# Which is the second law of thermodynamics?

There are many statements. https://en.wikipedia.org/wiki/Second_law_of_thermodynamics#Various_statements_of_the_law

But how do they say the same thing ? I don't understand. Why all of them are the same ?

• They are all equivalent. The most simple formulation is the one by Clausius, which is simply the definition of temperature. It says that, unless something else happens, heat only flows from hot to cold. That's it. Just like Newton's second law says that force is that which accelerates massive bodies, the second law of thermodynamics says that temperature (difference) is that, which makes heat flow. There is no other definition of temperature. Entropy and everything else can be derived from this by means of some fairly simple logical arguments which you can find in thermodynamics textbooks. Mar 13, 2016 at 7:28
• @CuriousOne, temperature was known before 2nd law of thermodynamics. It is only the absolute (Kelvin) temperature that is based on 2nd law of thermodynamics. Mar 13, 2016 at 10:25
• @JánLalinský: The question wasn't about the history of temperature but about the different versions of the second law of thermodynamics. If you are looking for a formal definition of temperature (and which physicist wouldn't?), then citing Clausius is the right choice. Other temperature scales than the absolute thermodynamic scale have no physical significance and we shouldn't be teaching that they do. Mar 13, 2016 at 10:32

The statement of the second law of thermodynamics that you have read about are all equally equivalent.

The one with entropy in it is more used because entropy is a state function and a numerical value can be assigned to its change.

The other statements of the second law are statements which are more qualitative and are about those processes which cannot happen. As such they are possibly less used unless the second law is to be introduced without any mention of entropy?

• All statements are equally quantitative, you just have to know how to read them. The second law doesn't tell you anything in detail about the entropy of a system, so it's not somehow "more" quantitative than the others. The entropy of a system is something that you have to measure. It can't be derived from first principles in thermodynamics. It can, in principle, be derived from first principles in statistical mechanics, but that's a pain for most non-trivial systems. Mar 13, 2016 at 8:13
• @CuriousOne I entirely agree with you but once entropy has been defined I think that because entropy can be measured the statement with entropy in it is used more (rather than useful). I did say that they were all equivalent and agree that I should have added the word "equally". Do you think I should change my answer to reflect your comment? Mar 13, 2016 at 9:12
• The derivation of the existence of entropy from the Clausius formulation is in every solid textbook on thermodynamics (or should be). Entropy is one of those double-edged swords... unless you are a chemist or process engineer, you are very likely to fall in it and cut yourself on it, but you are not likely be able to fight the enemy (an actual physical, chemical or technical process) with it. It doesn't really help the beginner to understand thermodynamics. Clausius does. You know what's the actual joke, though? That the very people who hand wave with entropy often don't know Clausius. Mar 13, 2016 at 9:20

The Second Law of thermodynamics simply states that entropy increases. For example when salt dissolves in liquid water, the amount of entropy or randomness increases with time. See A link from Georgia State University

The second law of thermodynamics explains the feasibility and spontaneity of a process. It was formulated to overcome the shortcomings of the first law i.e. feasibility and direction.

In essence, all specify similar ideas,

1. A process in which entropy increases tends to be spontaneous.
2. Heat naturally flows from hot to cold in the absence of any work.
3. Efficiency is never unity.
• Is temperature fluid?
– user36790
Mar 13, 2016 at 7:53
• @user36790 Sorry, I meant heat. Mar 13, 2016 at 7:54
• The first law of thermodynamics doesn't have any "shortcomings". It's the equivalence of heat and energy and it extends the energy conservation law to heat. The second law is the definition of temperature, which is completely independent of the first law (which, if you look carefully) doesn't say anything about temperature. The second law doesn't say anything about spontaneity of entropy increasing processes, it also doesn't say anything about efficiency, which can be (infinitesimally close to) unity, just not for a cyclical process. You need to read CAREFULLY. Mar 13, 2016 at 7:55
• The first law does not completely explain the concept of heat transfer. It only merely states that there is transfer of heat, nothing more. The second law gives the details. Is it not so? Mar 13, 2016 at 8:01
• The first law doesn't say anything about heat transfer. Read the statements carefully. Mar 13, 2016 at 8:08