Internal energy Definition and 381 Threads

The internal energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state. It does not include the kinetic energy of motion of the system as a whole, nor the potential energy of the system as a whole due to external force fields, including the energy of displacement of the surroundings of the system. It keeps account of the gains and losses of energy of the system that are due to changes in its internal state. The internal energy is measured as a difference from a reference zero defined by a standard state. The difference is determined by thermodynamic processes that carry the system between the reference state and the current state of interest.
The internal energy is an extensive property, and cannot be measured directly. The thermodynamic processes that define the internal energy are transfers of matter, or of energy as heat, and thermodynamic work. These processes are measured by changes in the system's extensive variables, such as entropy, volume, and chemical composition. It is often not necessary to consider all of the system's intrinsic energies, for example, the static rest mass energy of its constituent matter. When matter transfer is prevented by impermeable containing walls, the system is said to be closed and the first law of thermodynamics defines the change in internal energy as the difference between the energy added to the system as heat and the thermodynamic work done by the system on its surroundings. If the containing walls pass neither matter nor energy, the system is said to be isolated and its internal energy cannot change.
The internal energy describes the entire thermodynamic information of a system, and is an equivalent representation to the entropy, both cardinal state functions of only extensive state variables. Thus, its value depends only on the current state of the system and not on the particular choice from the many possible processes by which energy may pass to or from the system. It is a thermodynamic potential. Microscopically, the internal energy can be analyzed in terms of the kinetic energy of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energy associated with microscopic forces, including chemical bonds.
The unit of energy in the International System of Units (SI) is the joule (J). Also defined is a corresponding intensive energy density, called specific internal energy, which is either relative to the mass of the system, with the unit J/kg, or relative to the amount of substance with unit J/mol (molar internal energy).

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  1. W

    Why is Entropy a concave function of internal energy?

    Hello I may well be all wrong about this but I am trying to understand from a microscopic point of view why Entropy is a concave function of internal energy. I found this in the following .pdf: http://physics.technion.ac.il/ckfinder/userfiles/files/avron/thermodynamics_potentials.pdf I...
  2. O

    Internal energy equals to average kinectic energy ?

    For ideal gas , can I assume Cv dT = nkT (3/2) , thank you
  3. I

    Relationship between internal energy and PE and KE

    Hi, Firstly, I'd like to thank PhysicsForums and its members for helping me during my last couple of visits (around 7 months ago). With your help I managed to achieve an A at AS Physics (a UK exam)! I am doing some basic concepts on internal energy etc and I came across the following...
  4. Y

    Isobaric Process, finding Change in Internal Energy

    Homework Statement Assume nitrogen gas (N2) is an ideal gas. n = 7.57 moles of N2 gas are heated isobarically (at constant pressure) from temperature To = 18.6 oC to temperature Tf = 50.9 oC. Find: c) ΔIE, the change in internal energy of the N2 gas Homework Equations Change in IE...
  5. I

    Conservation of Energy and internal energy

    Homework Statement A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200N/m, the internal energy of the block and the table top must...
  6. S

    Temperature of gas when internal energy is constant

    Homework Statement A fixed mass of gas is trapped in a metal cylinder by a movable piston. The piston is moved outwards slowly. The volume of gas increases but the internal energy is unchanged. What happens to the pressure and to the temperature of the gas? Homework Equations none The...
  7. T

    Find the final internal energy of a gas.

    Homework Statement A thermally isolated container is filled with 2.3 mol of an ideal gas at T = 0°C.The gas is then compressed from 1.9 m3 to 0.3 m3. What is the final internal energy U of the gas? (Assume the process occurs at constant pressure.) Homework Equations U=3/2nRT U=Q+W W=pΔV...
  8. D

    Thermodynamics question(change of internal energy)

    The temperature of 2 kg of N2 changes from 300 K to 1000 K. Calculate the change of its internal energy during this process, assuming the ideal gas behavior, in two different methods: (1) Using constant heat capacity (2) Using the enthalpy function ı have to solve this question but ı...
  9. L

    Change in Enthelpy when Internal Energy does not Change

    Homework Statement The internal energy of a perfect gas does not change when the gas undergoes isothermal expansion. What is the change in enthalpy? Homework Equations H=U+PV The Attempt at a Solution The answer is 0 Since U, the internal energy, doesn't change, I assumed that...
  10. M

    Liquids, internal energy and specific heat capacity

    A liquid contained in an adiabatic container is shaked vigorously so that it its temp. Increases. The heat capacity for the liquid is given, the rise in temp. Is given. According to the first law of thermo, dQ=dW + dU here dQ is 0. Asked, is to find the work done on the system, i.e...
  11. A

    How Does Doubling Internal Energy Affect Pressure in a Sealed Container?

