What is Clausius: Definition and 34 Discussions

Rudolf Julius Emanuel Clausius (German pronunciation: [ˈʁuːdɔlf ˈklaʊ̯zi̯ʊs]; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he gave the theory of heat a truer and sounder basis. His most important paper, "On the Moving Force of Heat", published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy. In 1870 he introduced the virial theorem, which applied to heat.

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  1. C

    Proving Entropy statement is equivalent to Clausius statement

    For this, I don't understand how we can apply the change in entropy equation for each solid since the ##\frac{dT}{dt}## for each solid will be non-zero until the solids reach thermal equilibrium. My textbook says that the ##\Delta S## for a system undergoing a reversible process at constant...
  2. Ahmed1029

    A Free expansion of an ideal gas and changes in entropy

    For a freely expanding ideal gas(irreversible transformation), the change in entropy is the same as in a reversible transformation with the same initial and final states. I don't quite understand why this is true, since Clausius' theorm only has this corrolary when the two transformations are...
  3. B

    Clausius clapeyron and heat capacity

  4. Pouyan

    Clausius' Theorem: Solving the Mystery of T ∑(dQi/Ti) =< 0

    I see this in my book but there is something I don't get! If we consider a Carnot cycle where heat Qh enters and heat Ql leaves, We know Qh/Ql=Th/Tl And we define ΔQ_rev then : ∑(ΔQ_rev/T) = (Qh/Th) - (Ql/Tl) =0 I insert an image: Which shows the heat dQi entering the reservoir at Ti from a...
  5. F

    Machine in Clausius' 2nd law of thermodynamics?

    Hi all, sorry for the condensed title of my post. Any other version of the question I'm trying to ask turned out to be longer than allowed. So, my question is about the wording in some versions of Clausius' statement of the 2nd law of thermodynamics. From time to time I read something like...
  6. D

    Specific heat in the curve of equilibrium

    Homework Statement Consider a system formed by two phases of a substance that consists of a single class of molecules. Determine the specific heat ##c## of a vapor pressure and temperature ##p## ##T## on the curve of liquid-vapor equilibrium. Consider the steam as an ideal gas. Data: ##c_p##...
  7. M

    Doubts Arising from Clausius' Inequality and the Second Law

    I began reading Mehran Kardar's Statistical Physics of Particles and about halfway through the first chapter, there was a discussion on the second law of thermodynamics. He makes no mention of the old tenet that 'the total entropy in the universe must always increase' (I'll refer to this as the...
  8. weezy

    I Doubt regarding proof of Clausius Inequality.

    I have attached two images from my textbook one of which is a diagram and the other a paragraph with which I am having problems. The last sentence mentions that due to violation of 2nd law we cannot convert all the heat to work in this thermodynamic cycle. However what is preventing the carnot...
  9. Soumalya

    Development of Clausius Inequality

    I am facing some doubts trying to understand the illustration my textbook has adopted for the development of the Clausius inequality for thermodynamic cycles.I have attached an image of the content from my textbook. As one could see the author has assumed a closed system connected to a thermal...
  10. E

    How to apply the Clausius-Clapeyron to geysers

    Hi first post so forgive any break in widely accepted conduct, Currently involved in a physics competition one of the question is to investigate geysers. Time and time again I have stumbled upon reference to Clausius-Clapeyron relation. Probably the best source I have come across is a youtube...
  11. Robsta

    Fork pushed into ice (thermodynamics, clausius clapeyron)

    Homework Statement A person (mass 57.8 kg) tries to penetrate a garden fork (mass 1 kg) into a melting block of ice by standing on it with all his/her weight. Assume that no heat flows from the fork to the ice. The fork has four prongs, and each prong has a square cross section of area 1 mm2 ...
  12. C

    Understanding the Clausius Clapeyron Relation: Explained Simply

    Not sure if this was the right place for this but here goes. Hello all, so I'm trying to get an intuitive grasp of the Clausius Clapeyron relation dP/dT= L/TdelV. Where L is the latent heat of the phase transition. What I've got so far is this; the relation tells you how much extra pressure must...
  13. Q

    How Does Temperature Affect Water Vapor Pressure?

    Homework Statement Determine the vapor pressure of water at 50 degrees C. The molar heat of vaporization of water is 40.7 kJ/mol. Homework Equations Clausius-Clapeyron equation. The Attempt at a Solution P1 = 760 mm Hg T1 = 373 K P2 = ? T2 = 323 K ln (P2/760) = ln P2 - ln 760 =...
  14. R

    Clausius clapeyron problem - i have spent 3 hours on this problem

    spent 3 hours on this, getting nowhere find the change in transition temperature, given: P1,P2,T1,ΔH,density (mixed so gives d1 of metal 1 and d2 of metal 2,atomic weight Tried solving for T1 then for ΔT simply saying ΔT = (T1 - T2) , but its clearly not correct and i haven't made use of...
  15. C

    Derivation of Clausius Inequality

    I have been reading about the derivation of Clausius' Inequality and there are a few things I do not understand. I have attached an image of the cycles. B) shows one carnot engine performing work ##d W_i## per cycle and delivering heat ##d Q_i## per cycle. For ##T'## to remain unchanged, it...
  16. O

    Deriving the local field and Clausius Mossotti formula in a dielectric

    (My last https://www.physicsforums.com/showthread.php?p=4424810#post4424810 post did not get much attention so I try again without all these formulae. Think this will be more clear...) To derive the local field in a non-polar dielectric you assume a very small spherical cavity in which (since...
  17. L

    Clausius inequality temperature

    in the clausius inequality is the temperature that of the system or of the surroundings? or is it temperature of the body receiving positive heat? (assuming the irreversibility is due to heat transfer with finite temperature difference) [borgnakke and sonntag-principle of entropy increase for...
  18. P

    Clausius inequality correct for negative temperature

    is clausius inequality correct for negative temperature?, if you see the proof of it in positive temperature its not correct.
  19. T

    Why is entropy defined as a state property?

