Rotational Cut-Off and Anharmonicity Effects on Thermodynamic Properties of Gases at High Temperatures

1974 ◽  
Vol 25 (4) ◽  
pp. 287-292
Author(s):  
N M Reddy
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Harmonic Oscillator ◽  
Specific Heat ◽  
High Temperatures ◽  
Anharmonic Oscillator ◽  
Rigid Rotator ◽  
Temperature Range ◽  
Vibrational Levels ◽  
Harmonic Oscillator Approximation

SummaryThe exact expressions for the partition function Q and the coefficient of specific heat at constant volume Cv for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100°K to 100 000°K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigidrotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000°K for O2 and N2. Beyond these temperatures the error in Cv will be significant, owing to anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000°K.

Thermodynamic Properties of Ionized Gases at High Temperatures

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Kian Eisazadeh-Far ◽  
Hameed Metghalchi ◽  
James C. Keck
Keyword(s):  
Heat Capacity ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
High Temperatures ◽  
Mole Fraction ◽  
Specific Heat Capacity ◽  
Local Equilibrium ◽  
Equilibrium Conditions ◽  
New Model ◽  
Temperature Range

Thermodynamic properties of ionized gases at high temperatures have been calculated by a new model based on local equilibrium conditions. Calculations have been done for nitrogen, oxygen, air, argon, and helium. The temperature range is 300–100,000 K. Thermodynamic properties include specific heat capacity, density, mole fraction of particles, and enthalpy. The model has been developed using statistical thermodynamics methods. Results have been compared with other researchers and the agreement is good.

Normal Coordinate Treatments and Calculated Thermodynamic Properties of Phosphoryl Fluorodichloride, Phosphoryl Chlorodifluoride, Thiophosphoryl Bromide, Thiophosphoryl Fluorodibromide, and Thiophosphoryl Bromodifluoride

1971 ◽  
Vol 25 (2) ◽  
pp. 212-217 ◽  
Author(s):  
Joseph S. Ziomek ◽  
Frank J. Fillwalk ◽  
Edward A. Piotrowski
Keyword(s):  
Thermodynamic Properties ◽  
Harmonic Oscillator ◽  
Matrix Elements ◽  
Normal Coordinate ◽  
Rigid Rotator ◽  
Gaseous State ◽  
Harmonic Oscillator Approximation ◽  
The One ◽  
Raman And Ir Spectra ◽  
The Ideal

The Raman and ir spectra of phosphoryl dichlorofluoride, phosphoryl difluorochloride, thiophosphoryl tribromide, thiophosphoryl dibromofluoride, and thiophosphoiyl difluorobromide were collected and examined for the most probable values for the wavenumbers, intensities, and depolarization factors. The data are as follows: The Raman displacements Δσ in cm−1, the relative intensities I, and the depolarization factors ρ are for POFCl2: Δσ ( I) ρ = 207(3.6)0.55, 254(1.8)6/7, 330(1)0.6, 372(3.4)6/7, 386(5.5)0.3, 547(10)0.05, 620( w)6/7, 894( w)0.45, and 1331 ( m) p; for POF2Cl: 274(10)0.65, 274 (calculated), 410(17)0.23, 424(7)6/7, 424 (calculated), 618(10)0.05, 895( m)0.1, 948( w>)6/7, and 1358( m)0.2; for PSBr3: 115(5.5)6/7, 165(4.1)0.3, 179(5)6/7, 299(10)0.05, 438( w)6/7, and 718 ( m) p; for PSFBr2:129(7)0.6, 159.5(11)6/7, 219(10)0.5, 254(4)6/7, 274(5)0.3, 377(10)0.2, 470( w)6/7, 718( m) p, and 887 ( vw) p; and for PSF2Br: 175(28)0.5, 231(3)6/7, 288(29)0.3, 298( w)6/7, 384(7)0.25, 462( w)0.1, 474(10)0.1, 711(9)0.1, 899( w)0.75, and 930( w)0.75. No published ir spectral data were found for POFCl2, POF2Cl, PSBr3, PSFBr2, and PSF2Br. Also normal coordinate treatments were conducted for POFCl2, POF2Cl, PSFBr2, and PSF2Br on the basis of the Cs model and the one for PSBr3 on the basis of the C3 v model. The results of these treatments established the above listed wavenumbers as fundamentals and lend support for 424 and 274 cm−1 bands for POF2Cl as the missing Raman bands. The F matrix elements obtained for these molecules were determined in such a way that F matrix elements common to POF3, POF2Cl, POFCl2, and POCl3 had nearly the same values and those common to PSF3, PSF2Br, PSFBr2, and PSBr3 also had nearly the same values. Finally, the values of the thermodynamic properties for these substances were computed for the ideal gaseous state using the rigid rotator harmonic oscillator approximation at 1 atm from 200 to 1000 K.

