What is Free expansion: Definition and 36 Discussions

The Joule expansion (also called free expansion) is an irreversible process in thermodynamics in which a volume of gas is kept in one side of a thermally isolated container (via a small partition), with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.
The Joule expansion, treated as a thought experiment involving ideal gases, is a useful exercise in classical thermodynamics. It provides a convenient example for calculating changes in thermodynamic quantities, including the resulting increase in entropy of the universe (entropy production) that results from this inherently irreversible process. An actual Joule expansion experiment necessarily involves real gases; the temperature change in such a process provides a measure of intermolecular forces.
This type of expansion is named after James Prescott Joule who used this expansion, in 1845, in his study for the mechanical equivalent of heat, but this expansion was known long before Joule e.g. by John Leslie, in the beginning of the 19th century, and studied by Joseph-Louis Gay-Lussac in 1807 with similar results as obtained by Joule.The Joule expansion should not be confused with the Joule–Thomson expansion or throttling process which refers to the steady flow of a gas from a region of higher pressure to one of lower pressure via a valve or porous plug.

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  1. C

    Free expansion of Real Gases - Dieterici EoS, Change in Temperature

    I proceeded in the usual manner in which we take ##dU = 0## in the case of free expansion because there is no heat transfer in the box, as well as no work is done. We can write, taking ## U ## as the function of ##V## and ##T##, $$ dU(V,T) = \left( \dfrac{\partial U}{\partial V} \right)_T ~...
  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. T

    A Understanding Free Expansion of Gas: Velocity Distribution Function Evolution

    Hey all. I'm trying to understand the evolution of the velocity distribution function of a gas undergoing free expansion. I know that at t=0, the velocity distribution function is given by ##u(t=0, x)=Ax^{1/2}##, where ##A## is a known constant. From the momentum equation, I have: ##du/dt+u...
  4. Ron19932017

    Euler's equation of thermodynamics in free expansion (Joule expansion)

    Hi everyone, I am confused when I apply Euler's equation on the free expansion of an ideal gas. Consider a free expansion (expansion of gas in vaccum) where the volume is doubled (V->2V) The classical free expansion of an ideal gas results in increase in entropy by an amount of nR ln(2), a...
  5. A

    Is Entropy decreased for Free expansion of a Waals gas?

    Previous of this problem, there was another problem. that is "What is the change in Temperature of van der Waals gas in free expansion?". I got them. It was C_V dT= -aN^2/V^2 dV Then, I got T=T0-aN^2/2VC_V So i knew that the Temperature is decreased by free expansion in adiabatic process. Then I...
  6. hnnhcmmngs

    Minimum heat removed from gas to restore its state

    Homework Statement After a free expansion to quadruple its volume, a mole of ideal diatomic gas is compressed back to its original volume isobarically and then cooled down to its original temperature. What is the minimum heat removed from the gas in the final step to restoring its state...
  7. A

    I Free expansion of an ideal gas

    If considering the free expansion of an ideal gas adibatically such that the final volume is double of the initial volume. Since dU=0 for free expansion ,which implies Ti=Tf for ideal gas...(1) From adiabatic relation , TiViγ-1=TfVfγ-1, to satisfy (1) ,γ-1=0 and for ideal gas Cp-Cv=nR or...
  8. A

    Free expansion process and temperature change

    Good day all! I have the following exercise One kilo-mole of air expands adiabatically from an initial state p1=1 bar, T1=340 K to a final state V2= 2V1. Compute the temperature of the final state, for the following cases: Joule expansion (gas free expansion with W12=0) My problem is with the...
  9. P

    A Free expansion of a real gas vs Joule-Thomson effect

    I am writing a document on the Joule-Thomson effect. But in my research for it I have come across something that I am not completely clear on. In my document I explained the free expansion of an ideal gas and am trying to transition/segue into the Joule-Thomson effect. However now I am having...
  10. A

    B Free Expansion of Gas: Internal Energy & Work

    If a gas is suddenly allowed to expand freely and adibatically inside a container then from the first law of thermodynamics dQ=0, My question is whether the change of internal energy would be 0 and if it then how would the work done be 0 (since accessible volume of the gas changes inside the...
  11. D

    Is the Entropy in a Free Expansion Affected by the Gas Type?

