Intro to the Second Law of Thermodynamics Reference Page
Resistance is Futile. Entropy Always Wins

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Intro to the Second Law of Thermodynamics

The First Law of Thermodynamics states that energy is conserved, but it does not determine whether a process can actually occur.

The Second Law of Thermodynamics introduces directionality to thermodynamic processes.
It explains why heat flows from hot to cold, why engines cannot be perfectly efficient, and why entropy tends to increase.

Resistance is Futile. Entropy Always Wins

This video introduces the Second Law of Thermodynamics, heat engines, and the concept of entropy.

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Examples and Definitions

Definitions

The Second Law of Thermodynamics
The Second Law can be expressed in several equivalent forms:

Kelvin–Planck Statement
No device operating in a cycle can convert heat absorbed from a reservoir completely into work.

Equivalent statement
It is impossible by a cyclic process to convert all absorbed heat into work.

Clausius Statement
No process is possible whose sole effect is the transfer of heat from a colder body to a hotter body.

Heat Engine
A (usually cyclic) system that converts thermal energy (heat) into mechanical work.
Heat-Engine or Thermal Efficiency, \(\eta\)
The ratio of the work produced by a heat engine to the heat extracted from the high-temperature reservoir.

\[ \eta \equiv \frac{|W|}{|Q_\mathrm{hot}|} \]

Isothermal Heat Reservoir
A system that can absorb or supply heat while remaining at essentially constant temperature.

Any real reservoir has finite capacity. A common example is a well-mixed container of ice and liquid water at atmospheric pressure, which remains at \(0\ ^\circ\mathrm{C}\) until the phase change is complete.

Carnot Engine
A theoretical heat engine that operates with the maximum possible efficiency between two thermal reservoirs.

Its efficiency depends only on the temperatures of the reservoirs:

\[ \eta = 1 - \frac{T_\mathrm{cold}}{T_\mathrm{hot}} \]

where the temperatures are absolute temperatures.

Carnot Efficiency
The maximum theoretical efficiency for any heat engine operating between two reservoirs:

\[ \eta = 1 - \frac{T_\mathrm{cold}}{T_\mathrm{hot}} \]

Entropy
A thermodynamic property that measures the degree of energy dispersal within a system.

For a reversible heat transfer,

\[ dS = \frac{\delta Q_\mathrm{rev}}{T} \]

Entropy provides a criterion for the direction of spontaneous processes and plays a central role in the Second Law of Thermodynamics.