What is Equation of state: Definition and 97 Discussions

In physics and thermodynamics, an equation of state is a thermodynamic equation relating state variables which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature (PVT), or internal energy. Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, and the interior of stars.

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  1. J

    Equation of State for Solids (Dense Fluids?)

    Stumbled across an old journal a few weeks ago that suggested the equation of state for a solid could be written: V[P,T] = Vi - (C1)P + (C2)T with an internal energy: U[P,T] = (C3)T - (C2)PT C1, C2, C3 being constants of course. Does this make logical sense? It seems awfully...
  2. S

    What exactly constitutes and Equation of State?

    What exactly constitutes an Equation of State? As the title says I'm not quite sure what I need to get to have an equation of state in thermodynamics. I think I understand that an equation of state is an equation that relates different state variables of the system such as volume...
  3. D

    Help understanding the Tillotson equation of state

    I have the 1989 Melosh book, Impact Cratering, and it's an excellent book with one exception: it talks about the Tillotson EoS, and it details it a bit in an appendix, but it seems to leave something out. I was hoping someone here could help me to understand it. The book gives the equation...
  4. B

    Derive the fundamental equation from and equation of state

    Hello, I just need help deriving the fundamental equation from Equation of state for wan der waals fluids. P=\frac{RT}{v-b}-\frac{a}{v^2} and u=cRT-\frac{a}{v} where a,b, and c are constants. I know the fundamental equation is dS=\frac{1}{T}dU+\frac{P}{T}dvI solved the u equation so it's...
  5. C

    Alternative Real Gas Equation of State

    1. A friend suggests to you an alternative to the Virial equation of state: P=(RT/Vm)-(B/Vm2)+(C/Vm3) a.) Show that this equation is useful by proving that it demonstrates critical behavior. b.) Find the critical constants Pc, Vm,c, and Tcin terms of B, C and R. c.) Calculate the...
  6. T

    Showing equation of state is inaccurate based on compression factor

    Homework Statement If I was using an equation of state as so: Vm = (RT/P) - (aRT^2)/P, where the constant a is always positive, I would be able to determine that the compression factor is Z = Vm/Vm° = 1− a ⋅T . This leads me to the conclusion that there is something seriously wrong with...
  7. T

    Calculate a values given equation of state for gases

    Calculate "a" values given equation of state for gases Homework Statement For my equation of state: Vm = (RT/P) - (a/T) what kind of sign for the constant a (positive or negative) do you think the following gases will have and why: a. H2 b. He c. CH4 d. CO2 Hint: There is almost no...
  8. bcrowell

    Latest result for dark energy's equation of state

    Helder Velez brought the following paper to my attention: Carnero et al., "Clustering of Photometric Luminous Red Galaxies II: Cosmological Implications from the Baryon Acoustic Scale," http://arxiv.org/abs/1104.5426. They use a survey of galactic redshifts to measure baryon acoustic...
  9. T

    Gas equation of state and shape of container

    Does the equation of state of a gas of interacting particles depend on the shape of the container they are in? For instance, if the interaction force is gravity (a central force) and the particles are in a spherical container, then it seems reasonable that the pressure on the wall of the...
  10. A

    Determine equation of state from entropy

    Homework Statement The entropy is given as S=a \left(VNU \right)^{\frac{1}{3}} Find the equation of state. 2. The attempt at a solution I've tried writing dS in terms of dP and dT then using the fact that dS is a perfect differential equate the partial derivatives of the terms. This got...
  11. aleazk

    Equation of state for electron degenerate matter

    Hi, this may be a silly question. In the study of white dwarfs, why we change from the non-relativistic equation of state, P(ρ)=K.ρ^(5/3), to the relativistic case, P(ρ)=K'.ρ^(4/3), when there is an increase in the central density of the star, i.e., why the electrons, which compose the Fermi...
  12. D

    Factor a in Van der Waals equation of state off by a factor of 0.1?

    Hello So I have a lab exam in Joule-Thomson effect and I have given values for a and b for VdW equation of state for nitrogen and carbon dioxide. When I take the critical temp. and pressure and put it in the equations: a=\frac{27(T_c R)^2}{64 p_c} and b=\frac{T_c}{8p_c} b gives...
  13. Y

    Proving the Ideal Gas Equation of State

    Homework Statement Show that the equation of state of an ideal gas with N molecules in a container of volume V at temperature T is P=NkT. Use the result derived earlier. The result is A=-NkTlnZ, where Z is the partition function and A is the Helmholtz free energy. Homework Equations The...
  14. S

    Data/Model for Tait Equation of State (Liquids)

    Hello All, I'm not sure if this query belongs in the Atomic/Solid State/Comp. Physics category (vs. say, Classical Physics), but I'm fishing here anyway. I'm looking for current values of the empirical constants in the Tait equation of state, and/or the 'modified' (adiabatic) Tait EOS, for...
  15. Phrak

    What does it mean by an equation of state is a particle?

