What does the Second law define most fundamentally among thermodynamic quantities?

Introduction / Context:
The First law introduces energy conservation and defines internal energy differences. The Second law introduces directionality and the concept of entropy, enabling statements about feasibility and efficiency beyond mere energy accounting.

Given Data / Assumptions:

• Closed or open systems exchanging heat and work.
• Thermal reservoirs at absolute temperatures.
• Reversible and irreversible processes considered.

Concept / Approach:

The Second law defines entropy (S) through inequalities and equalities relating heat transfer and absolute temperature. For reversible processes, dS = δQ_rev / T. For any process, ΔS_total ≥ 0. This definition allows quantifying irreversibility and setting the maximum efficiency of heat engines and refrigerators.

Step-by-Step Solution:

Verification / Alternative check:

Entropy balance predictions match real observations (e.g., mixing increases entropy, heat flows from hot to cold spontaneously).

Why Other Options Are Wrong:

Heat and work are modes of energy transfer defined operationally, not by the Second law.Internal energy is defined via the First law and state equations.Temperature scale can be related to the Second law, but the property most directly defined is entropy.

Common Pitfalls:

Equating the Second law only with heat-engine limits; its deeper role is defining entropy and irreversibility.

Final Answer:

entropy