# Questions tagged [equation-of-state]

Questions related to a thermodynamic equation describing the state of matter under a given set of physical conditions.

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### What is the relation between universal gas constant R and amount of substance n?

I have found it mentioned in various sources that the value of R depends on the amount of substance $n$ in the ideal gas equation: $PV=nRT$ If this is true, it would imply that $R$ is a function of $n$...
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### Using Mathematica to Plot an Isotherm at its Critical Temperature

Hello I'm new to mathematica and I have been trying to plot an isotherm for a substance at its critical temperature, using Van der Waals equation of state. I have done all the work except I do not ...
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### Why can't equations of state be replaced by machine learning models?

The Peng-Robinson equation of state, for example, has no underlying physical meaning, and is just a model that was fit to data. Computer scientists have developed much, much better models for data ...
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### Why do some gases have lower value of Z for a particular pressure?

In the above graph,the minima of the curve for methane is more than that of nitrogen. Also, for a given value of pressure, the value of $Z$ for methane is less than that of nitrogen. They seem to meet ...
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### Does the van der Waals equation remain valid when repulsive intermolecular forces dominate?

The van der Waals equation for a real gas is: $$RT =\left(p+\frac{a}{V_\mathrm{m}^2}\right)(V_\mathrm{m}-b)$$ We have understood this formula by saying that $a$ is the term which is for force of ...
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### How can a sample that is in two different states be at a uniform temperature?

In my chemistry course, the professor has discussed how a sample that contains both solid and liquid water would be at 0 degrees Celsius no matter what the proportion of solid to liquid water is. I ...
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In Chemistry class yesterday, I learned that real gases with low atomic masses behave like an ideal gas at high temperatures and low pressure. Since on earth at sea level the pressure is close to 1\ \... • 313 2 votes 0 answers 63 views ### Determining the equation of state when given thermodynamic relations [closed] Empirical observations of a thermodynamic system have shown that: \begin{align}C_{\mathrm m,V} &\neq C_{\mathrm m,V}(T) \\[6pt] \left(\frac{\partial U}{\partial V_\mathrm m}\right)_{T} &... • 21 18 votes 2 answers 19k views ### Why is the van der Waals coefficient b equal to four times the volume of the particle? In the van der Waals equation of state\left[p + a\left(\frac{n}{V}\right)^2\right](V-nb) = nRT$$the coefficient b is supposed to represent the volume occupied by the particles. Why then is it ... 5 votes 1 answer 1k views ### Why is the ideal gas law so ubiquitous? Why is the ideal gas law usable in most gas problems? For example, in a problem like this: "Suppose you have 1.00\: \mathrm{mol} of a gas at 0\:^\circ \mathrm{C}, occupying a container which is ... • 169 1 vote 1 answer 262 views ### What are analytical expressions for the isothermal change of Gibbs energy? The change of Gibbs energy at constant temperature and species numbers, \Delta G, is given by an integral \int_{p_1}^{p_2}V\,{\mathrm d}p. For the ideal gas law, p\,V=n\,RT, this comes down to$$... • 992 3 votes 1 answer 54 views ### Getting the pressure using the equation of states - will the answer be the same? When I get the pressure using the different equations of state (e.g. van der Waals, Redlich-Kwong, etc.), will the answer still be the same? • 33 2 votes 1 answer 2k views ### Determining the boiling point of a substance given the triple point and critical point If I have the pressure and temperature of a substance in its triple point, as well as its pressure and temperature in the critical point, how can I determine the boiling point of the substance at 1 ... • 21 4 votes 1 answer 715 views ### Theoretical versus empirical equations I'm familiar with the fact that theoretical formulae are based on already known theory and are very frequently simplified (some equations don't include interactions between molecules for example) ... • 41 1 vote 2 answers 326 views ### Cohesive Energy Density table request Quick question: Any one knows a resource for Cohesive Energy Density of some organic materials ? I am not looking for any specific molecule, actually I want to plan my project based on available ... • 2,111 13 votes 3 answers 42k views ### Why does small value of van der Waals gas constant "b" ensure easier liquefication? Larger value of b signifies that the size of the molecules is larger and hence the forces acting should become larger due to increased surface area.This should ensure easier liquefication. But my book ... • 1,594 6 votes 1 answer 16k views ### Relation between the virial coefficients and van der Waals constants I don't know where to begin with this question. A functionf(x)$can be expressed as a special power series called the Taylor expansion. The common expansion is$(1-x)^{-1}=1+x+x^2$Note that the ... • 4,435 3 votes 1 answer 2k views ### How much pressure is needed to make dry ice? By compressing$\ce{CO2 (g)}$the gas gains a lot of heat. When the hot compressed carbon dioxide is left to cool, it attains the temperature of the surrounding material. When it is released into the ... • 1,353 6 votes 2 answers 649 views ### What meaning do multiple real solutions of a truncated virial equation have, if any? Let's say I truncate the virial equation after the third term for use as my equation of state: $${P\over\rho RT}=1+B\rho+C\rho^2$$ I have tabulated values for$B(T)$and$C(T)$. I know$P$and$T\$ ...
I am confused about the justification for the corrections to the ideal gas law in the Van der Waals equation: $$p=\frac{nRT}{V-nb}-a\left(\frac{n}{V}\right)^2$$ I understand that the equation ...