What is Internal energy: Definition and 380 Discussions

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. A

    Is enthalpy just the sum of internal energy and work against external pressure?

    This was the question This is my solution The problem arose after reading this post on PhysicsSE and this answer given So If I remember correct work done is ##-P_{ext}\Delta V## I don't understand why $$\Delta H=\Delta U+(5×4-1×10)L.atm$$ If that answer (the answer on the PSE post) is...
  2. C

    Internal energy contradiction?

    For this, They say internal energy is the sum of the all the mechanical energies of each particle in within the thermodynamic system, however, they then define internal energy differently using the average mechanical energy for all particles within the system (Pink equation). Does someone...
  3. yinnxz

    Change in internal energy

    Since the system is doing no work, would it be just 4513 J? I don't think there is any other information to use
  4. C

    What is the change in internal energy after two processes?

    So the question goes like this: find change in internal energy in process 1->2 using diagram. And offered solutions a)-400J b)400J c)600J d)800J. First I found T1 and T2 using (P*V)/T=R and got T1=24K and T2=72K. Then I found n(number of moles) using PV=nRT and got n1=1mol, n2=1mol. Then I...
  5. S

    I Internal energy of a comoving volume increasing as space expands?

    I was reading an article by Edward Harrison, which tackles the problems of conservation of energy at cosmological scales. At some part (point 2.4) he cites several article, including one by Rees and Gott, which he says indicates that the internal energy of a comoving volume (e.g. a cosmic...
  6. S

    I Cosmic strings increasing internal energy?

    I was reading an article by Edward Harrison, which tackles the problems of conservation of energy at cosmological scales. At some point (point 2.4) he cites several article, including one by Rees and Gott, which he says indicates that the internal energy of a comoving volume (e.g. a cosmic...
  7. Dario56

    I How Can Internal Energy of the Canonical Ensemble Change (Fluctuate)?

    Canonical ensemble is the statistical ensemble which is applicable for the closed system in contact with the reservoir at constant temperature ##T##. Canonical ensemble is characterized by the three fixed variables; number of particles ##N##, volume ##V## and temperature ##T##. What is said is...
  8. Tesla In Person

    Internal Energy of Gas and Work done

    This is a thermodynamics question. A gas absorbs 10 000 J of heat , it releases 3000 J and does 2000 J of work. How much has the internal energy varied? So I did 10 000 - 3000 -2000 = 5000 J so internal energy decreases by 5000 J. But the correct answer is A) it increased by 5000 J . How ?
  9. M

    A Experimental Studies of the Internal Energy of a real fluid

    https://www.nature.com/articles/s41598-022-11093-z In this new 2 May 2022 publication, an experimental effort was made to measure directly the internal energy changes of non-ideal CO2, from the decrease in temperature as the liquid-gas expanded from one cylinder into two. With the empirical...
  10. guyvsdcsniper

    Change in internal energy of a cylinder

    I believe I got the first part of this questions solved. For part b, we are asked to find the change in internal energy. We know ΔE=Q+W. The cylinder,gas and piston head are the system. The cylinder and piston head are well insulated, so there will be no head transfer, therefore Q=0. So now...
  11. F

    Internal Energy of an Ideal Gas

    a) We use the definition of heat transfer in a gas at constant volume: Q = n*C_v*delta_T = (0.01 mol)(12.47 J/mol*K)(40 K) = 4.99 J b) We use the definition of heat transfer in a gas at constant pressure: Q = n*C_p*delta_T = (0.01 mol)(12.47 J/mol*K)(40 K) = 8.31 J c) In both processes delta_U...
  12. Ashshahril

    Change in heat and internal energy

    ΔQ=mC(T3-T1) But, will this C be Cp or Cv. Both pressure and volume changes. So, neither of them can be. Feeling so confused
  13. Dario56

    Why Does Electrical Work Cause Changes in the Internal Energy of a System?

    If we look at system at constant temperature and volume which is galvanic cell, first law of thermodynamics states: $$ dU = dQ + dW' $$ Where W' is electrical work done by galvanic cell and Q is heat exchanged with surroundings. As far as I know electrical work is work done by electric field...
  14. AN630078

    Thermodynamics: Internal Energy, Heat and Work Problem

    Well, internal energy is the sum of the kinetic and potential energies of all the molecules within a given mass of a substance; this energy is associated with the random, disordered motion of the molecules. An example of internal energy is compressed gases; since gases occupy the total volume...
  15. S

    Thermodynamic Axioms: Establishing Temperature, Internal Energy & Entropy

    Is the purpose of the 0th, 1st & 2nd Laws of Thermodynamics simply to legitimate the thermodynamic properties of Temperature, Internal Energy & Entropy, respectively? It seems that all these laws really do is establish that these properties are valid thermodynamic state properties and the...
  16. L

    Engineering What is internal energy? Am I right?