    Homework Statement For example in the problem if we have a volume of 10L at 15 degrees Celsius, and there is initially 100Pascals pressure, what would the final pressure be if we double the Internal Energy? Homework Equations U=3/2nRT The Attempt at a Solution I though pressure was...
  12. J

    *Thermodynamics*: Adding air to a bottle, finding internal energy and so on

    Homework Statement In class we saw a demo where a pop bottle was pumped up with extra air. If we consider the bottle was pumped up to a gauge pressure of 50 psi and let sit until it returns to room temperature. Describe what happens when the air is rapidly released (for example if the top...
  13. S

    What Happens to Internal Energy in a Piston if Pressure is Increased?

    If the temperature is kept constant,what happens to internal energy if the pressure is increased in piston?
  14. M

    Question about change in internal energy

    Fair warning: This is more chemistry than physics but I know that thermodynamics and heat and work are all covered in General Physics but I'll post in the Other Science forum too. 1. Assume that one mole of H2O(g) condenses to H2O(l) at 1.00atm and 95 Celcius. Calculate q, w, ΔH, ΔS of the...
  15. P

    Comparing the Internal Energy of Gasoline and Hydrogen

    Calculating the internal energy of gasoline is fairly simple, because it wouldn't vary much with temperature or pressure. For hydrogen, though, it would vary significantly with each. What sort of ranges would we be looking at? I'm curious if it would be possible to get the same amount of...
  16. R

    Isobaric process; change in internal energy

    I know this question has been done to death and I have had a look through past questions on this forum and others but I can't find anything that is helpful to this particular question! Homework Statement An ideal monatomic gas expands reversibly at a fixed pressure of 10^5 Pa from a...
  17. G

    Work, heat and internal energy in pV diagram.

    hi i have this pV-diagram(ideal gas) and i am supposed to say something about the heat, internal energy and work transferred and done on these different paths( i have to bring them in an order like). i do not know how to do this, as this is a pV diagram and these paths are not further...
  18. C

    Internal energy change in isobaric system

    hi all, i have a confusion about the internal energy change and work done in a isobaric system... suppose i want to find the delQ in isobaric system in terms of P & V...now i may assume the delW part would be pdv=p(V2-V1)...as i m compressing the gas... but what happens to the du? and is the...
  19. A

    Internal Energy of an Isovolumetric Process

    [b]1. We have some gas in a container at high pressure. The volume of the container is 469 cm^3. The pressure of the gas is 2.52*10^5 Pa. We allow the gas to expand at a constant temperature until its pressure is equal to the atmospheric pressure, which at the time is .857*10^5 Pa. (a) Find...
  20. C

    Heat capacity and its relation with internal energy

    hi everyone, in thermodynamics, when we calculate the heat capacity in constant volume, we assume Cv=dQ/dT.. well, but at isothermal condition suddenly they came up with Cv=dU/dT... so i am getting stuck with this concept how they replace dQ with dU? i know U= internal energy is only a...
  21. 5

    Internal energy or enthelpy are minimized in isoentropic processes?

    Homework Statement How to demonstrate that U is minimized at constant V and S, while H at constant P and S? Homework Equations ΔS universe = ΔS system + ΔS environment ≥ 0 ΔU system = δq reversible + δw reversible = δq irreversible + δw irreversible ΔS environment = −∫(δq reversible / T) dU...
  22. D

    Total Internal Energy of an Ideal Gas

    Homework Statement Argon is stored in a container of volume 2L and a pressure of 5 atmospheres. The amount of gas present is 0.2 moles. Find: (i) The absolute temperature of the gas (ii) The number of atoms of gas in the container (iii) The total mass of the gas (iv) The total internal...
  23. K

    Internal Energy of Falling Stone in Vacuum: Is ΔU Zero?

