# Why do you need more energy to return an object to ordered state?

Someone said that you need more energy to put together broken glass than it took to shatter it. But wouldn't we be creating energy in such a closed system?

• At zero temperature, the energies would be the same. For finite temperature, the second law of thermodynamics says that there must be some heat associated with the entropy and the temperature. I think this is what "someone" meant. – Marius Ladegård Meyer Oct 5 '19 at 11:48
• @marius I don't understand why you don't add that as an answer? Why not? I would have upvoted? – Jossie Calderon Oct 5 '19 at 12:31
• Sorry, I did not have time to post something detailed and what I wrote seemed a little shallow to me. Please see my posted answer. – Marius Ladegård Meyer Oct 5 '19 at 12:48

The reason you need to supply more energy than was used to shatter the glass, is that a macroscopic piece of glass is subject to the laws of thermodynamics. Remembering that the definition of temperature is given by the derivative of the internal energy wrt. entropy,

$$T := \frac{\partial U}{\partial S}$$

this leads to the classical formula

$$dQ = T dS$$

where $$dQ$$ is the heat generated by the change in entropy $$dS$$ at temperature $$T$$. Note at zero temperature, the energy of restoration would have been the same as shattering. But at finite $$T$$, there is always some heat, and that energy has to come from somewhere.

• So isn't it a bit of a misnomer? Heat remains thermal energy in a closed system, so we just use that same amount of heat to "glue" the glass. – Jossie Calderon Oct 5 '19 at 13:41
• No, if we could do that then we would be violating the second law of thermo. The heat is generated when we interact with the glass from "the environment", because we have to interact from outside the glass system in order to repair it in the first place. – Marius Ladegård Meyer Oct 5 '19 at 13:43
• @Marius Ladegård Meyer, I do not quite understand what kind of change in entropy $dS$ is involved? Or do you think the process of breaking a glass on macroscopic pieces is similar, for example, to evaporation? – Aleksey Druggist Oct 5 '19 at 22:18
• @Marius but what if we were already part of the glass system? For example, what if we shattered it with a hammer? – Jossie Calderon Oct 6 '19 at 10:56
• @JosseCalderon I don't understand this commemt. You shatter glass by interacting with the glass system and the external hammer through a non-spontaneous process. – Marius Ladegård Meyer Oct 6 '19 at 11:16