# Second Law of Thermodynamics

The second law of thermodynamics states that, Whenever a spontaneous process takes place, it is accompanied by an increase in the total energy of the universe”.

More specifically the term universe means the system and the surroundings, thus,

$\Delta S_{univ.} = \Delta S_{syst.} + \Delta S_{surr.}$

The second law as stated above tells us that when an irreversible spontaneous process occurs, the entropy of the system and the surrounding increases. In other words$\Delta S_{univ.} > 0 (zero)$, when reversible process occurs, the entropy of the system remains constant. $\Delta S_{surr.} = 0$.

Since the entire universe is undergoing spontaneous change, the second law can not be most generally and concisely stated as the entropy of the system is constantly increasing.

(1)    Kelvin-Planck statement

“It is impossible to construct a heat engine which, operating in cycles, can perform work at expense of heat obtained from a single thermal reservoir”.

(2)    Planck statement

“It is impossible to construct a device which will work in a complete cycle and to convert heat into work without producing any change in the surroundings”.

(3)    Clausius statement

“It is impossible for a self active machine, unaided by any external agency, to transfer heat from a body at a low temperature to one at a higher temperature”.

(4)    Ludwig Boltzmann statement

According to this “Nature tends to pass from a less probable to more probable state”.

(5)    It is impossible to construct a heat engine (of) 100% thermal efficiency.

(6)    The Entropy of the universe increases in a spontaneous process and remains constant in an equilibrium process-

$\Delta S_{univ.} = \Delta_{syst.} + \Delta S_{surr.}$

For a spontaneous process:

$S_{univ.} > zero$

At equilibrium

$\Delta S =zero$

Although the second law has been stated in a number of ways but all the statements ultimately are modifications of the same fundamental concept i.e. work can always be converted into heat but the conversion of heat into work does not take place under all conditions.

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