushed out of cylinder

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Engines in General •  Energy transferred from source at high temp

•  Work is done by the engine

•  Energy expelled by the engine via heat to a source at low temp

•  Qh = W + Qc (conservation of energy, aka First Law. Note ΔU = 0 because process is cyclic)

•  Efficiency: e = W/Qh = (Qh - Qc)/Qh = 1 - Qc/Qh

•  100% efficiency is not possible

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Sample Problem •  An engine transfers 2 x 103 J of energy from a hot source,

does work, and transfers 1.5 x 103 J to cold. •  How much work is done and what is the efficiency of the

engine?

•  Find:

•  Given:

•  Concept(s):

•  Solution:

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Carnot Engine •  Ideal, theoretical engine with the highest

efficiency possible

•  Efficiency: e = 1 - Tc/Th

•  If Tc is low or Th is high à greater efficiency

•  All real engines are even less efficient due to friction

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Sample Problem •  The boiler of a steam engine operates at 500 K. The energy

from the boiler turns water into steam, which drives a piston. The exhaust is room temperature, 300K.

•  What is the maximum efficiency of the engine?

•  Find:

•  Given:

•  Concept(s):

•  Solution:

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Group Problem Solving A stream driven turbine is one major component of an electric power plant. Why is it advantageous to increase the temperature of the steam as much as possible?

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Group Problem Solving One of the most efficient engines ever built is a coal-fired steam turbine in the Ohio Valley, driving an electric generator as it operates between 1870 oC and 430 oC. What is its maximum theoretical efficiency? (Just FYI, its actual efficiency is 42%.)

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Group Problem Solving The US generates about 5.0 x 1016 J of electric energy per day. This

energy is equivalent to work, since it can be converted into work with almost 100% efficiency by an electric motor.

a.  If this energy is generated in power plants with an average efficiency of 0.30, how much heat is dumped into the environment each day?

b.  How much water would be required to absorb this heat if the water temperature is not allowed to increase more than 2.0 oC?

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Challenge Problem The intensity of sunlight (power per unit area) of the sunlight incident on Earth’s surface, averaged over a 24 hour period, is about 200 W/m2. If a solar power plant is to be built with an output capacity of 1.0 x 109 W, how big must the area of solar energy collectors be for photocells operating at 20% efficiency?

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Entropy •  Why does heat flow only one way? (Hot to cold.)

•  Entropy: ΔS = Q/T

o  Q is the energy transferred via heat o  T is the temperature

•  This means: o  When energy is expelled from a system, Q is negative so

ΔS is negative so entropy S decreases o  When energy is absorbed by a system, Q is positive so

ΔS is positive so entropy S increases

•  Entropy is a state variable like U, P, V, and T

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Second Law Revisited •  Second Law: the entropy of the universe

increases in all natural processes.

•  There are some processes where entropy decreases, but only when accompanied by ones where entropy increases.

•  Perpetual motion machines are impossible.

•  You CAN have increasing complexity AND increasing entropy. (e.g. evolution: increasing “order” in organisms à increasing “disorder” in the environment/surroundings.)

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Sample Problem •  What is the change in entropy when 300 g of lead melts at

327 oC? The latent heat for melting lead is 2.45 x 104 J/kg.

•  Find:

•  Given:

•  Concept(s):

•  Solution:

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Entropy and Probability •  Natural processes have an element of chance

e.g. trees in a forest are randomly spaced

•  Disorderly arrangements are more probable in nature because there are more ways to be disorderly than there are to be orderly

•  The second law of thermo is based on statistics of systems with many atoms/molecules

•  Another way to calculate entropy is: S = k log Ω

o  Ω is proportional to the probability of a certain configuration

o  k is Boltzmann’s constant

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Second Law and Probability •  The second law says what’s most likely rather

than exactly what must be •  Example of probability: coin toss.

o  Flip a coin 4 times. Only 1 way to get 4 heads (least likely) but 6 ways to get 2 heads and 2 tails (most likely)

•  Example: ice cube and pizza. o  A slow, cold ice molecule could impart some energy to a

hot, fast pizza molecule, but the other way around is more likely. Since there are so many molecules heat flows from hot to cold.

•  Example: air molecules in a room. o  Random distribution of speeds is most likely. Highly

unlikely for all to be going the same direction and speed. •  Example: cleaning your room.

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Second Law and Probability •  Tendency toward “disorganized” states because

there are many ways to be messy. This tendency affects a system’s ability to do work.

•  Consider a dish thrown at a wall. Before: dish has kinetic energy and is highly organized. After: it breaks in pieces and heats up. No energy is lost, but beforehand, the dish is more capable of useful work.

•  Energy can be easily converted to internal energy, but not necessarily the other way around. Internal energy is a lower “grade” of energy-- not always as useful.

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Summary of Thermodynamics •  First Law:

o  you can’t get out more energy than you put in à energy in = energy out)

•  Second Law: o  if that energy starts as internal energy, you can’t

break even o  as time passes, more of the energy in the universe is

in a less useful form o  entropy increases o  heat flows from hot to cold o  you can’t make a 100% efficient engine

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Group Problem Solving A thermodynamic process occurs in which the entropy of the system changes by -8.0 J/K. According to the second law of thermodynamics, what can you conclude about the entropy change of the environment?

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Group Problem Solving What is the change in entropy of 1 kg of liquid water at 100 oC as it changes to steam at 100 oC?

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Group Problem Solving After a day at the beach, a child brings home a bucket containing some salt water. Eventually the water evaporates, leaving behind a few salt crystals. The molecular order of the salt crystals is greater than the order of the dissolved salt sloshing around in the sea water. Is this a violation of the entropy principle?

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Group Problem Solving A student eats 2000 kcal per day. a.  Assuming that all of the food energy is released as heat, what is

the rate of heat released (in watts)? b.  What is the rate of change in entropy of the surroundings if all of

the heat is released into air at room temperature (20 oC)?