Fastest Frozen Temperature:Definition,significance And Applications

The equipartition theorem states that the mean thermal energy for each degree of freedom at a temperature T is given by kBT/2 where kB is Boltzmann's constant.The third law of thermodynamics states that any heat capacity of the system tends to zero when the temperature approaches absolute zero.For a thermodynamic system obeying both the equipartition theorem in hightemperature and the third law in low-temperature,the curve showing relationship between the specific heat and the temperature has two common behaviors:it terminates at zero when the temperature is zero Kelvin and converges to a constant value of specific heat as temperature is higher and higher.Since it is always possible to find the characteristic temperature Tc to mark the excited temperature as the specific heat almost reaches the equipartition value,when the temperature of the system exceeds the characteristic temperature TC,the system can be considered to satisfy classical statistics.Note that the definition of temperature is quite arbitrary,for example,the definition of the reciprocal of the general temperature 1/T can be called temperature.Then there must be another the low-temperature characteristic temperature complementary to the high-temperature characteristic temperature.When the temperature is lower than the low-temperature characteristic temperature,the heat capacity of the system is basically zero.This paper mainly studies the low-temperature characteristic temperature which is complementary to the characteristic temperature in the low-temperature range in the thermodynamic system,and discusses its application and significance.This thesis mainly composed of four parts.In the first part,we introduce the two theorems that the equipartition theorem and the third law of thermodynamics,which followed by the thermodynamic system.The original characteristic temperature Tc is used to mark the excitation temperature,but there is no temperature complementary to Tc in the low-temperature range.For example,in the Debye model of solid heat capacity,the Debye temperature is the high-temperature characteristic temperature,but there is no corresponding lowtemperature characteristic temperature in the low-temperature range.When temperature is lower than this temperature,the Debye T3 law works.In the second part,taking the solid Debye model as an example,define the lowtemperature characteristic temperature complementary to the characteristic temperature Tc in the low-temperature interval,which is called the fastest frozen freezing temperature g.In the third part,a theorem is proposed.First,a model system with a certain degree of freedom is constructed,and the partition function of the Boltzmann statistics in the D dimensional space is given.Then the energy and specific heat of each particle in different spatial dimensions are calculated.Finally,the fastest frozen temperature g is calculated and analyzed.The Fermi and Bose systems are also discussed.In the fourth part,examples are given to illustrate the fastest frozen temperature g,including the freedom of vibration and rotation of diatomic gas.The results of this study indicate that a possibly universal existence of the such a temperature g,defined by that at which the specific heat falls fastest along with decrease of the temperature.For the Debye model of solids,below the temperature g the Debye's law manifest itself.