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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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The mean free path of gas molecules is $$\lambda =\frac{RT}{\sqrt 2 \pi d^2 N_A P}$$ Where $R$ is the gas constant, $d$ the diameter of the molecule and $N_A$ Avogadro's constant. The average relative velocity of gas molecules can be obtained by the Maxwell-Boltzmann distribution and is equal to $$\langle v \rangle = \sqrt{\frac{8kT}{\pi m}}$$ The mean ...


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One way to look at the gas constant, R, is the constant of proportionality between pressure x volume and particle count (n) x absolute temperature T. Thus, the well known ideal gas law: PV=nRT. But, and this gets to what I think might be your question, that's only for 'ideal' gases. For 'real' gasses, the gas law no longer applies. Changes in pressure, ...


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Your equation (2) is trivially a solution of (1), because $v$ and $T$ are constant. This is a disappointing answer, because it leaves unanswered the question what makes the Boltzmann distribution unique. The answer is that you only wrote down the collision-less Boltzmann equation, but in the real world collisions are always present (and indeed, systems ...


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If we treat the collisions as a Poisson process then the probability of there being a collision within some interval $\Delta t$ is actually given by $1-\exp(-P\Delta t)$ which is less than or equal to one, as you'd expect. What your book has then done is implicitly assume that $P\Delta t$ is small (certainly less than 1), giving rise to the approximation $1-...


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I think there may be some confusion as to terminology: compressibility is defined as $$ -\frac 1V \frac{\partial V}{\partial p}$$ where something like temperature or entropy is held constant, whereas the compressibility factor is defined as a certain ratio. (ref: https://en.wikipedia.org/wiki/Compressibility) In the ideal gas, particles do not interact ...


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The compressibility factor was originally derived from empirical testing of gases to correct for the observed non-ideal behavior at more extreme pressures and temperatures. Although it cannot be derived from first principles in the kinetic theory of gases, the experimentally derived factors can be reconciled using Van Der Waal's equation that deals with the ...


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You said it yourself the molecules have direction rather than randomly moving about. Picture a wide spot in a river, slow water, maybe eddy currents, random water flow. River narrows, water is directed through the slot. I agree with you, speed before pressure differential. What do you think about this, molecules entering Venturi creating vacuum which sucks ...



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