AP® Physics 2: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics-2/units/9/9-6)
Unit 9 · Topic 9.6
9.6 Entropy and the Second Law of Thermodynamics
Entropy describes how spread out a system's energy is, and how much of it can no longer be used to do work. The second law of thermodynamics says the total entropy of an isolated system never goes down. That's why some processes only run one way, like ice melting in a warm room. In AP Physics 2 this is all qualitative.
Key terms
- entropy
- second law of thermodynamics
- isolated system
- closed system
- state function
- thermodynamic equilibrium
What entropy means
Energy that's packed into one place tends to spread out. A hot cup of cocoa warms the room; a puff of perfume fills the air; a gas released into an empty box spreads to fill it. Entropy is a way of describing that spreading. The more spread out the energy, the higher the entropy.
Entropy also tells you how much of the energy is unavailable to do useful work. Concentrated energy, like the internal energy of a hot block next to a cold one, can be used to run something. Once both have reached the same temperature, the total energy is the same, but you can no longer use that temperature difference to do work.
The second law
The second law of thermodynamics says the total entropy of an isolated system never decreases. It stays constant only for an ideal reversible process; every real process makes it increase.
Energy conservation alone doesn't forbid a cold room from heating a cup of coffee. The second law does: that would concentrate energy instead of spreading it, so entropy would drop. It's not that each atom is forbidden from doing it. With so many atoms, the spread-out arrangements are overwhelmingly more likely than the concentrated ones.
State function and equilibrium
Entropy is a state function: once you know a system's present condition (its temperature, volume and so on), its entropy is set. The history of how it got there doesn't matter, so two different paths between the same two states give the same change in entropy.
An isolated system moves on its own toward thermodynamic equilibrium, where nothing is changing on the large scale. Entropy is at its maximum there. A hot and a cold block sealed in an insulated box keep exchanging energy until they share one temperature; then the entropy can't climb any higher.
Isolated versus closed systems
An isolated system exchanges neither matter nor energy with its surroundings, so its entropy can't decrease. A closed system exchanges energy but not matter, so its entropy can go down if energy leaves it.
A freezer turns liquid water into ice, which is more ordered, so the water's entropy decreases. That doesn't break the second law, because the freezer pushes energy out into the kitchen. The kitchen's entropy rises by more than the water's falls, so the total entropy of everything involved still goes up.
You won't calculate entropy values (no equations like ΔS = Q/T) in this course. Expect to describe and compare entropy changes in words.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Ice cube in a warm room
An ice cube melts on a table in a warm room. Describe the entropy changes of the ice, of the room, and of the ice and room together.
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- Step 1: Energy flows from the warmer room into the colder ice (9.3), so the ice gains energy, and its molecules go from an ordered solid to a liquid. The ice's entropy increases.
- Step 2: The room loses energy, so its entropy decreases a little.
- Step 3: Treat the ice plus the room as an isolated system. The process happens on its own, so by the second law the total entropy increases: the ice's gain is bigger than the room's loss.
Answer: Ice: increases. Room: decreases slightly. Total: increases.
- Example 2
Gas filling a box (classic trap)
An insulated box is split by a wall, with gas on one side and empty space on the other. The wall is removed and the gas spreads to fill the box. A student says the entropy can't change because no energy entered or left. Is the student right?
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- Step 1: The box is isolated, so its total energy stays the same, and the student is right about that.
- Step 2: But entropy is about how spread out the energy is. The atoms, and their energy, are now spread through twice the volume, so the entropy increases.
- Step 3: The gas will never gather itself back into one half on its own, because that would lower the entropy of an isolated system.
Answer: No. Energy stays the same, but entropy increases as the gas spreads out.
Common mistakes
- Thinking entropy can never decrease anywhere. Only the total entropy of an isolated system can't drop; a closed system can lose entropy when energy leaves it.
- Treating entropy as the same thing as energy. Energy is conserved; entropy describes how spread out that energy is, and it can increase.
- Assuming entropy depends on the path taken. It's a state function, so only the starting and ending states matter.
On the exam
- Expect questions asking whether the entropy of a system goes up, down or stays the same, with a justification that names whether the system is isolated or closed.
- Strong answers connect entropy to energy spreading out and to the most probable state of many atoms.
Connected topics
Videos
Check yourself
4 questions on 9.6 Entropy and the Second Law of Thermodynamics. Pick an answer to see if you got it, and why.
Which of the following could NOT happen on its own in an isolated system?
Water in a freezer turns to ice, and its entropy decreases. Why doesn't this break the second law of thermodynamics?
A gas is taken from state 1 to state 2 by a fast process in one trial and by a slow process in another trial. How do the changes in the gas's entropy compare?
A box is split by a divider. One side holds a gas and the other side is empty. The divider is removed, and the gas spreads to fill the box. Which is true?
0 of 4 answered