The four laws of Thermodynamics

• The 0th Law (discovered 4th)• The 1st Law (discovered 2nd)• The 2nd Law (discovered 1st)• The 3rd Law (discovered 3rd)

The 0th Law

• If: – Objects A and B are the same temperature– Objects B and C are the same temperature

• Then:– Objects A and C are the same temperature

– Just the transitive property of mathematics.

1st Law of Thermodynamics

• The total sum of all energy in an isolated system will never increase or decrease.

• “Law of conservation of energy.”

• Energy cannot be created or destroyed, only transfer forms.

2nd Law of Therm.

• If two objects are not the same temperature then:

• Heat will always flow from high to low temperatures.o Hot object will decrease in temperature andcold object will increase in temperatureuntil they are both the same temperature.

2nd Law of Therm. Entropy is randomness, i.e., disorder, spread out,

lack of structure, messiness, etc.Entropy must increase (unless controlled by an

intelligence). Means that:Machines cannot be 100% efficient.Heat flows from hot to cold.

Examples: What happens to these if left alone?a.) A stack of lumber in the forest.b.)Your bedroom.

• Steam engines of the 1800s (video)

Cold water

Heated water

2.) Water Tank. Cold water enters, heated by fire box, exits to steam turbine.Heat lost to non insulatedwater tank and pipes.

1.) Fire box. Some heat rises up to heat water, but most escapes to air around box.

3.) Steam Turbine More heat wasted on Friction at joints.

Heat LossFire

© Jake Burkholder 2012

Heat Loss: goes where?

Heat is lost to air. It increases thetemperature of the air molecules, which means the speed of the air molecules increase, which makes them more random, i.e., it increases the entropy of air.

© Jake Burkholder 2012

So how efficient are engines?

Efficiency is Work Out = Work Out

Work In Q In

if you get 1000J of work producedgoing out and put 4000J of heat in, you have a 1000J/4000J = 25% efficient engine.

© Jake Burkholder 2012

Cold water

Heated water

Heat Loss

Fire

1.) Fire box. If only 2/7 of heat goes up to water, best efficiency is 28% (=2/7). More of the heat is lost from the hot water tank and due to friction in the turbine. These 1800 train engines were only 5 to 10% efficient.

Modern car engines are about 30% efficient. They best that modern cars can achieve is about 37% efficient.

© Jake Burkholder 2012

• Talk about the steam engines on trains in the 1800’s.

Cold water

Heated water

Heat Loss

Fire

2nd Law of Thermo leads to:Machines cannot be 100% efficient which means that 1.) you cannot build a perpetual motion machine and 2.) You cannot create energy, (i.e., efficiency cannot exceed 100%)

© Jake Burkholder 2012

New Idea

• “S” is for “Entropy”S = Q/T

• Internal Energy / Temperature (absolute)• Joule/Kelvin

What is going to happen?

• This system starts with same pressure and temperature on both sides. Then heat is applied to the left side. Which way will the boundary move? (What happens to the pressure on the left side when heated?)

What is going to happen?

The boundary will move, and temperatures and pressure will even out. 2 Actions: Increasing left pressure will push the boundary towards the right until pressures are the same. At the same time, the unequal temps will affect each other until they are equal.

• Entropy is a measure of disorder.

• In this low entropy state, there will be a net force, since there is more movement to the right than to the left.

• Operating principle of a steam engine. Some of the heat in the hot gas was turned into work done on the cold gas.

Question

• Can I get any more work out of these gasses?

Question

I would need to find a third gas sample at a lower temp to get more useful work.

Or supply my own energy to create another temperature difference.

Work of expanding gasses

• Work = (pressure times change in volume) then add all of PV together and convert to Joules

• Can be done on graph by finding area of shaded area

• See page 350• Compressed gas = negative work, expanded

gas = positive work

Thermodynamic processes

• Isothermal – temperature of system is constant, therefore internal energy is constant – all heat is converted to work

• Isochoric – volume is constant – thermal energy increases internal energy

• Isobaric – pressure is constant• Remember than energy and temperature are

linked

• Entropy is a measure of how evenly spread out the energy is.

• Entropy is a measure of energy that is no longer “useful,” or “workable.”

• Work is change in energy. It won’t change anymore if it’s spread out evenly. (Work won’t change anymore if the temperature is spread out evenly.)

