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Surface dependency in thermodynamics of ideal gases

The Casimir-like size effect rises in ideal gases confined in a finite domain due to the wave character of atoms. By considering this effect, thermodynamic properties of an ideal gas confined in spherical and cylindrical geometries are derived and compared with those in rectangular geometry. It is seen that an ideal gas exhibits an unavoidable quantum surface free energy and surface over volume ratio becomes a control variable on thermodynamic state functions in microscale. Thermodynamics turns into non-extensive thermodynamics and geometry difference becomes a driving force since the surface over volume ratio depends on the geometry.

Brayton refrigeration cycles working under quantum degeneracy conditions

At sufficiently low temperatures, quantum degeneracy of gas particles becomes important and an ideal gas deviates from the classical ideal-gas behaviour. In such a case, an ideal gas is called a quantum ideal gas. For quantum ideal gases, a corrected equation of state, which considers the quantum behaviour of gas particles, is used instead of the classical one. It is valid for both quantum and classical ideal-gases and it is reduced to a classical ideal-gas equation-of-state, under the classical gas conditions. There are two types of quantum ideal-gases. One of them is the Bose type and the other is the Fermi type. Here, Brayton refrigeration cycles working with Bose and Fermi type ideal quantum gases are considered and they are called Bose and Fermi Brayton cycles respectively. Coefficients of performance and refrigeration loads of these cycles are derived by using the corrected equation of state. It is seen that refrigeration loads are different from those of the classical Brayton cycle, which works with the classical ideal gas. On the other hand, coefficients of performance of these cycles are not effected by the quantum degeneracy of the refrigerant and they are the same as that of the classical cycle. Variations of the refrigeration load with low temperature (TL) and low pressure (PL) are examined. Under the quantum degeneracy conditions, it is shown that the refrigeration load of the Bose Brayton cycle is always greater than that of the classical Brayton cycle. On the contrary, the refrigeration load of the Fermi Brayton cycle is always lower than that of the classical one. Moreover, the minimum value of TL for the Bose Brayton cycle is restricted by the Bose-Einstein condensation temperature for a given value of PL.

On the power cycles working with ideal quantum gases: I. The Ericsson cycle

The Ericsson power cycles working with ideal Bose and Fermi monoatomic gases are examined. They are conveniently called the Bose and Fermi cycles. Efficiencies of Bose and Fermi cycles are derived ( and respectively). Variations of them with the temperature ratio and pressure ratio of the cycle are examined. A comparison of the efficiencies with each other and that of the classical Ericsson cycle is made. In the degenerate gas state it is seen that , although in the classical gas state. In a Bose cycle, it is shown that there is an optimum value for the lowest temperature at which the efficiency reaches its maximum value for a given pressure ratio. Furthermore, Bose-Einstein condensation restricts the value of of a Bose cycle for a given value of . In a Fermi cycle, there is no an optimum value for . However, goes to a finite value of less than unity when goes to zero.

The improvement effect of quantum degeneracy on the work from a Carnot cycle

The efficiency of a Carnot ([eta]C) cycle is independent of the physical properties of the working gas. Therefore, [eta]C does not change due to quantum degeneracy of the gas. On the other hand, cycle work depends on the physical properties of the working gas since it is determined by the equation of state of the gas. Therefore, cycle work can be influenced by the quantum degeneracy of working gas. Here, Carnot power cycles working with ideal Bose and Fermi gases are examined under quantum degeneracy conditions. They are called Bose and Fermi Carnot cycles respectively. Cycle works of Bose and Fermi Carnot cycles (WB and WF) are derived. By dividing these works into the work of the classical Carnot power cycle (WC), which works with classical ideal gas, work ratios are defined as RWB=WB/WC and RWF=WF/WC. Variations of RWB and RWF with high temperature of the cycle (TH) are examined for a given temperature ratio [tau]=TL/TH and specific volume ratio rv=vH/vL. It is shown that RWB>1 for some values of TH while RWF

Quantum size effects on the thermal and potential conductivities of ideal gases

Thermal and potential conductivities of ideal Maxwellian, Fermi and Bose gases are derived by considering the small corrections due to the wave character of gas particles. Potential conductivity is regarded as conductivity due to any potential gradient like electrical, gravitational or chemical ones. A long rectangular channel is considered as a transport domain. The size of the domain in the transport direction is much longer than the mean free path of particles l while the sizes in transverse directions are shorter than l. On the other hand, all sizes of the domain are assumed to be larger than the thermal de Broglie wavelength of particles. Therefore, quantum size effects (QSE) are weak enough to be considered as small corrections on conventional terms. Corrections on thermal and potential conductivities are examined. It is seen that the size and shape of the transport domain become additional control parameters on both conductivities. Since the size dependencies of thermal and electrical conductivities are different, the Lorenz number becomes size and shape dependent and deviations from the Wiedemann–Franz law may be expected in nanoscale due to QSE. Variations of the corrections with chemical potential are analysed.

