Physics 105 Physics for Decision Makers: The Global Energy Crisis Lecture 8 Thermodynamics II Fall 2011

Physics 105 Fall 11 Energy Audit Energy Audit Project: Download assignment info sheet from Elms -Group project -When you meet -> Each person should have a role one person needs to be responsible for organization. -Project Due Dates: Assignment #1 - Sept 30 only one person needs to turn something in, but the whole group needs to be involved Assignment #2 - Oct 7 Assignment #3 - Oct 21 Assignment #4 - Oct 28 Assignment #5 (Presentations in Discussion) Oct 29 - Nov 1. Page 2

Physics 105 Fall 11 Food Supply and Climate CNN today - Why is 'food security' sparking unrest -Russian Drought wiped out 25% of their wheat crop -This caused them to stop grain exports -Bread prices went up dramatically 30% in some countries -Riots ensued in Mozambique Decisions we make about using biofuels can affect people around the world Page 3

Physics 105 Fall 11 Activities: Guided Tours Thermodynamics: What is Thermodynamics?

Physics 105 Fall 11 Page 5

Physics 105 Fall 11 The Zeroth Law of Thermodynamics Temperature - if two objects are in thermal equilibrium with a third object (like a thermometer) then they are in thermal equilibrium with each other - -Another way of saying it is that temperature is a measurable quantity and it tells us about the energy content of an object - -this law asserts that we can define a temperature function, or more informally, that we can 'construct a thermometer'

Physics 105 Fall 11 Thermal Equilibrium if Q=0 then we are in thermal equilibrium T A = T B A B Q

Physics 105 Fall 11 Heat Transfer Three methods Conduction Transfer Of Energy Through Matter Air Is A Poor Conductor - Metal is a good one Only important at the earth's surface Convection Transfer of energy by movement of mass Can only take place in liquids & gases - e.g. Air Convection on a global scale creates worldwide atmospheric circulation Radiation Proportional to the 4th power of the temperature How we get energy from the sun Why it gets cold on a clear night

Physics 105 Fall 11 Fig. 2-2, p. 30

Physics 105 Fall 11

Radiation

Physics 105 Fall 11 The First Law of Thermodynamics Energy Conservation Many statements: - -Energy is conserved - -Heat is a form of energy - -The energy of an isolated system (e.g. the universe) is constant - -Energy is conserved during any change in state. Specifically: - -Heat absorbed by a system + work done on the system = change in internal energy of the system Mathematically: Q+W= U Q is heat, W is work and U is internal energy

Physics 105 Fall 11 The internal energy of a system does NOT depend on which of the following: 1. 1.The temperature of the system 2. 2.The amount of material in the system 3. 3.The type of material 4. 4.The amount heat that has been put into the system 5. 5.It depends on all of them

Physics 105 Fall 11 First Law - energy is conserved Where did energy to power the light come from?

Physics 105 Fall 11 Heat Capacity The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius (or Kelvin) Heat Capacity = Q/ T - -Heat Capacity of a lake depends on the size of the lake (extrinsic) - -Specific Heat = Heat Capacity/kg - property of the water (intrinsic)

Physics 105 Fall 11 Latent Heat Latent Heat of vaporization - -If we add heat to water - its temperature goes up - -1 Kcal - will raise 1kg of water 1 o C - -Until water hits 100 o C - then the temperature stops going up - -What happens? - -It vaporizes (boils). - -It takes 539 kcal to boil 1kg of water - -Eventually once its all steam the temp will start going up again - -539 kcal/kg is the latent heat of vaporization

Physics 105 Fall 11 Latent Heat Latent heat of fusion - -Take 1kg of ice at -20 o C and add heat at a rate of 1kcal/min - -The Ice will warm up at 2 o C/min - (why 2)? - -Once it hits 0 o C - (after 10 min) the ice will start to melt - -It will take 80 minutes to melt the ice - -So the latent heat of fusion of ice is 80kcal/kg

Physics 105 Fall 11 Does the 1st law prohibit a lake from freezing on a warm day? 1. 1.Yes 2. 2.No 3. 3.Doesnt apply

Physics 105 Fall 11 The 2nd Law of Thermodynamics Many formulations: - -It is impossible to convert heat completely into work. - -No perfect engine - -Cant just pull heat out of the environment - -Heat cannot spontaneously flow from a material at lower temperature to a material at higher temperature. - -No perfect refrigerator - -In an isolated system, a process can occur only if it increases the total entropy of the system.

Physics 105 Fall 11 The Perfect Heat Engine Takes heat out of the environment and turns it into work. The solution to all of our problems - -reduce global warming - -Solve the energy problem 2 nd Law T1T1 Q1Q1 W out

Physics 105 Fall 11 Perfect Refrigerator T 1 Hot T 2 Cold Q

Physics 105 Fall 11 Restatement Zeroth Law Lunch exists (temperature) First Law TANSTAAFL (energy conserved) Second Law (heat flows from hot to cold) - -Lunch will be expensive

Physics 105 Fall 11 Entropy Toss a penny N times What is probability that you get Heads every time? ans. (1/2)(1/2)(1/2)(1/2). = (1/2) N if N =2, p = 0.25 if N= 10, p =.001 if N= 100, p = 8 X 10 -31 if N = 10 4, p = 5 X 10 -3011 !!!! We expect about N/2 heads What is probability that we get within 1% of N/2? if N = 10, p = 0.25 if N=1000, p =.248 if N = 10 5, p =.998 if N = 10 8, p = 1 - 3 X 10 -2174 !!!!

