CHE - Feed https://chemjournal.researchfloor.org Mon, 20 Apr 2026 06:14:07 +0000 hourly 1 https://wordpress.org/?v=6.8.3 https://chemjournal.researchfloor.org//wp-content/uploads/2021/07/cropped-logo-che-32x32.png Description of Adiabatic Expansion and Compression of Gases – CHE https://chemjournal.researchfloor.org 32 32 Description of Adiabatic Expansion and Compression of Gases https://chemjournal.researchfloor.org/%ef%bf%bcdescription-of-adiabatic-expansion-and-compression-of-gases/ Tue, 27 Sep 2022 15:02:52 +0000 admin Igor A. Stepanov * https://www.che.com.es/?p=2479

Adiabatic expansion of gases can be described by the traditional equation. It is shown that such this equation successfully describes adiabatic compression and expansion of  some gases. It is shown that an equation of the mechanocaloric effect can also be used for the description of such compression and expansion. An alternative equation of an adiabatic process is derived which gives a good description for all these gases. The accuracy of this equation is the same one as that of the traditional one.

 https://chemjournal.researchfloor.org/%ef%bf%bcdescription-of-adiabatic-expansion-and-compression-of-gases/
  • Introduction

    • There is the equation of the adiabatic process [1]:

                                                                            ,                                                                                              (1)       

    where  g = CP/CV  is the ratio of isobaric and isochoric heat capacity. One can check Eq. (1) experimentally.

    There is a modified Clément-Desormes method for determination heat capacities of gases [3]: “A gas is maintained in a closed bottle, fitted with a stopcock and a manometer, at room temperature T1 and at a pressure P2 above atmospheric pressure P1. When the stopcock is opened, the gas expands almost adiabatically to atmospheric pressure. During this expansion the gas cools from T1 to T2. Then the stopcock is closed again, and the gas is allowed to return to thermal equilibrium with surroundings. To determine the heat capacity one can measure P1, P2, and T1, and T2”. In Table 1 there are many experimental  values of Pi and Ti for some gases.

    In the notations of Table 1, Eq. (1) will have the following form:

                                                                                                    ,                      (2)      

    • Theory           

    One can also apply the approach developed in [3]:

                During the adiabatic deformation, the enthalpy of the sample changes at DH(S,P) = DH(S,T). It follows that:

                                                                .                               (3)

    According to the tables of thermodynamic derivatives [3],

                                                                            ,                                   (4)

    where CP is the isobaric heat capacity, and a is the thermal expansion coefficient which is 1/T for an ideal gas. And from the same tables:

                                                                            .                                                                                       (5)

    From these equations, the equation for the mechanocaloric effect follows:

                                                                            .                                                                                    (6)

    Now let us check its correctness using the data from Table 1 and comparing with Eq. (2). One can assume that in Eq. (6) dT = T2  – T1 and dP = P2  – P1, and calculate T2/T1.                                                                                                                                                                                                                                                                    Let us derive the equation of an adiabatic process analogously to [1]. During adiabatic expansion or compression

                                                                                                                             (7)

    Here CA = CV is the adiabatic heat capacity [5]. Adiabatic expansion in theClément-Desormes metod is almost an isobaric process [2], therefore Eq. (7) can be written as:

                                                                                                           (8)

    If CA is independent of temperature, and if one introduces k = R/CA, one can obtain from Eq. (8)

                                                                                                                                  (9)

    And then:

                                                                                                                         (10)

    In the notations of Table 1, Eq. (10) will have the following form:

                                                    ,                                                          (11)     

    Calculations with Eqs (2). (6) and (11) are presented in Table 1. Eq. (11) gives a very good agreement with the experiment.

    Table 1. Measurements with a modified Clément-Desormes method and calculations with Eqs(2). (6) and (11) for some gases heated by compression [2].

    GasP1, mm HgP2, mm HgT1, KT2, KT1, / T2,T1, / T2, Eq.(2)T1, / T2, Eq.(6)T1, / T2, Eq.(11)
    Air [2]760.9825.7287.03280.401.023641.023631.032411.02363
    Air [2]754.4817.88285.98279.471.023291.023351.032041.02335
    O2 [2]757.6863.91288.11277.631.037751.037681.050701.03768
    H2CO3 [2]756.3845.35284.36277.241.025681.025621.031971.02562
    H2 [2]755.8868.84288.75277.381.040991.040871.055371.04087
    Air [2]756.25823.35292.99285.98  1.024511.024441.033421.02444
    Air [2]752.0814.11293.12286.551.022931.022931.031481.02293
    CO2 [2]756.5831.56293 .12286.851.021861.021831.027441.02183
    Air [2]886.9761.9288.91276.661.044281.044361.07023 
    Air [2]875.54752.4288.81276.541.044371.044261.07005 

    .