• The amount of work done or the efficiency of an engine is determined by the difference in the temperatures.

• Hotter engine and cooler water makes for a greater temperature difference and more work done.

• This means: 1.) more work will be generated from an engine and2.) the engine will run more efficiently. (estimated temps.)When the temperature differences are greatest. Car Engine Metal Oil Water Air 2000F 800 F 300F 180F 70F

• The greater these temperature differences, the more energy from the car engines.

Discuss why cars overheat in winter or summer. © Jake Burkholder 2012

More examples of entropy

• Entropy is randomness. Which is more random? A or B?

A B

More examples of entropy

• 2nd Law of Therm. says that nature always goes from order to disorder.

A B

More examples of entropy

• In nature, do you move from A to B or B to A?

A B

More examples of entropy

• 2nd law says that nature always, always moves from A to B and never from B to A.

A B

More examples of entropy

More examples of entropy

• On the large scale, the ice “looks” more disordered.

• On the small scale, the solid phase severely limits where the molecules could be.

• The ice crystal molecules are much more ordered than the free moving liquid water molecules.

• Entropy is a measure of disorder.

• In this high entropy state, there will be no net force, since there is only random particle motion on both sides.

3rd law of Thermodynamics

• “Absolute zero” is a state of zero motion.–This means absolutely no entropy.–So it can’t be reached.

Entropy is a measure of repeatability

• I throw two dice. What is the most likely outcome? What is the least likely outcome?

Entropy is a measure of repeatability

• I throw two dice. What is the most likely outcome? What is the least likely outcome?

• Thirty six possible microstates – 36 ways the dice could come up.

• 11 Possible macrostates– 11 possible “scores” or states with meaningful

differences. – Macrostates with more microstates have a higher

probability of occuring.

• Since there are more disordered states than ordered states, they are inherently more repeatable.

• New symbol “W” for multiplicity W is the number of other microstates that could have the same value.

• Roll a 2? W = 1• Roll a 4? W = 3• Roll a 7? W = 6

An entropic state is more probable

• Which is more probable?

An entropic state is more probable

• Which is more probable?

• There are many more possible disordered states than ordered states, so repeatability is a sign of disorder

• How many ways can you arrange bricks into a “neat pile”?– Not that many.

• How many ways can you arrange bricks into a “total mess”?– A whole lot.

• S = k log W– k is Boltzmann’s constant

• The more repeatable the state is, the more entropy there is.

Restating the second law

• ΔS ≥ 0

• For just about every process, entropy will increase.– If you’re very, very lucky it will stay constant.

Restating the second law

• Order to disorder.

• Since disordered states have much higher multiplicity, the are much more likely, so nature will drive every system in that direction.

Entropy as “Time’s Arrow”

• Newton’s laws work equally well forwards and backwards.

• Momentum, SHM, equal and opposite reactions, all of these principles are reversible.

• The increase in entropy isn’t. An increase in disorder is the only way to tell forwards from backwards.

Time’s Arrow

Which came first?

Which direction are the balls moving?

Restatement of 2nd law

• States where energy is not spread out evenly will evolve into states where energy is spread out more evenly.

Can’t you just restack the bricks?

• Entropy can be lowered by doing work on the system.

• You can stack the bricks back up by hand.

• By providing energy, you can drive chemical reactions backwards.

Can’t you just restack the bricks?

• Entropy on a larger scale will always increase.

• The energy you put in had to come from somewhere.

• Factor in where that work came from, entropy will increase.

• If you do it yourself, you will perform chemical reactions inside you that increase entropy.

Large scale entropy

• The human body is a good example of “low entropy”.

• Think about how much matter (food) has made unusable to develop one and maintain it.

• Think about a city, and then think about how much waste it produces.

Chemical reactions occur all the time. Where does all the energy come from to lower entropy to make life possible come from?

Plants use sunlight to do work to lower entropy on sugars that get burned by every living thing on Earth.

• Now, compare the mass of every living thing on Earth to the amount of useful hydrogen that got converted to entropic helium ash in the suns core to maintain that.

• Eventually the sun will “burn out”• There won’t be enough Gibbs energy, and all

processes will stop.

Heat Death

• Eventually, all energy will be entropic.

• Chemical reactions will burn themselves out.

• Temperatures will equalize.

• Matter and energy will be spread out evenly across the universe, and no more chemical or physical processes will occur.