Thermodynamics9-12

What you absolutely have to know aboutThermodynamics to pass the AP Physic B test!

Why Heat flows from Hot to Cold, Entropy, and the 2 nd Law of Thermodynamics Molecules are in constant random motion. On average “hot” objects have faster moving molecules than “cold” objects. As you can see in the graph at the right, it is possible for some of the “cold” molecules to be moving faster than the “hot” molecules. However, on average, the “hot” molecules are moving faster.

Why does heat always move from hot to cold? Molecules in a hot object tend to collide and transfer more energy to the molecules in a cold object because they are moving faster. (Conservation of Momentum.)

Is it possible for a “cold” molecule to collide and transfer energy to the “hot” molecule? Sure! But on average it is much more likely for energy to transfer from “hot” to “cold”. Just like it is much more likely for a speeding car to transfer energy to a slow moving car in a collision than the other way around. For net heat to transfer from a cold object to a hot object most of the “cold” molecules would have to transfer energy to the “hot” molecules. While this might be theoretically possible in the magic would of physics, it is statistically and practically impossible.

When does the heat transfer between objects stop? In reality the heat transfer between objects never really stops. Hot objects transfer lots of heat to cold objects. But remember that “cold” objects have a few fast moving molecules that can transfer heat to the “hot” object. Overall, the net heat transfer is from hot to cold. (See the diagrams to the right.) Once the two objects reach the same temperature, the average molecular motion is the same for both. So, they transfer heat back and forth between each other at equal rates. When two objects have the same temperature they are in Thermal Equilibrium and the net heat transfer between them is zero.

What is Entropy?Entropy is a measure of disorder. Objects that are colder have less entropy because they have less random motion in their molecules. Hot objects have higher entropy. When a hot “high entropy” object is placed next to a cold “low entropy” object heat is exchanged. The hot object looses entropy and the cold object gains entropy.

The equation for change in entropy is: . Calculating the entropy lost by the hot object and gained

by the cold object, you will find that the overall entropy of the system has actually gone up! The disorder of the system as a whole has increased because the “hot area” is no longer separated from the “cold area”. The thermal energy has been “mixed up” into an overall disorderly “warm”. Remember for the AP Exam: When heat flows into a system entropy increases and when heat flows out of a system entropy decreases.

The 2 nd Law of Thermodynamics is a statement that tells us the direction energy will move:The entropy of an isolated system either remains the same or increases until equilibrium is achieved.

Here are two of the important consequences of the 2nd Law: 1) Net heat always moves from hot to cold until thermal equilibrium is achieved. 2) Kinetic and potential energies are “ordered” forms of energy. They can spontaneously and completely be

converted into “random” thermal energy. Thermal energy won’t spontaneously convert into other forms of energy. In fact, it is impossible to completely convert thermal energy into other forms of energy.

Chris Bruhn Page 1 4/18/[email protected](972) 749-2314

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So what the heck to do we use all this stuff for? The Heat Engine

Heat naturally moves from hot places to cold places. As the hot place cools off and the cold place warms up the heat transfer slows. When the two locations finally reach the same temperature the heat transfer stops.

This process is represented below in an Energy-Transfer Diagram.Notice something very important: The heat flow out of the hot place = the heat flow into the cold place!

What we want to do is steal or “siphon off” some of this energy as it moves from the hot place to the cold place. This stolen energy can be used to do useful work like generating electricity or moving our car down the street. The problem is that we can only siphon off energy while heat is being transferred. Once the hot place cools off the heat flow stops and we can’t steal any more energy.

We solve this problem by either finding or making an energy reservoir. An energy reservoir is an object or part of the environment that is so big that its temperature and thermal energy don’t change very much when heat flows into or out of it. For instance: 1. When you jump into a pool to cool off you don’t change the temp of the pool very much because it is so big.

The pool is an example of a Cold Reservoir. Cold reservoirs absorb heat without increasing in temperature.2. If you place your hand in a fire, your hand will heat up. However, the fire does not cool down very much

because it has a fuel source to burn that keeps it hot. The flame is a Hot Reservoir. A hot reservoir gives off heat without loosing its hot temperature.

Here is an example: Build a fire (hot reservoir). As the heat (Q) from the fire naturally flows to the atmosphere (cold reservoir) you steal some of the energy as use it to do work. As long as you have fuel to keep the fire hot, you can siphon off energy.

The device that is used to siphon off the energy is called a Heat Engine. The energy-transfer diagram of a heat engine is shown at the right. The Heat that flow out of the hot place is labeled . The Heat that flows into the cold place

is labeled . The energy that is siphoned off to do useful work is labeled .




Notice several things about a Heat Engine. The heat that exits the hot place is no

longer equal to the heat entering the cold place .Conservation of Energy tell us that the work stolen from the system must be

or .Look at the energy-transfer diagram at the right. If 100J of heat energy leaves the hot place and we steal 40J of it to run a machine only 60J of heat energy is let to flow into the cold place.

Heat Engine Efficiency:The more heat we siphon off the more efficient our heat engine is. The efficiency of our heat engine is equal to

the work we can get it to do divided by how much available heat we had to steal from:

At this point some of you are thinking… “Why don’t we just turn all of the heat ( ) into work ( ) and produce a heat engine with 100% efficiency?” This is indeed a great idea but unfortunately, it can not be done because it violates the 2nd Law of Thermo by turning disordered thermal energy completely into ordered work. There is always wasted thermal energy in a heat engine. Efficiency ( ) is always less than 1 or 100%.

What does a Heat Engine look like on a pV diagram?On a pV diagram, a heat engine will be a cycle that moves in a clockwise direction. Here is an example:




Continued on the next page!

How does all this relate to our heat engine? First of all, remember our energy-transfer diagram for a heat engine shown to the right. Remember that is shows heat flowing in from a hot place and them work being siphoned off and the rest of the heat moving away to a cold place.

Now lets look at our pV diagram again and the data table we just calculated:

Where is the heat flowing into the cycle on the pV diagram? In other words, where is ? It is .

Where is the heat flowing out of the cycle? Where is ? It is the combination of .

How much work is siphoned off in the cycle? It is the net work of the cycle:

Remember that for a heat engine: and this is true:

What is the efficiency of this heat engine?

An energy-transfer diagram shows only the net energy flow for a heat engine in a very general picture. A pV diagram shows all the details of what is going on inside the gas as the heat engine is operating.Both diagrams show the same heat engine in a different format.




A heat engine takes advantage of the natural flow of heat from hot to cold and uses it to produce useful work.



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Thermodynamics9-12