    Am i right Is internal energy for engineering just the sum of energy stored with a system of a substance. which is only affect by heat and work coming out of the system
  17. G

    Change in Internal Energy in Accelerated Gas Chambers

    Summary:: How internal energy changes in a acclerated cabin. There are two tourus shaped insulated closed pipes containing equal amounts of ideal gas under same conditions. B has a adiabatic partion wall. If both are to change angular velocity by w radians per second. How internal energies...
  18. F

    Internal energy vs Enthelpy

    Hello, In thermodynamics, with systems being represented by gases (can liquids be also included?), the internal energy ##E_{int}## of a system represents the total kinetic energy + the total potential energy of the system: $$E_{int} = KE_{tot}+ PE_{tot}$$ The term ##KE_{tot}=Q## is also called...
  19. E

    Is the rotational KE of a rigid body considered as internal energy?

    I'm inclined to say no, but am by no means certain. The total kinetic energy of a system of particles is $$T = \sum_{i} \frac{1}{2} m_{i}\vec{v_i}\cdot\vec{v_i} = \frac{1}{2} m_{i}(\vec{v_{COM}} + \vec{v_{i}^{'}})^{2} = \frac{1}{2}M\vec{v_{COM}}^{2} + \frac{1}{2}\sum_{i} m_{i}...
  20. r12214001

    Chemistry Internal energy calculation

    Question: Solution manual: Is the solution manual correct or not? why does not contain heat transfer?
  21. V

    Finding the amount of a uranium-238 atom's internal energy that is released

    I assume this interaction is an explosive separation one, and as such, I thought the problem gave me the numbers to satisfy the second equation. I converted the 238 amu and 234 amu and plugged the results into the second equation of 0 = m1v1f + m2v2f. I got 0 = (3.95*10^-25kg)v1f + 3.88*10^-25kg...
  22. E

    B Internal energy in the context of rest energy

    I've come across some conflicting definitions and hoped someone more in-the-know could clarify a few points. The rest energy is the total energy of the system in its rest frame; I read about the following (approximate!) semi-empirical mass formula earlier, and if we multiplied this through by...
  23. Z

    Thermodynamics: find the change of internal energy, the work and Q

    According to the first principle of thermodynamics: ΔU = W + Q Also noting that: W = -P⋅ΔV (Question: This P is the initial pressure or the final?) To find V2: (P1⋅V1) / T1 = (P2⋅V2) / T2 → Therefore, (P⋅V1) / T1 = [(P/5)⋅V2] / T2 → (P⋅V1) / T1 = (P⋅V2) / (5⋅T2) → V2 = (5⋅T2⋅V1) / T1...
  24. E

    Internal energy of a container filled with water & steam

    I've worked out that half of the steam must condense (since the pressure of the steam needs to remain constant for the forces on the massless piston to balance). Also, if the total volume of the container is ##V##, the work done on the system equals ##\frac{P_{atm}V}{4}##. When half of the steam...
  25. Frigus

    Why don't we consider ordered motion as part of the internal energy of a gas?

    Why we do not considered the translational energy of the gases particles in the internal energy due to ordered motion but only due to random motion.
  26. K

    Deriving an expression for change in internal energy

    Homework Statement: A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work...
  27. danyull

    Internal Energy of a Mole of Particles each with 3 Energy Levels

    Hello, I'm doing some refreshers before going back to school. Stat mech is my shakiest and I'd appreciate some help on this problem. I know that for a single particle, the partition function will be $$Z = 1 + 2e^{-\beta\Delta} + 2e^{-4\beta\Delta}$$ and so its internal energy is $$\frac{1}{Z}...
  28. T

    Enthelpy vs Internal Energy in Phase Change

    Is there anybody who can advise wether the heat lost / gained during vaporisation, is best calculated from enthalpy, or from internal energy, in the steam tables? I am trying to establish the increase in the volume of milk when the temperature is raised by adding saturated steam at 1 bar (1...
  29. J

    Work and Internal Energy for Adiabatic Processes

    Using (2) on (1) give ## dU = -dW##... (4) A.For expansion since the gas goes from ##(P_1, V_1, T_1)## to ##(P_2, V_2, T_2)##, does this imply ##T_1 \leq T_2 ##? B. If so, then ##W## for adiabatic expansion would be negative (using (3))? Using negative ##dW## in (4) gives us a positive result...
  30. VEReade

    Explaining internal energy (A level physics)

    I’m having a mental block re. teaching internal energy. Here’s the issue: For ideal gas, internal energy is entirely kinetic energy. I explain to students this is because there are no interatomic forces of attraction. Now, a solid...internal energy is sum of kinetic energy and potential...
  31. T

    Internal energy in ideal gas

    I have the definition of change in internal energy. $$ \Delta U = Q - W $$ I can get the work by $$ W = \int_{V_1}^{V_2} p dV = p \Delta V $$ however the pressure isn't constant so this won't do. ## W ## is work done by the gas and ## Q ## is amount of heat energy brought into the system. I'm...
  32. A

