Even when energy is conserved, natural processes have a direction. We will understand “irreversibility” through the second law of thermodynamics and the concept of entropy.
Basic Knowledge
The second law of thermodynamics has several equivalent formulations:
・Clausius statement: Heat does not naturally move from a low-temperature object to a high-temperature object
・Kelvin–Planck statement: A cycle that absorbs heat from a single heat source and converts it entirely into work is impossible (denial of a perpetual-motion machine of the second kind)
Entropy S is a measure of the “randomness (degree of disorder)” of a system.
Infinitesimal entropy change in a reversible process: dS = dQ/T
Law of increasing entropy: In an isolated system, entropy increases or remains constant (ΔS ≥ 0).
Reversible process: ΔS = 0; irreversible process: ΔS > 0.
Second law of thermodynamics (a law that determines the direction of natural processes; the basis of reversible and irreversible processes)
Entropy S [J/K] (a measure of a system’s randomness and disorder; dS = dQ/T)
Reversible / irreversible process (a process whose reverse can / cannot be completely realized)
Efficiency η of a heat engine (η = W/QH = 1 − QC/QH; W: work, QH: heat absorbed from the hot source, QC: heat released to the cold source)
Perpetual-motion machine of the second kind (a hypothetical machine that continuously extracts all work from one heat source; impossible to realize)
Further Exploration (Background and Significance)
Boltzmann defined entropy statistically as S = kB ln W (kB: Boltzmann constant, W: number of microscopic states). This mathematically shows that the probability of a gas naturally gathering in half of a container is astronomically small.
The law of increasing entropy is also said to provide the basis for the arrow of time. Many fundamental laws of physics are time-reversal symmetric, but only the second law gives time a direction.
Entropy appears in many fields of physics, including information theory (Shannon entropy) and the Bekenstein–Hawking entropy of black holes.
- First law = conservation of energy; second law = direction of change
- Heat naturally moves only from high temperature to low temperature
- Increasing entropy: In an isolated system, ΔS ≥ 0
- Reversible process: ΔS = 0 (an ideal limit)
- The second law of thermodynamics rejects perpetual-motion machines of the second kind
Points to Note (Common Confusions)
① Increasing entropy applies to an isolated system. An open system (such as a refrigerator) can locally decrease entropy, but entropy increases when the surroundings are included. ② The second law does not include the first law; it concerns direction. ③ Clearly understand the correspondence “irreversible = increasing entropy” and “reversible = no entropy change.” ④ dS = dQ/T holds exactly only for reversible processes.
Practice
- State the Clausius formulation of the second law of thermodynamics in one sentence.
- 600 J of heat moved reversibly from an object at 300 K. Find the change in entropy.
- Based on the second law of thermodynamics, explain why no natural process exists in which entropy decreases in an isolated system.