    There was a recently posted thread titled "What does it mean by a particle is a "wave"? I think it might be more appropriate to ask, what does it mean by an equation of state is a particle?
  16. H

    Most accurate equation of state

    I've come across many equations of state in physical chemistry. (only a fraction of those that actually exist) Does anybody have any idea of the most accurate one to date. By accurate, I mean that it is accurate for the largest ranges of pressure and temperature by taking into account the least...
  17. L

    P)_r = 1, proving the desired result.

    Homework Statement Given the Equation of State f(P,V,T)=0 and r=r(P,V,T) be a constraint show that these are all partials i can't get latek to work for me sorry about that (dp/dV)_r (dV/dT)_r (dT/dP)_r = 1 the _r means holding r constant. hint consider dr I have tried several...
  18. O

    Find equation of state of material usiing its compressability and expansivity.

    1. Homework Statement A substance has an isothermal compressibility k= (aT^3)/(P^2) and an expansivity B = (bT^2)/P where a and b are constants, T is temperature, P is pressure. Find the equation of state of the substance. 2. Homework Equations B= 1/v(dv/dT) (v is specific volume aka...
  19. O

    Finding Equation of State for Substance

    Homework Statement A substance has an isothermal compressibility k= (aT^3)/(P^2) and an expansivity B = (bT^2)/P where a and b are constants, T is temperature, P is pressure. Find the equation of state of the substance. Homework Equations B= 1/v(dv/dT) (v is specific volume aka V/n)...
  20. A

    How Does the Dieterici Equation of State Compare to Reality?

    [SOLVED]Dieterici equation of state Homework Statement Establish the relationship between the critical constants and the parameters of Dieterici equation of state. Show that Z_c=2e^{-2} and deduce the reduced Dieterici equation of state. Compare the predicted Z_c from both Dieterici's and...
  21. Ranku

    Gravitational Energy Equation of State Parameter

    Cosmological constant dark energy has equation of state parameter = -1. What is the equation of state parameter of gravitational energy?
  22. T

    Defining Expressions from the Equation of State

    Homework Statement Starting from the expression for g(E) derived in the lectures, show that for a solid of volume V containing N free electrons which obey Fermi-Dirac Statistics, E_F, k_F, and v_F can be expressed as: E_F = \left( \frac{N}{V} \right)^{1/3}(3\pi^2)^{2/3}\left(...
  23. M

    The equation of state of radiation

    the EOS of radiation (photon gas surrounding a black hole) Why does the EOS of radiation set to 1/3? Where does this come from?
  24. T

    Proof that Heat Capacity is independent of Pressure for a new Equation of State

    For a gas that obeys the equation of State P(v-b) = RT, where b is a constant, show that Cp is independent of Pressure, i.e., (\deltaCp/\deltap) at constant T is equal to zero Homework Equations Maxwell Relations H = U+PV dh = TdS + PdV dh/dT at constant P is defined as Cp The...
  25. D

    Deriving an Thermodynamic Equation of State

    Homework Statement Derive the following: \left(\frac{\partial U}{\partial V}\right)_{T}=T\left(\frac{\partial p}{\partial T}\right)_{V}-p Homework Equations Use the partner equation: \left(\frac{\partial H}{\partial p}\right)_{T}=-T\left(\frac{\partial V}{\partial T}\right)_{p}+V...
  26. S

    Berthelot equation of state - virial coefficient and taylor series

    Using the taylor series result Vm / Vm - b = 1 + b / Vm + ... and the definition of hte compressibility factor Z = PVm / RT, derive an expression for the first virial coefficient in terms of a and b for the Berthelot equation of state.
  27. A

    DE equation of state parameter

    Homework Statement Plot \Delta w as a function of spectroscopic redshift for some given biases between spectroscopic and photometric redshifts. Homework Equations \Delta w = \frac{\partial D_{A}}{\partial z}\frac{\partial w}{\partial D_{A}} \Delta b D_{A} = \frac{c}{H_0} \cdot...
  28. T

    Van der Waals equation of state and Maxwell construction

    Hello people :), I have a question because I couldn't understand something written in Schwabl's book of Statistical mechanics. Can you please explain why we in the Van der Waals equation of state choose a constant pressure under the critical temperature. I understood the part that we want to...
  29. M

    Thermodynamics of Spacetime: The Einstein Equation of State?

    Hi, I have recently been delving into Quantum gravity related material... and I came across a paper by Ted Jacobson "Thermodynamics of Spacetime: The Einstein Equation of State" http://arxiv.org/abs/gr-qc/9504004 and as far as I understand the argument it is very impressive who would have...
  30. M

    Evidence for dark energy equation of state paramater w = -1

    I'm having trouble finding an article or paper on the observational evidence for dark energy being a cosmological constant. I'm looking at this Living Review by Sean Carroll http://relativity.livingreviews.org/Articles/lrr-2001-1/ and he only describes how supernova data constrain the...
  31. D

    What is Equation of state for the Dark Matter?

