Negative Absolute Temperature Thermodynamics

Negative Absolute Temperature ThermodynamicsT.H. TennahewaThermodynamics and Statistical mechanics at Negative Absolute TemperatureWe define the temperature, T by in present S stands for data which describes the measure of swage in the system and U for Internal heftiness. In hither x stands for the partial differentiation that should break constant in the thermodynamical equation relating TdS and dU. this relation comes from the head start uprightness of Thermodynamics. That isWe brush off define temperature with relating Enthalpy (H) also. That is in here too y stands for the partial differentiation that should hold constant in the thermodynamic equation relating TdS and dH. Below is the derivation of above equation.We c ein truthed peremptory temperature as a temperature where on the Kelvin scale 0 K as the absolute cryptograph point, where all motion in a classical gas would stop. almost systems, including a classical gas argon limited to tyrannical absolute temper atures. In order to be sufficient to r all(prenominal) banishly charged temperatures, a system deals to possess an upper bound for the nada of its particles, which is a maximal thinkable energy a particle of the system suffer be in possession of. This limit is non an external limit in the sense that in that respect is just no more(prenominal) than energy available. It is an internal limit the particles stinkernot reap more energy even if there is plenty available. It is consequential to grade that the prejudicial temperature region, with more of the atoms in the in high spiritser allowed energy order, is actually lukewarm than the positive temperature region. If this system were to be brought into contact with a system containing more atoms in a glare energy assert (positive temperatures) commove would feed in from the system with the electronegative temperatures to the system with the positive temperatures.By the definition of temperature we can describe ab ove figure.If the energy in the system is minimum (Emin), all particles are in the lowest possible energy country and the atomic figure of speech 16 is zero. The loop is vertical at this point with an infinite slope and temperature is wherefore zero. If the energy increases, the particles begin to occupy high(prenominal) energy states, and the entropy increases. on that point are, however, always more particles at low energies than at high energies this is same as the usual Boltzmann distri providedion. (Figure 2 below) The slope of the entropy versus energy bias decreases and the temperature therefore increases. At or so point, when there is enough energy in the system, the particles distri thoe equally over all energy states. thitherfore the disorder and the entropy are maximum. The curve is completely flat at this point, with a slope of zero, and the temperature is therefore infinite. If the total energy in the system is save increased, more particles impart occupy hi gh energies than low energies this is same as the inverted of the Boltzmann distribution. Because the energy distribution becomes narrower once again, disorder and entropy starts to decrease. This is not a usual behavior because usually entropy increases with increasing energy. The slope of the curve is negative in this region and therefore the absolute temperature is negative. If the energy in the system is maximum (Emax), all particles are at their maximum possible energy. The entropy is again zero. The curve is again vertical therefore the temperature is again zero, but this time it is negative values. Thus, while a temperature of positive and negative infinity is physically identical, temperatures of positive and negative zero are very different. Because of that we could write temperature range as +0 K, +300 K, , + K, K, , 300 K, , 0 K.Figure 2- The Maxwell- Boltzmann distributionIn the Carnot cycle of a arouse railway locomotive heat absorbed from the hot reservoir and hea t rejected to the dust-covered reservoir while hold up through with(p) by the system. In that facial expression we define the efficiency of the process as,In here Q1 is a heat absorbed at temperature T1 and Q2 is a heat rejected at temperature T2. In heat locomotive engine T2 / T1 2 / T1 1, therefore efficiency is negative and can be very large. In this case work has to be supplied to carry on the cycle.It should be noted that when Carnot cycle is operated between deuce negative temperatures that is work is mounte by the machine while heat absorbed from gelid reservoir and rejected to hot reservoir. Efficiency of the system is not scarcely positive but it is also less than unity. Thus at some(prenominal) positive and negative temperatures cyclic heat engines which convey work have efficiencies less than unity that is they absorb more heat than produced work. Second impartiality of thermodynamics should have to modify to use with this kind of Carnot cycle. In there, ent ropy grammatical piddleion and Clausius statement remain unchanged and Kelvin-Plank formulation has to be changed. They are mentioned below.Entropy formulationThe entropy of a system is a variable of its state and the entropy of an isolated system can never decrease.Clausius StatementIt is impracticable to construct a device operating in a unkindly cycle that will produce no other gist than the transpose of heat from a cooler to hotter body.Kelvin- Plank formulationIt is impossible to construct an engine, which is operating in a cycle produces no other effect except to external heat from a single reservoir and do equivalent amount of work.Modified statementIt is impossible to construct an engine that will operate in a closed cycle and produce no effect other than the extraction of heat from a positive temperature reservoir with the performance of an equivalent amount of work or the rejection of heat into a negative temperature reservoir with the corresponding work being done o n the engine.Carathodory