Repository: DepositOnce – institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - EJOUR
AU - Hoffmann, Hans‐Jürgen
PY - 2020
TI - From heat to entropy
T2 - Materialwissenschaft und Werkstofftechnik
DO - 10.1002/mawe.202000067
UR - https://doi.org/10.1002/mawe.202000067
VL - 51
IS - 9
SP - 1191
EP - 1233
N1 - Available Open Access publishedVersion at https://depositonce.tu-berlin.de/handle/11303/12366
LA - en
AB - Milestones in the development of thermodynamics are the discovery of the absolute temperature scale and the recognition that differential “heat” is a form of energy given as the product of absolute temperature and differential entropy. Following a new path, the last statement results from a careful analysis of the heat transfer applying the first theorem without reference to the usual cycles in thermodynamics. This confirms also characteristic properties of entropy. In particular, the total entropy can never decrease in a process. In thermal equilibrium, the differential thermal energy is proportional to the differential entropy with the constant of proportionality being the temperature of the heat and entropy. Hence, thermal energy and entropy are transferred simultaneously into the same storage facilities, some of which are mentioned. However, the issue which one is the superior quantity is obsolete. The entropy is maximum for a given amount of exchanged thermal energy and, vice versa, for a given amount of exchanged entropy the concomitant energy is minimum. We calculate the thermal energy and entropy of phonons (as bosons) in oscillators and of electrons (as fermions) in their states of solids and melts as examples from statistical thermodynamics. The thermal energy or heat is the sum of the energies of all bosons and fermions in their elementary states or quantum states according to Bose Einstein and Fermi Dirac statistics in thermal equilibrium minus the total energy in the limit T→0 K. The entropy can be written as mixing entropy of all of these quantum states weighted with their occupancies, in agreement with an earlier publication. Thus, entropy is a logarithmic metrics of the number of all possible variants to distribute the respective total energy over all elementary states in thermal equilibrium.
KW - thermal energy
KW - entropy
KW - mixing entropy
KW - statistical entropy
KW - thermal equilibrium
KW - negative absolute temperature
KW - Wärme
KW - thermische Energie
KW - Entropie
KW - Mischungsentropie
KW - statistische Entropie
KW - thermisches Gleichgewicht
KW - negative absolute Temperatur
ER -