    Homework Statement The question is: What happened with the entropy in a free expansion? The system is isolated and the state equation is: $$p=AT/V+B/V^2$$ Homework Equations $$dU=TdS-pdV$$ The Attempt at a Solution My attempt is: Because the system is isolated and corresponding to an free...
  12. Mayan Fung

    Why does the entropy increase in free expansion of an ideal gas?

    I learned that $$ dS = \frac Q T$$ In free expansion of Ideal gas, it is obvious that Q = 0. However, the entropy increases. I guess the reason is that it is because the process is not quasistatic. If I am right, why is this process not quasistatic. If I am not, what's wrong with the formula...
  13. V

    Thermodynamics -- Free expansion of gas

    We have 2 (insulated) partitions, one with the gas, another vacuum, separated by a stop cock. We remove the cock, letting the gas expand into vacuum . I understand that since there is no opposing force on the expanding gas ,the work done by the gas is zero . But work done by gas is given by...
  14. S

    Why is the internal energy change of free expansion 0?

    ΔU=q-w and in a free expansion w=0 and Free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber. Does this mean that free expansion is an isolated system? Meaning the walls of the container are adiabatic in which no heat can enter the system and so q=0...
  15. kelvin490

    Why dU may not equals dW in free expansion?

    From a video lecture, it is mentioned that "dU≠dW in Joule's free expansion if the process is irreversible and adiabatic" Mentioned in around 36:00-38:00 in the video: What I would like to ask is why in this irreversible adiabatic process, dU≠dW? Is it because the W here doesn't include other...
  16. S

    Adiabatic Free Expansion and Reversible Isothermal Path

    Homework Statement Consider an ideal monatomic gas that undergoes an adiabatic free expansion starting from equilibrium state A with volume 500 cm3, pressure 40 kPa and temperature 300K to state B, which has a final equilibrium volume of 1000 cm3. Construct an reversible isothermal path that...
  17. MexChemE

    Free energy in the free expansion of an ideal gas

    Hello PF! Consider the free expansion of an ideal gas. The process occurs at constant temperature, therefore, ΔU = 0, Q = 0, and W = 0. Suppose we are given the initial and final pressures of the gas, and we calculate ΔG = nRT ln(P2/P1). As P2 < P1, ΔG < 0. This is intuitive, as a free expansion...
  18. fluidistic

    Free expansion of a Van der Waals gas, physical explanation

    Hello! Today I've learned that when a Van der Waals gas undergoes a free expansion, it cools down a bit. :bugeye: This is in contrast with the ideal gas in which case since it does no work and since the process is adiabatic, the internal energy of the ideal gas remains unchanged by the...
  19. K

    Free Expansion of Ideal Gas: Isothermal or Adiabatic?

    Let's consider free expansion of an Ideal gas into vacuum. We have 2 (insulated) partitions, one with the gas, another vacuum, separated by a stop cock. I lift the cock, letting the gas expand into vacuum. I am aware that in free expansion of a gas into vacuum, the change in internal energy i.e...
  20. brainpushups

    Adiabatic Free Expansion Question

    A typical free expansion scenario described in texts is that of a gas confined to a thermally insulated container with a removable membrane. When the membrane is removed the gas expands into vacuum. I understand that no work can be done because the gas does not exert a force. However, I am...
  21. N

    Thermodynamics problem: Adiabatic free expansion

    Homework Statement A rigid ( ie. Constant volume), non-conducting ( ie. Perfectly insulated, no heat losses or gain) tank with a volume of 4.6 m^3. The tank is divided into two unequal parts by a thin membrane. One side of the membrane representing 1/3 of the tank is filled with nitrogen ( may...
  22. X

    Semi-idealized atomic gas and it's free expansion in vacuum

    Hello! I was thinking about what would happen if an atomic gas was allowed to expand in vacuum and concluded I don't have much of a handle on the subject, so if anyone would help me out - I'd really appreciate it. So, let's say we have an ideal gas in a container located in vacuum...
  23. S