    A stone is falling under gravity in a vacuum. Is its internal energy increasing? Well, since internal energy(Microscopic level) is defined as the energy associated with molecules(Sum of kinetic energy and potential energy of the molecules). The molecules inside the ball will not gain any K.E...
  24. L

    Thermodynamics: Internal Energy and Enthelpy

    H = U+ pV pV = nRT H= U+ nRT H= H (T) I don't understand the transition from U+ nRT to H (T) Can someone explain this? I get that H = U + pV But how is H= U+ nR
  25. H

    What is the difference between enthalpy and internal energy?

    Hello, I'am new here and having some troubles with understanding the difference between 2 related subjects. I learned that internal energy contains 2 main components: kinetic energy and potential energy. U=E_{K}+E_{p} The related first law of thermodynamics (for closed systems)...
  26. W

    Total internal energy change of a gas

    Homework Statement If ΔWi denotes the amount of work done by a gas in being compressed isothermally to a given volume, ΔQ the amount of heat absorbed by the gas in this process, and ΔWa the amount of work done by the gas in being expanded adiabatically back to its original volume, then the...
  27. W

    Change in pressure and Internal Energy

    I'm aware of the equation ΔU = Q + W ΔU is the change in internal energy which equals 3/2 nRΔT Q is heat transfer W is workdone so PV = nRT would it be correct to say that ΔP V = nRΔT? For isovolumetric process (i.e. no volume change, no work done), can i say that change in internal energy =...
  28. V

    Change in temprature is zero. what about change in internal energy?

    change in internal energy is a function of temperature. So if there is no change in temperature then there should no change in internal energy. But consider this example. work done in process work done(W)= nRT*ln(P1/P2) (Δ)T=0; so it's isothermal) heat supplied(Q)=0 (No heat is supplied...
  29. H

    Thermodynamic- Internal energy of dry air

    Homework Statement a) what is the density of dry air when the surface pressure is 1010hPa and the temperature is 27°C. b) what is the internal energy of 1kg of dry air under these conditions? Homework Equations P=p*R*T where P is pressure and p is density. The Attempt at a...
  30. alemsalem

    Can internal energy levels of atoms affect chemical potential of ideal gas?

    μ/T represents the change in entropy if we change the number of particles,, so according to the fundamental assumption of statistical mechanics μ/T should tell us about the tendency of two systems to exchange particles... but I am having a hard time imagining how rotational or vibrational...
  31. T

    Thermodynamics - Internal Energy in Isochoric and Isobaric Processes

    Assuming that the gas in these processes is an ideal one, is the change in internal energy in an isochoric process (volume remaining constant) the same as the change in internal energy of isobaric process (pressure remaining constant)? Mathematically I can derive that they're equivalent, but...
  32. X

    Ideal gases thermodynamic enthelpy and internal energy change

    Homework Statement See attachment ecxample001. Homework Equations See attachment D11. The Attempt at a Solution In the first equation (Cp/R = a+bT+cT^2...etc.), Cp/R is the constant pressure specific heat. The general formula for enthalpy change is h2-h1 = integral[Cp]dT, so does...
  33. L

    Internal energy and heat question.

    how would you determine an error at the 100C mark in a given mercury thermometer?Your answer should consist of a labelled sketch of the apparatus you would use and brief notes on procedure. Why is it important, at the same time, to note the atmospheric pressure? If the thermometer registers 103...
  34. C

    Understanding Work, Friction, and Internal Energy

    Homework Statement A block slides to a stop along a table top. Which is true? A. The work done by friction is equal to the force of friction times the distance that the block slid. B. The work done on the block is equal to the force of friction times the distance that the block slid. C. The...
  35. B

    Internal Energy: Definition & Difference from Enthalpy of Formation

    I am reading on wikipedia about internal energy and the describe it as the energy required to create a system. Ithought that this was the definiton for enthalpy of formation. Was it meant by the definition of internal energy?
  36. A

    Internal energy and state functions

    Hello all, I have following questions dangling in my mind, with a positive attitude of seeking help i want put them infront you geneus people, in my earlier post i get a good result and now i want to more insight of the very matter. kindly help me. Using the concept of state of system, i...
  37. G

    U, V, and T: Internal Energy, Specific Volume, and Temperature

    u denotes internal energy; v denotes specific volume; T denotes temperature.
  38. J

    General Question Regarding Internal Energy

    Hi all! I have a quick question. In my Physical Chemistry textbook, the author states, "For a closed system in equilibrium, the internal energy (and any other state function) can be expressed as a function of temperature and volume." Can anyone explain just how that is true? I'm quite...
  39. Z

    Relationship between work, internal energy and enthelpy.