Physics 105 Fall 11 I flip a coin 10 times - the first 9 come up heads.. What is the probability that the next toss is also heads? 1. 1..001 2. 2.1 - 9/10 = 0.1 3. 3.(9/10)(1/2) = 0.45 4. 4.0.5 5. 5.9/10 = 0.9

Physics 105 Fall 11 Entropy - microstates Why is all heads so rare and ~50/50 so common? - -Lets call each possible outcome a microstate - -There is only one microstate that is all heads HHHHHHHHHH - -There are many microstates that are ~ 50/50 HHHHHTTTTT HHHHTHTTTT HHHTHHTTTT HHTHHHTTTT TTTTTHHHHH THTHTHTHTH Each microstate is equally likely.

Physics 105 Fall 11 Entropy and Particles in a box Particles start all on left - -What happens? - -What are the odds that later we find all of them on the left? Just like the coin tossing! After mixing, chance of all on the left is (1/2) N It would take work push all the molecules back to the left side

Physics 105 Fall 11 Entropy and the macrostate We can define macroscopic properties - -more-or-less uniform distribution between right and left When a physical system is allowed to evolve in isolation, some single macroscopic outcome is overwhelmingly more probable than any other Second Law: If a system of many particles is permitted to change, it will evolve to the macrostate made of the largest number of microstates, and stay there.

Physics 105 Fall 11 Entropy We define a quantity called entropy - -Entropy = S = k B ln (no. of microstates) - -With this definition, it can be shown that: - -S final - S initial = energy input from heating/T = Q/T Second Law: S > Q/T -

Physics 105 Fall 11 Definition of Entropy Change in entropy S= Q/T - -Take an example - - -Q=30J S cold =+30J/283 o K= +0.106 S warm =-30J/333 o k= -0.09 S total = +.07J/ o k - -Entropy of the entire system increases 10 o 60 o Q=30J

Physics 105 Fall 11 The 2nd Law of Thermodynamics Most systems are microscopically reversible - -Particles in a box The 2 nd Law tells us the direction of time

Physics 105 Fall 11 Reversible and Irreversible Processes

Physics 105 Fall 11 Heat Engines Heat engines take heat from a hot reservoir and does work and expels heat to the cold reservoir Note that the first law says - -Q 1 =W+Q 2 The 2nd law tells us the amount of work we can get from a temperature difference Efficiency = (work output)/(energy in)

Physics 105 Fall 11 Carnot Engine The Carnot Engine is an idealized engine that works in a reversible way -reversible -What is a reversible engine? - -A refrigerator - -By adding work we can take heat from the cold reservoir and deposits it to the hot reservoir - -Again - 1st law works - -W+Q 1 = Q 2 - -Notice more heat is delivered than work done!

Physics 105 Fall 11 Heat Pump Cools in summer Heats in winter What is temperature of the air blowing out in summer and winter?

Physics 105 Fall 11 Heat Pump Page 42 Winter Summer Outside

Physics 105 Fall 11 Carnot Efficiency The efficiency (work/energy in) of a Carnot Engine T 1 -T 2 )/T 1 When is the efficiency high? - -When T 2 is low - -Example - -T 1 = 500 o C = 773K - -T 2 = 0 o C = 273K T 1 -T 2 )/T 1 = 500/773= 65% - -This says W=65% Q 2 = 35% - -So if we take 100J from T 1 we get 65J of work - -Redo if T 1 is 100 o C = 373k T 1 -T 2 )/T 1 = 100/373= 26% - -so our 100J of energy only gives us 26J of work

Physics 105 Fall 11 Proof that no engine can have efficiency greater than Carnot Assume Engine 1 is higher efficiency than Carnot - -Operating between T 1 & T 2 it produces W 1. - -W 1 is greater than Wc would produce for the same Q 1. (i.e. Q 2 is less) - -Since the Carnot is reversible run it backwards powered by W 1. - -This will pump more heat out of the cold reservoir than engine 1 put in as Qc >Q 2 Net result - a perfect refrigerator - which violates the 2nd law since we are moving heat from cold to hot with no external work (lake freezing) 1 1

Physics 105 Fall 11 What is the net effect of putting a refrigerator in a room opening the door an turning it on? 1. 1.The room cools down a little 2. 2.The room cools down a lot 3. 3.The room heats up a little 4. 4.The room heats up a lot

Physics 105 Fall 11 System Properties Extensive quantities (depend on amount of material) - -U = Internal energy - - V = Volume - - N i = # of Moles - -Heat Capacity The intensive quantities (do NOT depend on amount of material) - -Pressure - -Temperature - -Specific Heat

Physics 105 Fall 11 Real Heat Engines Real heat engines always are less efficient than Carnot engines In all heat engines there is waste heat from the 2 nd law - -Electric motors are not governed by the 2 nd although generally the production of electricity is In real engines there is additional waste heat The Carnot engine gives us a goal

Physics 105 Fall 11 Real Engine T1T1 T2T2 Q1Q1 Q2Q2 W out Q waste

Physics 105 Fall 11 Car Engines efficiency of about 25% - -The efficiency may be as high as 37% at the optimum operating point. - -Most internal combustion engines waste about 35% of the energy in gasoline as heat lost to the cooling system and another 35% through the exhaust. - -The rest, about 5%, is lost to friction

Physics 105 Fall 11 Car Engine

Physics 105 Fall 11 Does it cost you fuel to use your car heater while driving? Yes No

Physics 105 Fall 11 Q1Q1 Work out Q 2 out Q Waste

Physics 105 Fall 11 Real Engine heat recovery T1T1 T2T2 Q1Q1 Q2Q2 W out Q waste T3T3 T2T2 Q3Q3 Q2Q2 W out Q waste

Physics 105 Fall 11 Its possible to reduce the entropy of an object? True False

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Physics 105 Physics for Decision Makers: The Global Energy Crisis Lecture 8 Thermodynamics II Fall 2011