Explaining the entropy concept and entropy components

2017-09-25T20:42:15Z (GMT) by Marko Popovic
Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy <i>S<sub>TM</sub></i> as a function of temperature <i>T</i> and heat capacity at constant pressure <i>C<sub>p</sub></i>: <i>S<sub>TM</sub></i> = <i>∫(C<sub>p</sub>/T) dT</i>. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state). It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy <i>S<sub>0</sub></i> as a function of the number of molecules <i>N</i> and the number of distinct orientations available to them in a crystal <i>m</i>: <i>S<sub>0</sub> = N k<sub>B</sub> ln m</i>, where <i>k<sub>B</sub></i> is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system <i>S</i>: <i>S = S<sub>0</sub> + S<sub>TM</sub></i>. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.