The situation with a simple two-energy level system does illustrate a situation where temperature can increase (in this case it is increasing by becoming less negative) while the entropy decreases. As you ( ) implied: It's very much a case of needing to keep our definitions of temperature straight (and it does become a little dull then). if the energy is increasing, and the entropy decreasing, then the system has a negative temperature (ie below absolute zero) One reasonable definition of Temperature is: T = ∂U/∂S (constant volume). Think this isn't realistic? It's how lasers work.Īlso, going back to my initial remark about temperature: I never said anything about the temperature of the system of bits, only that you are adding energy. But once the 50/50 state is reached, any additional energy going in is going to decrease the entropy of the system, until finally it is 100% energized, and has regained its initial low entropy. Initially the entropy increases with increasing temperature. Imagine all the bits start out in the low energy state, and you start feeding energy into the system. More broadly, we can imagine any system made up of bits that can be in two states (one high energy, one low). If some light is absorbed, the resulting system has both more energy and less entropy than it did before (it's not a closed system). The first example that springs to my mind is the electronic structure of a transition metal ion. There are plenty of systems one can imagine (or even observe!) in which increasing energy of the system results in there being fewer available micro-states, and therefore lower entropy. I think you need to be careful about specifying whether you mean temperature or thermal energy. Also, using a statistical mechanics definition of entropy you don't seem to be asking for too much: If there was a substance where you can increase the total energy content from E i to E f but the number of microstates availble for total energy E f is less than the number of microstates available for total energy E i - then you would seem to be on to something.) I'm asking because I don't know for certain if there is a substance with C v < 0. (It doesn't seem possible to me, using a thermodynamic definition of entropy, just because C v = specific heat capacity at constant volume is always positive for every substance I know about. Now if we insist that all changes are restricted to maintaining a constant volume, we have the question that I was really hoping to ask: Is there a substance where the temperature can be increased but the entropy of that substance decreases and all changes are done at constant volume? There are probably other examples but you can hopefully see that the situation or the combination of changes you make, can be as important as the substance you choose. You can determine this by looking at the Sackur-Tetrode equation for the entropy of an ideal gas. It should be possible to reach a higher final temperature but lower final entropy. An ideal gas, starting from an initial state with pressure and volume P i and V i can be subjected to compression (to a volume V f < V i ) and then some surplus heat can be removed while maintaining the volume at V f. Typically when you transfer heat to a substance, its temperature increases and also the entropy of that substance (or the entropy of the system which is just that substance) increases. 4, 086002 (2020).I apologize for the title, it had to be very compressed to fit in the space available. Seto, M., Yoda, Y., Kikuta, S., Zhang, X. Nuclear Condensed Matter Physics Using Synchrotron Radiation (Springer, 2005). Invar and Elinvar, Nobel Lecture (The Nobel Foundation, 1920). Now, writing in Nature Physics, Stefan Lohaus and colleagues have reported that a cancellation between the contributions of atomic vibrations and magnetic spins to Invar’s thermal expansion may explain its special behaviour 3. Over the years, various models and theories have been proposed but a full solution to the so-called Invar problem 2 has remained elusive. More recently, large slabs of Invar can be found in many laser optics applications that require any thermal expansion in apparatus to be smaller than optical wavelength scales. Its properties helped to increase the reliability and accuracy of spring watches and enabled the construction of instruments that provide atomic time standards. At the time of its discovery, this unusual property had a considerable effect on engineering of new instruments for precision metrology, for which its discoverer Charles Édouard Guillaume was awarded the Nobel Prize in Physics in 1920 1. Invar is a magnetic iron–nickel alloy that displays almost no change in length and volume upon change of temperature.
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