internal energy Definition and Topics - 39 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. 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 wont do. ## W ## is work done by the gas and ## Q ## is amount of heat energy brought into the system. I'm...
  2. Rahulx084

    Heat supply to a system

    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...
  3. 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...
  4. 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...
  5. cooldudeachyut

    Enthalpy & 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 +...
  6. 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?
  7. 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...
  8. WeiShan Ng

    I Why drop the vibrational ground state energy

    This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...
  9. E

    Internal energy of an ideal gas as a function of temperature

    Homework Statement Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A. The internal energy of the gas in container B is (a) twice that for container A (b) the same as that for...
  10. H Psi equal E Psi

    Finding compressibility from given internal Energy function

    Hi everyone! 1. Homework Statement Given is a function for the internal energy: ##U(T,V)=Vu(T)## Asked is to derive the entropy balance equation. In order to do so i need to find the "isothermal and adiabatic compressibility": $$\kappa_{T}=-\frac{1}{V}\left(\frac{\partial V}{\partial...
  11. M

    Naive Doubt About Thermodynamic Equilibrium

    This is more of a recurring conceptual doubt that I keep on running into when solving thermodynamics problems. We are taught that variations between extensive state variables in equilibrium are given by the following 'fundamental formula': dE = TdS + \mathbf{J}\cdot{d}\mathbf{x} +...
  12. S

    Equation for Internal Energy?

    Homework Statement Sketch a diagram of internal energy (y-axis) versus temperature in the range from -10°C to +112°C to indicate how energy would change for a fixed quantity of water in its three phrases. Label and explain the main features of the variation. Homework Equations The Attempt at...
  13. R

    Change in internal energy when water is heated from 0 to 4c

    Homework Statement : [/B]Find the change in internal energy of 2kg water as it is heated from 0°C to 4°C. The specific heat capacity of water is 4200J/Kg and its densities at 0°C and 4°C are 999.9 kg/m3 and 1000kg/m3 respectively. Atm pressure=105Pa Homework Equations :ΔU= Q-W W=PΔV M/V=D[/B]...
  14. D

    Thermodynamics -- Internal Energy of Water

    Homework Statement Water is initially at P = 1 bar and T = 20°C. 100kg of water is pumped to a higher pressure at which P = 10 bar and T = 25°C. Find ΔU and ΔH Homework Equations H = m*h du = c*dT dh = c*dT + v*dP The Attempt at a Solution So far I have looked in my table and found that at P...
  15. D

    Internal Energy Thermodynamics

    Homework Statement CO2 is at P=3atm, T = 295K and V=1.2m3. It is isobarically heated to T = 500K. Find ΔU and ΔH Homework Equations dU = cpdT The Attempt at a Solution I am having a hard time in general in this class. I understand that in this problem, ΔP = 0. Does this mean that there must...
  16. Ian Baughman

    Change in internal energy during water vaporization

    According to the first law of thermodynamics, dQ = dU + dW and you can find dU = nCvdT If this is the case then when water at 100°C vaporizes to steam at 100°C shouldn't the change in internal energy be zero because it is dependent on temperature change?
  17. I

    Confusion: Internal energy u vs enthalpy h

    I've been given the following relations where as I understand it subindex 2 equals subindex e and subindex 1 equals subindex i: ***EDIT*** More accurately subindex 1; initial state of a control mass subindex 2: end state of a control mass (end state is simply state 2 in the problem at hand)...
  18. arpon

    I Can internal energy be calculated from equation of state?

    We know, $$dU=TdS-PdV$$ ##\int PdV## can be calculated if the equation of state is given. I tried to express ##S## as a function of ##P ,V## or ##T## (any two of those). $$dS=\left(\frac{\partial S}{\partial V}\right)_T dV+\left(\frac{\partial S}{\partial T}\right)_V dT$$ $$=\left(\frac{\partial...
  19. E

    Enthalpy problems...

    In a trasformation in which P=costant, but internal pressure is different from external pressure, ΔH=Q? I'm asking this question because I know that Q=ΔU+PΔV (where P is the external pressure) and H=U+PV (where P is the sistem pression, so the internal pressure) Am I right?
  20. S

    Internal energy in irr. process with molar heat not constant

    I'm a bit confused about the following situation. In a irreversible thermodynamics process the molar heat of an ideal gas changes according to a function of the temperature, say ##c_v=f(T)## (which also leads to ##c_p=R+f(T)##) and I'm asked to determine the heat exchanged during that process...
  21. Dr. Who

    I Relation between 'P' and 'V' for an Adiabatic process

    Hi All, I have a little query concerning the derivation of PV γ = constant. In my text book of Physics, first they give the equation for adiabatic process using the first law of Thermodynamics, as; dEint = W → (1) where, ΔEint ⇒ change in internal energy and W ⇒ workdone Then, they used...
  22. M

    B Gravitational collapse

    During gravitational collapse, gravitational potential energy of the gas is converted to its internal kinetic energy so the internal energy of the clous of gas is said to be increased But isn't gravitational potential energy included in the internal energy? Shouldn't the internal energy remains...
  23. J

    Why don't we include VdP in U equation ?

    Homework Statement I was trying to obtain Tds=dh-Vdp by differentiating the internal energy equation U=Q-PV and doing some arrangements but at the end I couldn't achieve my goal.The part that I don't understand is when we differentiate H=U+PV we obtain dH=dU + PdV + VdP and then from there we...
  24. C

    What is the Internal Energy of 158 moles of CO2

    Homework Statement A gas bottle contains exactly 158 moles of carbon dioxide CO2. Find the change in the internal energy of this much CO2 when it is cooled from 36C down to exactly 25C at a constant pressure of 1 atm. The gas can be treated as an ideal gas with γ=1.289. The gas constant reads...
  25. K

    How is internal energy U(S,V) a function of temperature?

    In my chemical thermodynamics class/notes (and other references I've used) it is stated throughout that internal energy U is a function of entropy and volume , i.e. it's "natural" variables are S and V: U = U(S,V) I suspect that I must take this "axiomatically" and move on. Since U is a state...
  26. S

    Change in internal energy during vapourization of water

    Homework Statement Assuming water to be an ideal gas, enthalpy of vaporization is x joules per mole. I have to find change in internal energy an 100 degree Celsius for one mole of water. also find heat absorbed. Homework Equations The Attempt at a Solution I initially thought that during...
  27. H

    Example of entropy as function of temperature only

    Hi, I know that changes in entropy can be expressed as a function of temperature, specific volume, and pressure using the fundamental equations of thermodynamics: ds = du/T+pdv/T, where the changes in entropy can be caused by either changing the specific volume or the internal energy. I also...
  28. A

    Calculating work heat, and efficiency given a TS diagram

    Homework Statement Is it possible to calculate the work done heat transfer, and efficiency of an object in a thermodynamic system, given the Temperature vs Entropy graph? Example: Homework Equations ∆U=Q-W ∆S=dQ/T e=1-(Qc/Qh) e=W/Qh The Attempt at a Solution Since this is a T vs S...
  29. fricke

    Internal energy's lower bound

    Thermodynamics question: Why does the internal energy have a lower bound? I tried to explain it using postulates, but cannot get the connection between the postulates. Please do explain it briefly. Thank you.
  30. D

    Variation of system energy in Canonical Ensemble

    A system is in contact with a reservoir at a specific temperature. The macrostate of the system is specified by the triple (N,V,T) viz., particle number, volume and temperature. The canonical ensemble can be used to analyze the situation. In the canonical ensemble, the system can exchange...