scholarly journals On the Complementarity of the Harmonic Oscillator Model and the Classical Wigner–Kirkwood Corrected Partition Functions of Diatomic Molecules

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 853
Author(s):  
Marcin Buchowiecki
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Harmonic Oscillator ◽  
High Temperatures ◽  
Low Temperatures ◽  
Diatomic Molecules ◽  
Partition Functions ◽  
Harmonic Oscillator Model ◽  
Harmonic Oscillator Approximation ◽  
Classical Partition Function

The vibrational and rovibrational partition functions of diatomic molecules are considered in the regime of intermediate temperatures. The low temperatures are those at which the harmonic oscillator approximation is appropriate, and the high temperatures are those at which classical partition function (with Wigner–Kirkwood correction) is applicable. The complementarity of the harmonic oscillator and classical integration over the phase space approaches is investigated for the CO and H2+ molecules showing that those two approaches are complementary in the sense that they smoothly overlap.

THE COMBINED ANALYSIS OF SPECIFIC HEAT AND THERMAL EXPANSION OF Nd1−xLuxMn2 COMPOUNDS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 810-813
Author(s):  
N.H. KIM-NGAN ◽  
P.E. BROMMER ◽  
J.J.M. FRANSE
Keyword(s):  
Magnetic Properties ◽  
Thermal Expansion ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Crystal Field ◽  
Spin Fluctuation ◽  
Spin Reorientation ◽  
Antiferromagnetic Order ◽  
Combined Analysis ◽  
Temperature Range

Specific heat and thermal expansion measurements have been performed on Nd1−xLUxMn2 in the temperature range between 1.5K and 300K. Below 10K, anomalies are observed which are ascribed to a spin reorientation of the Nd sublattice. These anomalies are only slightly affected by the substitution of Nd by Lu. Large effects, however, are observed on the magnetic properties of the Mn sublattice. The antiferromagnetic order disappears for x exceeding 0.30. The data are analysed in terms of Grüneisen parameters. In the paramagnetic compound LuMn2, a spin-fluctuation contribution to the thermodynamic properties is observed. In the Nd-containing compounds, distinct contributions from the crystal field acting on the Nd ions can be distinguished. The variation of the magnetic properties of the Mn sublattice with the concentration of Lu is discussed.

Estimation of the heat capacity of CdTe semiconductor

2016 ◽  
Vol 30 (04) ◽  
pp. 1650026 ◽  
Author(s):  
Hüseyin Koç ◽  
Erhan Eser
Keyword(s):  
Heat Capacity ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Specific Heat Capacity ◽  
Binomial Coefficient ◽  
Debye Model ◽  
The Other ◽  
Temperature Range ◽  
Theoretical Results ◽  
Good Agreement

The aim of this paper is to provide a simple and reliable analytical expression for the thermodynamic properties calculated in terms of the Debye model using the binomial coefficient, and examine specific heat capacity of CdTe in the 300–1400 K temperature range. The obtained results have been compared with the corresponding experimental and theoretical results. The calculated results are in good agreement with the other results over the entire temperature range.