    Internal Energy for Water

    Good day all ! I have a confusion regarding the use of the formula dU=CdT for computing internal energy for liquid or solid like for instance in this exercice We have an isothermal process so I thought that dU=0 so according to the first law of thermodynamics dQ=-dW (we want to calulate the...
  33. S

    Correct statement about internal energy

    Homework Statement Which statement about internal energy is correct? A. When two system have the same internal energy, they must be at the same temperature B. When the internal energy of a system is increased, its temperature always rises C. The internal energy of a system depends only on its...
  34. Rahulx084

    Understanding the Concept of Heat Supply to a System: Explained in My Book

    My book states that Heat and work represent energy in transit. The state of the system undergoes a change after heat is supplied to it and before work is extracted from it because energy gets stored in it. My doubt is here that ,heat has been transferred to the system and it says heat is energy...
  35. F

    Increase in internal energy due to polarization of a dielectric

    I have a plate capacitor with a given charge. It is then dipped in a dielectric fluid and I must determine which height the fluid reaches(all the necessary parameters are given). I can solve this problem if I make the following assumption: the polarization of the dielectric does not( or...
  36. S

    Algebraic Improvement needed in Comparing enthelpy and internal energy change

    MODERATOR'S NOTE: I have been having difficulty explaining to this member the error in his algebraic development, in particular being cavalier in his attentiveness to proper algebraic manipulation of signs. I explained his error in post #7 (and the problems that could arise if he continues to...
  37. C

    Heat released during combustion at constant pressure vs volume

    Greetings! I've been brushing up on some thermodynamics recently and came across a perplexing sentence in my notes and text from undergrad. It says that for a combustion reaction, such as the combustion of heptane: C7H16 (l) + 11O2 (g) ---> 7CO2 (g) + 8H2O (l) That this process carried out at...
  38. E

    Internal energy and thermal energy

    I'm watching a lecture introduction internal energy and in it, the lecturer states the following for some system: E_{internal} = E_{translational} + E_{vibrational} + E_{rotational} + E_{other} where ## E_{other} ## could be chemical energy, magnetic energy, electrostatic energy etc. Then...
  39. cooldudeachyut

    Enthelpy & Internal Energy Change relation with Cp & Cv

    Homework Statement Match the following Given : Processes do not include chemical reactions. Assume CP,m and CV,m are independent of temperature for given substance and consider only pressure-volume work in given all processes. Homework Equations ΔU = Q - W ΔH = ΔU +...
  40. NoahCygnus

    Calculation of the change in internal energy of water

    Homework Statement If water vapor is assumed to be a perfect gas, molar enthalpy change for vaporization of 1 mol of water at 1 bar and 100 C is 41 kJ/mol . Calculate the internal energy, when 1 mol of water is vaporized at 1 bar pressure and 100 C. Homework Equations $$\Delta U = \Delta H =...
  41. E

    Why is internal energy not a function of pressure?

    I'm reading a book on thermal physics and the author says this: "In general, the internal energy will be a function of temperature and volume, so that we can write U =U(T,V) " How do we know this intuitively and how do we know that internal energy is not a function of pressure as well?
  42. Vectronix

    B Why do objects have internal energy?

    From what I understand, the molecules/atoms that make up an object are in constant, random motion. Do electromagnetic forces cause this motion or what is the cause of it? If so, why would net electromagnetic forces exist between "neutral" atoms?
  43. T

    Calculate the Internal Energy of Monoatomic Gas

    Homework Statement Re-arranging the equations of potential (internal) energy in a monoatomic gas, i get this differential equation: \gamma (dV/V ) + (dP/P) = 0. where V is volume and P is pressure. I have to integrate it. Homework EquationsThe Attempt at a Solution I tried, but i wasnt able...
  44. A

    Thermodynamics- Piston problem, pressure, internal energy

    Homework Statement Homework Equations F= ma P= F/A The Attempt at a Solution a). Assuming the piston is in equilibrium, I'm applying Newton's second law F=ma=0 Equals zero because it is not moving Note: P=F/A which I rearrange to solve for the force for F= PA. This represents the...
  45. C

    Internal energy and total heat of universe

    Hello. I am starting to learn about thermodynamics. (i'm going to use lower case "d" for delta) Energy is neither created nor destroyed. So dU = 0 for the universe as a whole. If the universe is constantly expanding, then it must be doing work on the vacuum around it, right? So W is a...
  46. VSayantan

    Energy of a Gas in equilibrium with BB-radiation

    Homework Statement A closed, thermally-insulated box contains one mole of an ideal monatomic gas G in thermodynamic equilibrium with blackbody radiation B. The total internal energy of the system is ##U=U_{G}+U_{B}##, where ##U_{G}## and ##U_{B} (\propto T^4)## are the energies of the ideal gas...