    • Conclusions and Discusions

    It is shown that compression an expansion of gases can be successfully described by an equation for the mechanocaloric effect. Formerly we thought that in an isobaric process a change in the enthalpy is equal to the heat of the process. Here the conclusion of [4] is confirmed: in all processes a change in the enthalpy is equal to the heat of the process. An alternative equation of an adiabatic process is derived which also gives a good description of compression and expansion of gases.It is obvious that this alternative equation is not worse than the traditional one.

    Statements and Declarations

    Competing  Interests

    The author declares that he has no competing interests or personal relationships that could have appeared to influence the work reported in this paper

    The author has no relevant financial or non-financial interests to disclose.

    References

    1. R. J. Silbey, R. A. Alberty, M. G.Bawendi Physical Chemistry, 4th edn. (John Wiley&Sons, Inc. USA, 2005),
    2. [2]        I. A. Stepanov, Journal of Chemical, Biological and Physical Sciences. Section C. (2020) Free online.

    https://doi.org /10.24214/jcbsc.C.10.1.10816

    1. I. A. Stepanov, Journal of Chemical, Biological and Physical Sciences. Section C. 2020. Vol. 10. No 2. 51 – 57. Free online.

    https://doi.org /DOI: 10.24214/jcbsc.C.10.2.05157.

    1. I. A. Stepanov, Physical Science International Journal (2017) Free online. https://doi.org /DOI: 10.9734/PSIJ/2017/32822
    2. I. A. Stepanov, Journal of Chemical, Biological and Physical Sciences. Section C (2021) Free online.