Schwingungsspektren und Thermodynamische Funktionen von PF3, PCl3, PBr3, P J3, PF2Cl, PF2Br, PF2J, PFCl2, PFBr2, PCl2Br, PCl2J, PClBr2, PClJ2, PBrJ2, PBr2J, PFClBr, AsCl2Br und AsClBr2

1968 ◽  
Vol 23 (5) ◽  
pp. 588-594 ◽  
Author(s):  
A. Müller ◽  
E. Niecke ◽  
B. Krebs ◽  
O. Glemser
Keyword(s):  
Harmonic Oscillator ◽  
Infrared Spectra ◽  
Thermodynamic Functions ◽  
Frequency Data ◽  
Rigid Rotator ◽  
Temperature Range

The complete Raman and infrared spectra of PF2Cl, PF2Br, PFCl2 and PFBr2 are reported. The frequency data for several mixed phosphorus and arsenic halides (see title) given in the literature are revised and completed. Assignments are made for all spectra. Thermodynamic functions in the temperature range 200—2000 °K are calculated for all molecules, assuming the harmonic oscillator — rigid rotator approximation.

SPECIFIC HEAT OF Tb0.5Sr0.5CoO3 CERAMICS

2013 ◽  
Vol 22 ◽  
pp. 391-396
Author(s):  
RASNA THAKUR ◽  
RAJESH K. THAKUR ◽  
N. K. GAUR
Keyword(s):  
Experimental Data ◽  
Thermodynamic Properties ◽  
Bulk Modulus ◽  
Specific Heat ◽  
Debye Temperature ◽  
Cohesive Energy ◽  
Grüneisen Parameter ◽  
Temperature Range ◽  
Proper Interpretation ◽  
Rigid Ion Model

We have investigated the thermal and allied properties of Tb0.5Sr0.5CoO3 for the temperature range 1K≤T≤300K using the Modified Rigid Ion Model (MRIM). The calculated bulk modulus, specific heat, and other thermodynamic properties obtained from MRIM have presented proper interpretation of the experimental data, for Sr ions doped TbCoO3 . In addition, the results on the cohesive energy (φ), Debye temperature (θD) and Gruneisen parameter (γ) are also discussed.

The rotational specific heat of a polyatomic molecule for high temperatures—correction

1933 ◽  
Vol 29 (3) ◽  
pp. 407-407 ◽  
Author(s):  
Irene E. Viney
Keyword(s):  
Asymptotic Expansion ◽  
Partition Function ◽  
Specific Heat ◽  
High Temperatures ◽  
Polyatomic Molecule ◽  
Department Of Commerce ◽  
Image Position

I am indebted to Mr L. Kassel of the Department of Commerce, U.S.A., for pointing out an error of computation in a recent paper in these Proceedings.The asymptotic expansion for the partition function should readwhere

Determine the Specific Heat Capacity, the Entropy, and the Standard Deviation of Particle Vibration Bound-State under the Anharmonic Oscillator Asymmetric Potential by Partition Function Method

2019 ◽  
Vol 886 ◽  
pp. 206-212
Author(s):  
Metaporn Apiratigosol ◽  
Katang Jeeradit ◽  
Pattadon Keawpeai ◽  
Supaporn Hutem ◽  
Artit Hutem ◽  
...  
Keyword(s):  
Heat Capacity ◽  
Standard Deviation ◽  
Partition Function ◽  
Specific Heat ◽  
Specific Heat Capacity ◽  
Single Particle ◽  
Anharmonic Oscillator ◽  
Bound State ◽  
State Problem ◽  
Bound State Problem

In this work, we consider is the single-particle bound-state problem. A single-particle moves in the absence of the anharmonics oscillator asymmetric potential. The bound-state problem then is to solve the partition function for single-particle in the presence of anharmonics oscillator asymmetric potential. The factor second exponential function of partition function of particle bound in the anharmonics oscillator asymmetric potential can also be expanded in power series of the temperature and parameter , , and is the position of single-particle bound-state problem and using the integrate Gaussian. The purpose of this works, we will compute the partition function as a function of temperature, entropy, specific heat capacity and standard deviation which depend on the parameter and frequency.

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