formIn any neighborhood of any state there are states that cannot be reached from it by an adiabatic process.Both first and second laws of thermodynamics can be used at negative temperatures as at positive ones to derive other thermodynamic relations. From these laws it is interpreted that the barrier of heating a hot system at negative temperatures is analogous to the difficulty in cooling a cold system at positive temperature.The important requirements for thermodynamical system to be capable for negative temperature areThe elements of the thermodynamical system must be in thermodynamical equilibrium among themselves in order to describe the system by temperature.There must be an upper limit of the possible energy of the allowed states of the system. It is need a lour bound for the energy in order to master positive temperatures and an upper bound in order to get negative temperatures.The system must be caloricly isolated from all systems which do not satisfy both of the above particularizes.To satisfy the second condition negative temperatures are to be fulfild with a finite energy. In thermal equilibrium the number of elements in the mth state is proportional to the Boltzmann factor here Wm is energy of the mth state.Boltzmann distribution function which is formed victimization Boltzmann factor is wedded below. In negative temperature case when Wm increases with that Boltzmann factor increases exponentially therefore high energy states are more occupied than low energy states. As a result of this we could say that without an upper limit to the energy negative temperatures could not be achieved with a finite energy. Since most of the systems do not satisfy this conditions negative temperatures are occurs rarely.Spin systems sometimes form the thermodynamic systems which can describe by using temperature. In there for a system of electron constructions in a lattice, a temperature such that the macrocosm of the energy level s of the revolve system is given by the Boltzmann distributionwith the spin temperature. To achieve thermodynamic equilibrium various nuclear spins must interact among themselves. This happened delinquent to nuclear spin-spin magnetized interaction.Subatomic particles like electrons, protons and neutrons can be imagined as spinning on their axes. In many an(prenominal) atoms these spins are paired against each other, such that the core group of the atom has no overall spin. In some atoms the nucleus has shown overall spin. The rules for determining the net spin of a nucleus are given belowIf the number of neutronsandthe number of protons are both even, past the nucleus hasNOspin. (Classical Particles)If the number of neutronsplusthe number of protons is odd, then the nucleus has a half-integer spin (i.e. 1/2, 3/2, 5/2) (Fermions)If the number of neutronsandthe number of protons are both odd, then the nucleus has an integer spin (i.e. 1, 2, 3) (Boson)It is defined in Quantum mec hanics that a nucleus of spinIwill have 2I+ 1 possible orientations. A nucleus with spin 1/2 will have 2 possible orientations. In the absence of an external magnetic subject field, these orientations are of equal energy. If a magnetic field is applied, then the energy levels split. When the nucleus is in a magnetic field, the initial populations of the energy levels are determined by thermodynamics, as described by the Boltzmann distribution. It means thatthe start energy level will contain slightly more nuclei than the higher level. It is possible to excite these nuclei into the higher level with electromagnetic radiation. The relative frequency of radiation needed is determined by the difference in energy between the energy levels.This spin-spin process can be characterized by using comfort process. Nuclei in the higher energy state return to the lower state by emitting the radiation. At radio frequencies, re-emission is negligible. There are two main relaxation processesSpin lattice (longitudinal) relaxationSpin spin (transverse) relaxationSpin lattice relaxation (T1)Nuclei which are in a sample create a complex magnetic field. The magnetic field caused by motion of nuclei at heart the lattice is called thelattice field. This lattice field has many components. Some of these components will be equal in frequency and stage to the Larmor frequency of the nuclei of interest. These components of the lattice field can interact with nuclei in the higher energy state and cause them to lose energy returning to the lower state. The energy that a nucleus loses increases the amount of vibration and rotation within the lattice resulting in a tiny rise in the temperature of the sample.The relaxation time,T1(the average lifetime of nuclei in the higher energy state) is dependent on the magnetogyric ratio of the nucleus and the mobility of the lattice. As mobility increases, the vibrational and rotational frequencies increase, making it more likely for a component of the lattice field to be able to interact with huffy nuclei. However, at extremely high mobilities, the probability of a component of the lattice field being able to interact with excite nuclei decreases.Spin spin relaxation (T2)This is describing the interaction between neighbouring nuclei with identical precessional frequencies but differing magnetic quantum states. In this case, the nuclei can exchange quantum states a nucleus in the lower energy level will be excited, while the excited nucleus relaxes to the lower energy state. There is nonetchange in the populations of the energy states, but the average lifetime of a nucleus in the excited state will decrease. This can result in line-broadening.Most of the nuclear systems dont satisfy the conditions in negative temperatures.By looking at all these things we can conclude that although the phenomena of negative temperature is a fully effectual concept in thermodynamics and statistical mechanics they have less important tha n phenomena of positive temperature.1