    Just to clarify, I am NOT talking about the Dark Energy, I am talking about the Dark Matter w=?
  32. O

    Alternative equation of state?

    I'm aware that the equation of state for a perfect fluid (when considering single fluid cosmology) is p=w*rho However I've come across an equation of state of p=w*rho - xi*H, H being Hubble's parameter. However I cannot find an explanation of why you can put this in? Can anyone explain this...
  33. Q

    Finding the equation of state and internal energy of a given gas.

    Consider a gas contained in volume V at temperature T. The gas is composed of N distinguishable particles at zero rest mass, so that the energy E and momentum p are related by E = pc. The number of single-particle energy states in the range p to p + dp is 4\pi Vp^2 dp . Find the equation of...
  34. L

    Equation of State of an Ideal Gas

    Homework Statement Show that:- a) the expansivity \beta = \frac{1}{T} b) the isothermal compressibilty \kappa = \frac{1}{P} Homework Equations P\upsilon = RT where \upsilon = molar volume The Attempt at a Solution A big mess!
  35. S

    Find the equation of state (thermo)

    Homework Statement A hypothetical substance has an isothermal compressibility k = a/v and an expansivity B = 2bT/v where a and b are constants and v is the molar volume. Show that the equation of state is v-bT2+aP = g where g is a constant. Homework Equations k= -v(dP/dv)T B =...
  36. A

    Equation of state of a hard sphere gas

    Homework Statement I am trying to solve problem 1.4 from Statistical Mechanics by R.K. Pathria 2nd edition. This is the problem: In a classical gas of hard spheres (of diameter \sigma), the spatial distribution of the particles is no longer uncorrelated. Rougly speaking, the presence of n...
  37. N

    Cosmology: Equation of state parameter

    Homework Statement Hi all. The pressure in a multi-component universe is additive, just as the energy-density is: P = \sum\limits_i {w_i \varepsilon _i } \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{and}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\varepsilon = \sum\limits_i {\varepsilon _i } But...
  38. V

    Equation of state of an electron gas

    Could anyone tell me the equation of state of an electron gas, or where I could read it from? By equation of state I mean a relation between pressure, density etc etc.
  39. C

    [Thermo] Equation of State Given, Find Internal Energy and Specific Heat

    Homework Statement P=RT/(v-b) - a/(T(V+c)^2) Homework Equations u2-u1= Integral ( Cv dT) + Integral ( T * (dP/dT)v - P) dV The Attempt at a Solution I've differentiated P with respect to T to get R/(v-b)+a/(T^2(V+C)^2 and plugged the relevants back into the equation for...
  40. H

    Equation of State from Partition Function

    Homework Statement Find the partition function for a two-dimensional nonrelativistic classical gas. Find the equation of state. Calculate the specific heat at constant volume cv and the entropy S. Homework Equations The partition function is Z = (A^N / N!) [(2 pi m k T / h^2)^N]...
  41. L

    Finding critical temperature from equation of state

    Homework Statement Given the equation of state PV=nRT. So, I get the first derivative and second derivative (P with respect to V) and equate them to 0. Then, I found out that they cannot be equal to 0, so I make the conclusion that no critical temperatue exists for an ideal gas. If the van...
  42. I

    Equation of state for an ideal gas

    Homework Statement What condition must the gas be in for this equation to hold true? Homework Equations The Attempt at a Solution the gas has to be in constant pressure and volume and temperaute
  43. P

    Understanding Friedmann Equations Equation of State: Step-by-Step Walkthrough

    I've got some difficulties trying to understand the equation of state derived from Friedmann equations. I'd greatly appreciate it if someone walked me through this. Now if the equation of state is stated as: \Large \dot{\rho}+(3\rho +p)\frac{\dot{R}}{R}=0 \ \ |p=\omega \rho Then (in the case...
  44. Clausius2

    Ideal Gas: Equation Of State in Diatomic Gases: still valid?

    That came out in my qualifying exam. The question was if a gas with rotational and vibrational energies enhanced, does obey the Ideal Gas Equation PV=NKT. You can answer with all the tools you have at hand. My comitee member didn't agree with me, but anyway I persisted in my answer and I...
  45. G

    Modified equation of state of an ideal gas

    I have this problem, it doesn't seem very complicated but I can't figure out how to do it. A gas obeys to the equation of state P(V-b) = Nk\zeta where k is the Boltzman's constant. The internal energy of the gas is a function of \zeta alone. Show that \zeta=T using a Carnot cycle. Any help...
  46. N

    Van der Waal's equation of state

    Help me on this one - Van der Waal's equation of state suggest ways of reconciling Van der Waal's equation of state with experimental observations
  47. F

    Deriving the coefficients a and b in the Van der Waalls Equation of State

    I've looked in my textbook and asked my fellow classmates, but I have had no luck in figuring out how to derive these coefficients. Can anyone tell me how I would go about doing this?
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