    Hi, I'm taking a thermodynamics class and I'm stuck on how work relates to enthalpy and internal energy. Does work done by a system equal change in internal energy, change in enthalpy or does it depend on the situation? The question I'm stuck on asks for the work produced by a steam turbine...
  40. F

    How Does Water Vapor Dissociation Affect Internal Energy in a Closed System?

    Homework Statement In a closed vessel there was some water vapor. After the water vapor dissociated, the temperature decreased by 10%, and the volume by 20%. Find the change in internal energy. (U{initial}-U{final})/U{initial} Homework Equations The Attempt at a Solution Let's...
  41. N

    Internal Energy and Temperature Changes When Mechanical Work is Done on a System

    Homework Statement What happens to the internal energy of a system and its temperature when mechanical work is done on it? Homework Equations ΔU=Q-W The Attempt at a Solution First Law of Thermodynamics say:the change in internal energy of the system is equal to the heat added to the...
  42. L

    When does the change in enthelpy=change in internal energy?

    Sometimes in my book, a problem justifies ΔU=ΔH for a process, such as combustion in a bomb calorimeter, by saying that since the number of moles of gas doesn't change, they are equal. In other questions, the number of moles doesn't change (such as an irreversible expansion of a perfect gas)...
  43. I

    Internal Energy and Work Done in an Adiabatic Process

    Homework Statement The question is as following: http://i56.tinypic.com/se547s.png Homework Equations W = F x distance or p d(v) . Potential energy : mgh , k.e : 1/2mv^2 The Attempt at a Solution Well I am stuck on part c, now I am aware that in adiabatic process Internal...
  44. D

    Thermodynamics: internal energy change

    Homework Statement Enthalpy of formation of a mole of atomic hydrogen = 218kJ. Enthalpy changes when a mole of atomic hydrogen is formed by dissociating half a mole of molecular hydrogen. Calculate ΔU of the process of molecular hydrogen dissociation. Homework Equations ΔH = ΔU + Δ(PV)...
  45. J

    Internal energy when stirring a liquid.

    Homework Statement A liquid is irregularly stirred in a well-insulated container and thereby undergoes a rise in temperature. Regard the liquid as the system. (a) Has heat been transferred? How can you tell? (b) Has work been done? How can you tell? Why is it important that the stirring is...
  46. R

    Calculation of enthelpy and internal energy or air in chemical equilibrium

    Homework Statement Consider air in chemical equilibrium at 0.1 atm and T=4500 K. The chemical species are O2, O, N2, N (Ignore NO). Calculate the enthalpy and internal energy per unit mass of the mixture. Neglect electronic excitation in your calculations. K_{p,O_2}=12.19 atm...
  47. L

    Difference between enthelpy and internal energy.

    U=q+w U is the total kinetic and potential energy of the system. H=U+PV Enthalpy is the internal energy of the system, plus how much energy it takes to set up the system. I don't understand how the PV term from enthalpy is not included in the internal energy. It seems like it would...
  48. L

    Difference between Temperature and Internal Energy

    Hi :) Uhh, this question is quite simple but I'm still confused between these two terms... Am I right to say that internal energy is the sum of kinetic energy and potential energy of all the particles in a system? Meaning the two factors are the number of particles, and the energy of each...
  49. P

    P.Chem1: Internal energy in isothermal, reversible reactions

    I have these two homework problems, as well as solutions. What I do not understand is why the solution for one is not the solution for the other. First problem: A sample consisting of 1.00 mol Ar is expanded isothermally at 0 deg Celc from 22.4 dm3 to 44.8 dm3 reversibly. Calculate q, w, delta...
  50. I

    Is Internal Energy Always Constant in Thermodynamic Systems?

    So, is the internal energy of a system always constant? I mean, if work done on the system is negative by convention. dU = dQ - pdV Then if work is done on the system, does that mean that it has to absorb heat to keep the internal energy constant? and if the system does work, it has to...
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