Universality of the quantum boundary layer for a Maxwellian gas

For an ideal gas confined in a rectangular domain, it has been shown that the density is not homogenous even in thermodynamic equilibrium and it goes to zero within a layer near to the boundaries due to the wave character of particles. This layer has been called the quantum boundary layer (QBL). In literature, an analytical expression for the thickness of QBL has been given for only a rectangular domain since both energy eigenvalues and eigenfunctions of the Schrodinger equation can analytically be obtained for only a rectangular domain. In this study, ideal Maxwellian gases confined in spherical and cylindrical domains are considered to investigate whether the thickness of QBL is independent of the domain shape. Although the energy eigenvalues are the roots of Bessel functions and there is no analytical expression giving the roots, the thickness of QBL is expressed analytically by considering the density distributions and using some simplifications based on the numerical calculations. It is found that QBL has the same thickness for the domains of different shapes. Therefore, QBL seems to have a universal thickness independent of the domain shape for an ideal Maxwellian gas.

Discrete nature of thermodynamics in confined ideal Fermi gases

Abstract Intrinsic discrete nature in thermodynamic properties of Fermi gases appears under strongly confined and degenerate conditions. For a rectangular confinement domain, thermodynamic properties of an ideal Fermi gas are expressed in their exact summation forms. For 1D, 2D and 3D nano domains, variations of both number of particles and internal energy per particle with chemical potential are examined. It is shown that their relation with chemical potential exhibits a discrete nature which allows them to take only some definite values. Furthermore, quasi-irregular oscillatory-like sharp peaks are observed in heat capacity. New nano devices can be developed based on these behaviors.

Quantum forces of a gas confined in nano structures

In nano domains, thermodynamic properties of gases considerably differ from those in macro domains. One of the reasons for this difference is the quantum size effects, which become important when the thermal de Broglie wavelength of particles is not negligible in comparison with domain size. In this study, it is shown that quantum forces may appear in gases confined in nano structures due to the quantum boundary layer caused by quantum size effects. In the case of experimental verification of these quantum forces, a macroscopic manifestation of the effect of the quantum boundary layer on the thermodynamic behavior of gases can be confirmed.

Joule-Thomson coefficients of quantum ideal-gases

The temperature drop of a gas divided by its pressure drop under constant enthalpy conditions is called the Joule-Thomson coefficient (JTC) of the gas. The JTC of an ideal gas is equal to zero since its enthalpy depends on only temperature. On the other hand, this is only true for classical ideal gas which obeys the classical ideal gas equation of state, pV=mRT. Under sufficiently low-temperature or high-pressure conditions, the quantum nature of gas particles becomes important and an ideal gas behaves like a quantum ideal gas instead of a classical one. In such a case, enthalpy becomes dependent on both temperature and pressure. Therefore, JTC of a quantum ideal gas is not equal to zero. In this work, the contribution of purely quantum nature of gas particles on JTC is examined. JTCs of monatomic Bose and Fermi type quantum ideal gases are derived. Their variations with temperature are examined for different pressure values. It is shown that JTC of a Bose gas is always greater than zero. Minimum value of temperature is limited by the Bose-Einstein condensation phenomena under the constant enthalpy condition. On the other hand, it is seen that JTC of a Fermi gas is always lower than zero and there is not any limitation on its temperature. For high temperature values, JTCs of Bose and Fermi gases go to zero since the quantum nature of gas particles becomes negligible. Moreover, variation of temperature versus pressure under the constant enthalpy condition is also examined. Consequently, it is understood that the quantum nature of a Bose-type gas contributes to the positive values of JTC while the quantum nature of a Fermi type gas contributes to the negative values of JTC. Therefore, a Bose-type gas is more suitable for cryogenic refrigeration systems.

Discrete density of states

Abstract By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, theyre almost completely flattened out after summation or integration operation. Its seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyls conjecture always preserve their lower error characteristic.