    Mostly Free Expansion of Ideal Gas

    Hey All, Had a problem to solve and wanted to know how others would approach it. Problem is as follows: An insulated container of known volume has an orifice of know size. Container is filled with air and left to rest so that temperature and pressure is that of atmospheric surroundings...
  24. A

    Thermodynamics: proof about free expansion

    Homework Statement prove that for a free expansion the following equality holds: \left( \frac{\partial T}{\partial V} \right) _{U} = - \frac{1}{C_{V}} \left[ T \left(\frac{\partial P}{\partial T} \right)_{V} - P \right]Homework Equations thermodynamic potentials, maxwell equations etc.The...
  25. M

    Free Expansion is non-spontaneous?

    I searched in the fora, and I did find https://www.physicsforums.com/showthread.php?t=292278" asking pretty much the same thing. Internal energy change and work done are zero, so no heat is absorbed. Thus entropy is zero, hence it isn't spontaneous. What am I doing wrong? Could you also...
  26. A

    Entropy change in free expansion.

    Suppose there are two parts in an insulated chamber, one filled with ideal gas and other is complete vaccum, separated by a partition. Now if partition is removed then gas will rush in other part to fill the whole chamber. PROBLEM- Now there should be increase in entropy of system but i have...
  27. S

    Free expansion and adiabatic process

    I hope someone in here can help me out of this problem. I know that for calculating the change in entropy of a system (\Delta S) we can use this formula : \Delta S=\intδq/T Well the problem is here, when we calculating ΔS for an adiabatic process we know Q= 0 so ΔS=0 in this process, but...
  28. M

    Free expansion of a Van der Waal's Gas

    Homework Statement There are two vessels connected by a stopper. Both have the same volume. One has "N_a" moles of gas, the other "N_b". Find the expression for the change in temperature when the stopper is opened and the system is allowed to come to a new equilibrium state. The...
  29. B

    Free expansion of a gas problem

    Hello. This is my first post in this forum, so bear with me on any flaw or mistake please. Homework Statement Imagine a gas confined within an insulated container as shown in the figure below. The gas is initially confined to a volume Vi at pressure Pi and temperature Ti. The gas then is...
  30. S

    Free expansion of an ideal gas.

    I know that the work done on the system in any free expansion is 0 since the external pressure is 0. However.. is q necessarily 0? Does the temperature necessarily stay constant for an ideal gas? I've been trying to justify the reasons for which q is necessarily 0, but I can't find a...
  31. F

    Work during free expansion of a gas

    Hello, I have a small problem concerning the free expansion of a gas. https://www.physicsforums.com/attachment.php?attachmentid=20388&stc=1&d=1252066499 The two chambers are separated by a movable piston (without friction). Obviously the gas will expand because it puts pressure p on the...
  32. B

    Entropy variation during free expansion

    Homework Statement A system that consists of n moles of ideal gas does a free expansion (to the vacuum) from a volume V to a volume 2V. a) What is the variation of entropy of the gas?; b) of the universe?; c) if the expansion was reversible and isothermal, what would be the variation of the...
  33. M

    Van der waal gas in isothermal free expansion

    Homework Statement A gas obeys the Van Der Waal equation of state. The gas undergoes a free expansion from volume Vi to Vf at a constant temperature T. Find the change in entropy of the gas.Homework Equations du=Tds-Pdv+mdn The Attempt at a Solution I can solve the problem assuming du= 0 but...
  34. A

    What Happens During Free Expansion?

    what happens in a free expansion?
  35. A

    Understanding the Limit of Irreversibility: Free Expansion Explanation

    Why does free expansion represent the limit of irreversibility at which all of the "potential" work is degraded to heat.
  36. D

    Free expansion of an ideal gas

    For the free expansion of an ideal gas into an evacuated chamber, I know that Work=0 and Q=0. Correct? This implies that the change in internal energy dU also equals 0. Since U depends solely on T, this should mean that the final temperature of the chamber is equal to the temperature of the...