    https://doi.org /DOI: 10.24214/jcbps.C.11.3.15155

    ]]>     Acceptability Adiabatic compression Adiabatic expansion adoption adsorption Agricultural tools agriculture Agro wastes Allivum sativum L AMMI ammonification Ammonium nitrate and ammonium sulphate solution And Cropping and DAP – Days after pruning Antibodies Application aqueous solution Arc-Gis aroma treatment assets Association analysis Astrobiology Autotrophic Bacteria Ayurveda B- cells Backyard batch studies BC ratio Belt Conveyor Bio-fertilizers Bioaccumulation bioadsorbents Biofertilizers Biofuel bioremoval biosignatures Biplot analysis BLUP Box plot and Bienniality Box-plot Brassica juncea Breathable textiles Bulb yield bulk density CaCl2 callus Cancer cells capsicum Cashew Cassia fistula Chebulagic acid chemical properties chemistry cherry tomato Chickpea CHIKV E2 Chilli growers Cicerarietinum Clément-Desormes method climate change clinical cure Cluster cluster analysis Cluster Front Line D Coated Urea Coatings Colloidal processing Colored sweet pepper Comfortability Compact cotton composite flours composting computer conservation Conservation agriculture Correlation correlation analysis Correlation coefficient Coss cost cotton COVID-19 Cow dung and urine Cowpea CPE – Cumulative pan evaporation Crop coefficient Crop evapotranspiration crop growth rate crop production cropping system crops Crosstalk Crude protein Culm strength culture media Curry leaf Czern D2 DCT tools Dealers Debris deinition demonstration Disease Diversity docking Dosage Drip irrigation drought mitigation Drought tolerance Dry matter drymatter Ebola virus Eco-friendly insecticides Economics Ecosystem Effectiveness Efficacy Eichornia crassipes Electron microscope EM-AMMI Emulsion activity environment equilibrium Erodibility ethanol Ethylene Evaluation exoplanets explants extremophiles Extrusion cooking farmers Farming FDA fertigation fertility fertilizer fibre Field trails Finger millet Firming FITCON flax Fly-ash Fodder Cowpea Fold Foliar nutrition foliar spray food Food Security Forage yield forest Front line Demonstration front line demonstrations fruit fruit physical parameters fruit yield Fruits; Nutrients; Value addition Fungicide FYM GEI genetic advance Genetic diversity genetic variability genetic variation Genotype genotype x environment interaction Genotypes Geometrical Parameters germplasm GIS GPS-GIS grain Green forage Green nanopesticides gross returns Groundnut Crop Groundnut or peanut properties Growth Growth and Attributes Growth and Attributes. growth and yield attributes growth parameters growth retardant habitability Health; Self-life Heisenberg group heritability heritability and genetic advance Heterotrophic Bacteria High density planting high- density planting system High-density planting high-density planting system Host-pathogen hull Humic acid hydrogel Hydrophilic and Microporous ICT imazethapyr Immunotherapy Impact in vitro Incidence Incorporation Indigenous collections Influence of Sulphur Influenza information INM Input Agency Inputs integrated nutrient management intercultivation IPM Irrigation Isolation Jeevamrutha JG -63 kharif kinetics Knowledge labour Land Use Laplace operator Lassa virus Leaf learning Lebesgue life Lignin linseed Linum usitatissimum L. liquid biofertilizers Local Non-descript Goats Lodging Long-term fertilizer experiment longitudinal expansion Maize management practices Mango Marine Environment Marine Pollution marker maturity Membranes Mepiquat chloride Metal halide meteorological variables method of sowing MGNREGA beneficiaries Microbial studies Micrococcus lutes micronutrients Microorganism mines MLT moisture Moisture content Molar absorptivity Molasses mole technology mulching municipal solid waste Murraya koenigii Mustard Nanofibres Natural plants net assimilation rate net returns net returns and B:C ratio net returns B:C ratio NICRA nitrification Nitrobacter Nitrogen nitrogen levels and yield Nitrogen sources Nitrogen Use Efficiency (NUE) Nitrosomonas Non Basmati rice nutrient management nutrient removal and nutrient uptake Nutrient uptake nutrients c Nutritional composition Ochrobacterum pitutisom of Oil absorption capacity oil cakes organic Organic agriculture organic carbon pools organic manures organic product Organoleptic acceptability origin Packaging pad-dry-cure method Parameters Pathogen entry performance Perovskite Quantum dots Pest Control Pesticide pests pH physical properties Phytochemicals Pigeon pea Pigeonpea planetary plant Plant defense plant height Planting geometry Plastic Waste PM2.5 poly house polymers potassium iodate Poultry poultry farming prebiotic Principle component analysis (PCA) priority inputs Production productivity properties Protective clothing Protein and Crude fibre pulp Pulse beetle Pulse Magic pumpkin flour pumpkin seed flour Pusa 1121 Grain quality Pusa Basmati 1 Pusa hydrogel Pusa Sugandha qualitative quality quality parameters quantitative Quinoa R-8808 and KADARI-9 varieties ready-to-eat recommended dose of fertilizer relative growth rate remediation Resistance breeding response surface rhodamine-B dye Rice Riemann-Liouville RMSPD RNA polymerase RNA polymerase activity Rock phosphate Rural Salt affected soil SAMETI sampling sandal’s sensitivity Sandy soil season Seasonal Incidence Seed hardening Seed priming seed rate seed yield seeds Sequence cropping SFunctional property Simulation and Bienniality Sirohi SISGYS Skill Skimmed milk slope map smartphone Socio-economic impact Soil soil aggregation Soil amendments soil characteristics Soil Erosion soil fertility maps and nutrientindex Soil health soil moisture content and maize Soil organic carbon Soil organic matter soil properties Soil Test Crop Response (STCR) Solar energy materials Solid works Sorghum Soybean SPAD (Soil Plant Analysis Development) values spectrophotometer Spectrophotometric Spectrophotometry stability standardization STCR equation Sugarcane ratoon crop Sulphur Sunflower Super absorbent polymer Superiority index Supplementation sustainability Sustainable agriculture sustainable productivity sustainable productivity and vertisols Sweet corn Sweet sorghum Swelling capacity techniques Technological need; Awareness; Dairy farmers Technology Index Terminal Velocity textile applications the mechanocaloric effect thermodynamics Threshing Cylinder tomato total cost Trainees Training Tuberose Unani Universal soil loss equation up gradation Upliftment Urea USWC utilization Vaccines for cancer Validation Variability Varieties vegetable producers Vermicompost Vermicomposting vertisols Vetiver oil microcapsules volumetric expansion Waste Management wastewater Water absorption capacity Water hyacinth Water productivity water resources Water vapor permeability waterlogged soils Waterproof weather Weeding wheat wheat flour Wilt wool fabric Yield yield and economics yield attributes yield parameters zero tillage and soil organic carbon zero-order method Zinc Zinc and Boron on Uptake and Availability of Nutrients in Onion ziprasidone hydrochloride (ZPN) Ziram