Does the second law say entropy always increases everywhere?

It says the total entropy of an isolated system does not decrease. Entropy can fall locally if a larger increase occurs elsewhere, so order can grow in one place at the cost of greater disorder in the surroundings.

Why can no engine be perfectly efficient?

Converting all absorbed heat into work with no waste would violate the Kelvin-Planck statement; some heat must always be rejected to a colder reservoir, capping efficiency at the Carnot value set by the reservoir temperatures.

Second Law and Entropy

The second law of thermodynamics introduces entropy and the irreversibility of natural processes, asserting that the entropy of an isolated system never decreases.

Definition

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time and is constant only for reversible processes, establishing entropy as a state function and a direction for spontaneous change.

Scope

This topic covers the equivalent statements of the second law (Kelvin-Planck and Clausius), the Carnot cycle and its maximal efficiency, the Clausius inequality, the definition of entropy as a state function, and reversible versus irreversible processes. The connection to the arrow of time and to available work is included; the microscopic statistical definition of entropy is developed in the statistical-mechanics areas.

Core questions

Why are the Kelvin-Planck and Clausius statements of the second law equivalent?
How does the Carnot cycle set an upper bound on the efficiency of heat engines?
How does the Clausius inequality lead to entropy as a state function?
In what sense does the second law define the arrow of time?

Key concepts

Kelvin-Planck and Clausius statements
Carnot cycle and maximal efficiency
Clausius inequality
Entropy as a state function
Reversibility and irreversibility

Key theories

Carnot's theorem: All reversible heat engines operating between the same two temperatures have the same efficiency, and no engine can exceed it, establishing an absolute limit on converting heat into work.
Entropy and the Clausius inequality: For any cyclic process the integral of dQ/T over the cycle is non-positive, vanishing only for reversible cycles; this defines entropy as a state function whose change measures irreversibility.

Clinical relevance

The second law sets the ultimate efficiency limits of power generation and refrigeration, governs the spontaneity of chemical and biological reactions through entropy and free energy, and frames foundational questions about irreversibility and the thermodynamic arrow of time.

History

Carnot's 1824 study of ideal engines gave the second law its first form; in the 1850s and 1860s Clausius and Kelvin sharpened it into general statements and Clausius introduced entropy, giving irreversibility a precise quantitative meaning.

Debates

Origin of the arrow of time: Whether the macroscopic increase of entropy can be fully reconciled with time-reversible microscopic dynamics remains debated, with explanations leaning on special low-entropy initial conditions of the universe rather than the dynamical laws alone.

Key figures

Sadi Carnot
Rudolf Clausius
William Thomson (Lord Kelvin)

Seminal works

carnot1824
clausius1865

Frequently asked questions

Does the second law say entropy always increases everywhere?: It says the total entropy of an isolated system does not decrease. Entropy can fall locally if a larger increase occurs elsewhere, so order can grow in one place at the cost of greater disorder in the surroundings.
Why can no engine be perfectly efficient?: Converting all absorbed heat into work with no waste would violate the Kelvin-Planck statement; some heat must always be rejected to a colder reservoir, capping efficiency at the Carnot value set by the reservoir temperatures.