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The way you calculate (classically) the heat capacities for gases is by comparing the expressions for the internal energy given by thermodynamics and kinetic theory. The Equipartition Theorem says that at thermal equilibrium at temperature $T$ each quadratic term in the (mechanical) energy of the molecule contributes with $kT/2$. For a gas with $N$ ...


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In the temperature range you are talking about, and assuming we are talking about pressure that are not close to vacuum, then a monotomic gas (and I'd prefer talking about Ar, or He, and not a monotomic O, or H) Cp/Cv=5/3 (billiard ball atoms - no vibration/rotation) Cp-Cv =R (R is gas constant, and there is a universal gas constant) and from these, I ...


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Leaving this here for now... Will update with more information and references later. Einstein and Debye showed that specific heat is a function of temperature, but is asymptotic at high* temperatures. Here is a simple explanation why: Heat, with regard to everyday applications, is simply a measure of the motion of atoms and molecules. Let's start with ...


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$$\% Ionic Character = 100(1 - e^{-({\frac{\Delta{\chi}}{2}})^2})$$ The factor of 0.25 comes out when you simplify because of the electronegativity difference $\Delta \chi$ is halved before squaring. The formula is stated empirically by Pauling and has NO proof.


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Consider Fick's second law of diffusion, in one dimension, where $u$ is the concentration of the diffusing gas (in $\mathrm{mol/m^3}$) and $D$ the diffusion coefficient: $$\frac{\partial u}{\partial t}=D\frac{\partial u}{\partial x}$$ If we assume the concentration of gas outside the container to be much smaller than inside (a reasonable assumption), then ...


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It is important to be aware of you are using a very primitive model to represent the molecule. Although the concept of "bonds" is ubiquitous to chemistry, there is not such a thing in reality. Even more, it does not exist in a more rigorous treatment. Many times we try to think things in terms of bonds due to it is simple to picture out. Having said that, ...


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I think your mistake comes from assuming that there is an absolute zero temperature. Your formula should be corrected as below: $$\Delta S =\lim _{{T_1}\to 0}\int_{T_1}^{T_2}\frac{c_v(T)\mathrm dT}{T}$$ And as it is said in comments this is not a divided by zero. This includes an indeterminate form. Because when $T_1\to 0$, $c_v(T)\to 0$.


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I thought it is related to dissociation and confirmed that from the book by Michael Liberman. The assumed reaction $2H_2+O_2 \Rightarrow 2H_2O$ is not true at high temperature. The molecules will dissociate to $H_2, H, O_2, O, OH, HO_2$. The dissociation reactions (e.g. $H_2O \rightarrow OH + H + O$) are endothermic and thus reduce the flame temperature. ...


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Your question is short on details, so to answer your question I am assuming a particular configuration. Hope it helps with whatever your actual configuration is. A closed porous container consists of a gas at partial pressure $p_1$ which is less than partial pressure $p_2$ of that gas in the ambient. We shall assume that $p_2$ is constant and to further ...


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The equation you wrote is for steady state flow through a porous wall of thickness d. Q is the volumetric flow rate. Q/A is the so-called superficial velocity. The equation inherently assumes that the pressures on both sides of the wall are constant, and not varying with time. The only way that you would get an increase in pressure difference with time ...


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I cannot find sources confirming this (apart from some google books results, but those were all collections of wikipedia articles). Somewhat related is this source: "Dehydration of Ethanol-Water Mixture Using Activated Carbons from Sawdust and Palm Kernel Shells". The abstract says that the sawdust was chemically activated with ammonium chloride as catalyst, ...


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This is somewhat conjectural, but I think that sawdust is selective in terms of how polar the liquid is. Water and ethanol are both polar, but water significantly more so (ethanol is significantly less nonpolar at the CH3 end). To determine if this is indeed the case, I tried pouring some very low-viscosity (so that it tends to ball up less) cooking oil on ...


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As this is a closed system but not an isolated system, so we can add heat to the system. And, at the same time, we can increase its volume. By doing so, we may be able to keep temperature and pressure and increase entropy (note microstate increases because the position opportunity is increased). If this can reduce Gibbs free energy continuously? I guess ...


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Interatomic potentials have a finite minimum which means that the overall enthalpy of the system has a finite minimum. And any finite system also has a finite maximum entropy.


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In most reactions the energy is released as kinetic energy of the reaction products. If you consider some reaction: $$ A + B \rightarrow C + D $$ then if you add up the kinetic energies of $A$ and $B$ before the reaction and add the kinetic energies of $C$ and $D$ after the reaction you'll find that the kinetic energy after the reaction is higher than ...


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The released energy does indeed take the form of heat, which is why fire is hot. Cells use this energy to heat another molecule over the the threshold at which it will have an endothermic reaction, thus allowing them to force a reaction which would not normally occur at room temperature, or simply to heat the body, mantaining body heat even in an ...


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Hard though it is to believe, pH does have an effect on sound absorption in water. There are some reactions that are affected by pressure, that is pressure changes their equilibrium. One example is the equilibrium between boric acid and the borate ion: $$ B(OH)_4\,^- + H^+ \rightarrow B(OH)_3 + H_2O $$ Increasing pressure pushes the reaction over to the ...


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The author should have been more specific on the matter or at least provide a reference. The speed of sound in water depends on the bulk modulus and density of the water, so in the open oceans the factors that most affect the speed of sound are salinity, depth (pressure) and temperature. I was an ocean engineering major and have taken courses in physical and ...


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The motion of N atoms in three dimensions (x,y,z) produces 3N degree of freedom. Every molecule also has whole body rotation (as the atoms are now bonded together) about each of the 3 axes and translational motion along each axis making 6 motions altogether. If the molecule is linear, rotation about the principal symmetry axis in not measurable so there ...



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