    Hi,I m just beginner in physics,but actually I don need exact expression of physical laws in math language.I know,math is language of physics but still... So,I m looking for answer to my questions about origin of Clausius s entropy. I this article: http://www.panspermia.org/seconlaw.htm is...
  20. B

    Clausius-Mossotti Equation and Dielectric Constants of Air

    Homework Statement http://img809.imageshack.us/img809/5676/unavngivetk.png Additional table info: The molarmass ##M_{air}## is ##29 * 10^{-3} g/mol = 29*\frac{10^{-3}}{1000} kg/mol## The mass density ## \rho_{air} ## is ##1.3 kg/m^{3}## The dielectric constant ## K_{air}## is 1.00059 My...
  21. L

    What Units Should Pressure Be in for the Clausius Clapeyron Equation?

    Homework Statement Trying to figure out the boiling point for a substance using this equation. I have 3 temperatures along with the pressure at those three temperatures. Homework Equations lnP=−ΔHvap/RT+b The Attempt at a Solution Ok, so obviously a plot of ln(P) vs. (1/T) gives you a...
  22. A

    Calculating Boiling Point Using Clausius Claperon Equation

    Homework Statement cal the boiling point of water at 300m. assume its 100 degree centigrade at sea level. given g, R, T=300K, molecular weight of air is 29g/mol and latent heat of evaporation is 540 cal/g at STP Homework Equations The equation is dp/dt= L/T(v2-v1) where v is the...
  23. J

    Clausius clapeyrion equation Hfg

    Hi guys I'm trying to figure out a way of calculating the enthalpy of vaporisation using the clapeyron equation. So far I have two different forms of the clapeyron equation. However, I'm not sure how to go any further. Ln(P2/P1) = (ΔHfg / R) ( 1/T1 - 1/T2) eqn(1) Ln(P) = -(ΔHfg...
  24. H

    Clausius inequality and irreversible heat transfer

    I don't seem to understand Clausius inequality at all. Really. It was deduced to me that the Clausius inequality is given by dS = \frac{\delta Q_i}{T} > 0 where Q_i is the irreversible heat transferred to a system. Though I cannot find a way to prove an assertion my teacher said: through...
  25. B

    Clausius Clapeyron Equation of lead

    Homework Statement When lead is melted at atmospheric pressure the melting point is 327.0 degrees C, the density decreases from 1.101 x 10^4 to 1.065 x 10^4 kg/m^3 and the latent heat is 24.5 kJ/kg. Estimate the melting point of lead at a pressure of 100 atm. Homework Equations...
  26. D

    Solve Clausius Clapeyron Eqn for Vapor Pressure @95C

    It has been years scene I have taken a math class and I need help to see if I am setting the equation up correctly and if I have solved the problem correctly. Diethyl ether has ∆Hvap of 29.1kJ/mol and a vapor pressure of 0.703 atm at 25.0 C. What is its vapor pressure at 95.0 C? I converted...
  27. C

    Is my calculation ok? - clausius clapeyron eq.

    I would like to calculate isosteric heat of adsorption (H). I have a series of adsorption isotherms for different temperatures and it appears that the adsorption increases with increasing temperature. This suggests that the process is endothermic. Using Clausius Clapeyron law, the slope of 1/T...
  28. P

    Origin to the 'virial theorem' by Clausius

    Hello, I wonder if there is a common origin to the 'virial theorem' by Clausius and the 'virial expansion' or equation of state used to express the compressibility of a gas. I am just wondering about this because the two concepts do not seem to have a common mathematical origin (that I can...
  29. B

    Equivalence of Boltzmann and Clausius entropy

    I can't figure out how to show that the Clausius entropy \Delta S= \int_{T_1}^{T_2} \frac{dQ}{T} is equivalent to the Boltzmann entropy S=kln \Omega at thermal equilibrium. Does anyone know how to do this?
  30. M

    How Do You Calculate Heat of Vaporization Using the Clausius Clapeyron Equation?

    Homework Statement slope: -8.000 x 10^3 K The graph is of ln vapor pressure of a gas vs. invert kelvin temperature Using the Clausius Clapeyron equation, find Hvap (heat of vaporization) Homework Equations Clausius Clapeyron equation: ln P= (-delta Hvap/R)*(1/T) + C The Attempt...
  31. M

    What is the Delta H in the Clausius Clapeyron equation?

    Hi I am stuck on this question. I am given the slope of a ln vapor pressure vs. invert kelvin temp equals -8.000 x 10^3 K. I am supposed to find delta H (or the heat of vaporization). If anyone could help that would be great!
  32. B

    Clausius mossoti equation in the liquid state

    If one wishes to calculate internal field for a liquid dielectric , what will be the assumptions?can anyone guide me through mathematical steps...
  33. Clausius2

    Historical Meeting: Astro & Clausius in SD

    Historical Meeting: Astro & Clausius in SD! Yeah man! Although it was a very fast meeting, we were talking in my new place at San Diego!. A nice guy!. And yeah, his beard is original (I tried to pull out his beard hair and after some Astro screams I realized is beard is true!). Behind a...
  34. marlon

    Is Your Private Message Box Full for Clausius?

    you need to do some housekeeping in your private message box man. I cannot send you any answers to your question because it's full marlon :smile:
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