Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [equation-of-state]

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

3
votes
0answers
5k views

dU/dV in van der Waals equation of state derivation

Previous, I proved that $$\frac{T_2}{T_1}^{C_V/(C_p-C_V)}=\frac{V_1}{V_2}$$ I've been asked to derive a similar expression for a gas that obeys the equation of state $$p=\frac{RT}{(\overline{V}-b)}$...
2
votes
1answer
50 views

Simple alternative to UNIFAC to prove that a mixture containing 1ml of x and 5 litres of propylene glycol is not flammable?

Section 2.6.1 of the REGULATION (EC) No 1272/2008 (CLP) defines a flammable liquid as: Flammable liquid means a liquid having a flash point of not more than $60 ^{\circ}$C. So data on flash ...
2
votes
1answer
56 views

Reaction energy of oxygen and hydrogen

From the bonding energy of following bonds that I found in a Wikipedia article, I calculated the reaction energy that would be released when oxygen and hydrogen are reacted to produce water. The phase ...
7
votes
2answers
9k views

Why is the pressure correction in the van der Waals equation proportional to (n/V)^2?

The van der Waals equation for real gases is stated as follows: $$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$ For the coefficient $b$, we can reason out that more the number of molecules, the ...
1
vote
1answer
61 views

Why is excluded volume in van der Waals equation divided by 2?

Source: Physics Stack Exchange The excluded volume calculated based on the diagram is 8 times the volume of a molecule. The volume is then divided by 2 to give the so-called excluded volume per ...
2
votes
0answers
56 views

Calculating the number of energy states in a particular momentum direction

Given is a 2D scenario of a particle within a container: The circumference shows all the possible 2D spatial directions for a given momentum value of the particle. One of those momentum directions is ...
3
votes
2answers
59 views

Intuituve reason for the constant of proportionality 2/3 in pv=nRT=(2/3)U

Why is there a $\frac23$ term? I fully understand that it makes sense for pressure to be the volume weighted average kinetic energy. And the equation above shows that this is so (for an ideal gas). I ...
11
votes
3answers
27k 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 ...
2
votes
1answer
228 views

Why is the pressure correction constant 'a' independent of temperature?

In the van der Waals equation of state, 'a' which is the correction value is based on inter-molecular forces of attraction? Then should inter-molecular forces decrease when temperature increases, and ...
-1
votes
1answer
50 views

How to determine if pressure surpasses capacity with the van der Waals equation of state?

I have to decide whether a $\pu{20 L}$ container with $\pu{0.8 kg}$ ethane can withstand the pressure at $\pu{373.15 K}$. The following information is given: \begin{align} b &= \pu{6.448x10^-2 ...
8
votes
1answer
312 views

Is this equation of state original?

I created this equation of state as a personal undergraduate summer project (here is the link) seven years ago: $$\frac{PV}{nRT}-1 \propto \left(\frac{nRT}{PV}\right)^2 \left[\left(\frac{nRT}{PV}\...
1
vote
1answer
293 views

How to use a modified Peng-Robinson equation to calculate a density?

I'm trying to use the Peng-Robinson-Stryjek-Vera 2 (PRSV2) Equation of State to calculate the density of a compound, in this example: methanol. At ambient temperature and pressure, shouldn't I be able ...
10
votes
2answers
344 views

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 ...
-5
votes
1answer
3k views

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 $n$...
24
votes
5answers
904 views

Why are equations of state for a non-ideal gas so elusive?

The ideal gas equation (daresay "law") is a fascinating combination of the work of dozens of scientists over a long period of time. I encountered Van der Waals interpretation for non-ideal gases ...
-1
votes
1answer
728 views

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 ...
9
votes
1answer
2k views

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 ...
12
votes
3answers
11k 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 ...
12
votes
1answer
880 views

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 ...
5
votes
1answer
985 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 $...
19
votes
2answers
3k views

What is a rigorous definition of gas volume, and how is the Van der Waals equation derived?

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 ...
16
votes
2answers
2k views

PV=nRT approximation on other planets?

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\ \...
3
votes
2answers
80 views

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 ...
2
votes
0answers
79 views

understanding redox reaction

I am a total noob in chemistry, so sorry in advance if this is a very stupid question... I am trying to solve this redox reaction: $$\ce{KClO3 + FeSO4 + H2SO4 -> Fe2(SO4)3 + KCl}$$ $$\ce{K^{+1}Cl^{...
1
vote
2answers
197 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
votes
0answers
58 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} &...
1
vote
1answer
198 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 $$...
3
votes
1answer
41 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?
4
votes
1answer
504 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) ...
2
votes
1answer
1k 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 ...
6
votes
2answers
551 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 $T$ ...