The second law of thermodynamics is very useful because it can not only help us design efficient machines but also explains the arrow of time(which direction a process will follow). This law has been stated at least in three different yet equivalent forms:

Clausius’s Statement

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

Note that the words “sole result” are important here. No process in isolation can occur when the heat flows from colder to hotter body. Otherwise a warm cup of tea put in a cold room would get hotter and hotter until it burst into pieces.

Kelvin’s Statement

No process is possible whose sole result is the complete conversion of heat into work.

Again, the words “sole result” are important. If this weren’t true, we could have perpetual motion and an infinite supply of energy which would violate the first law of thermodynamics.

Carnot’s Theorem

Of all the heat engines working between two given temperatures, none is more efficient than a Carnot Engine.

By heat engines, we mean machines that produce work from a temperature difference between two heat reservoirs. An engine is a system that operates a cyclic process to generate (convert heat into) work. The efficiency of the Carnot Engine is

    \[\eta_{Carnot }=1-\frac{T_{l}}{T_{h}}\]

Where Tl and Th represent temperatures of the colder and hotter reservoirs respectively.

Yet another, more concrete form of the second law is the statement that

Entropy of the Universe always increases.

    \[\Delta S \geq 0\]

Entropy is related to the degree of randomness in a system. However, it is more subtle than that and involves the possible arrangements of microstates of a system.

Second Law of Thermodynamics
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