1. What Is Entropy?
Entropy is a measure of the disorder, randomness, or spreading out of energy in a system. A system with higher disorder has higher entropy.
Nature tends to move towards states with greater randomness because such states are more likely and more stable.
2. Microscopic Meaning of Entropy
On a microscopic level, entropy is related to the number of ways the particles in a system can be arranged. More possible arrangements mean more entropy.
2.1. Disorder and Arrangements
An ordered arrangement has fewer possibilities, so it has low entropy. A disordered arrangement has many possibilities, so its entropy is high.
2.2. Example
A deck of cards in perfect order has low entropy. Shuffling it increases entropy by creating many more possible arrangements.
3. Entropy and the Second Law
The Second Law of Thermodynamics states that the total entropy of the universe always increases in any natural process. Processes that increase entropy happen spontaneously.
3.1. Natural Direction of Processes
- Heat flows from hot to cold (entropy increases).
- Gases spread out to fill a container (entropy increases).
- Ice melts into water (entropy increases).
4. Entropy Change in Processes
Entropy changes when heat is added or removed from a system. For a reversible process:
\( dS = \dfrac{dQ_{rev}}{T} \)
where \( dS \) is the change in entropy, \( dQ_{rev} \) is the heat added reversibly, and \( T \) is the temperature.
4.1. Meaning of the Formula
More heat added at higher temperature increases entropy slightly, while adding heat at lower temperature increases entropy much more.
5. Examples of Entropy in Daily Life
- When perfume spreads in a room, particles move to a more disordered state.
- Ice melting increases entropy because water molecules move more freely.
- Hot coffee cooling down increases entropy in the surroundings.
- Mixing two liquids increases entropy because the molecules become more randomly distributed.
6. Entropy and Irreversibility
Higher entropy states are more likely and more stable, which explains why many processes are irreversible. Once energy spreads out, it is difficult to gather it back into a more ordered form without doing work.
6.1. Real-Life Examples
- Unmixing two gases is practically impossible without external work.
- A broken egg cannot return to its original form.
- Heat lost to surroundings cannot be fully recovered.
7. Entropy in Thermodynamic Cycles
Entropy plays an important role in engine and refrigerator cycles. Reversible processes keep entropy constant, while irreversible processes increase entropy.
7.1. Entropy in Heat Engines
Heat engines must reject some heat to a colder reservoir because entropy of the surroundings must increase. This limits engine efficiency.
7.2. Entropy in Refrigerators
A refrigerator decreases entropy inside by removing heat, but overall entropy increases because the compressor adds heat to the surroundings.