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. P

    Exploring Internal Energy, Heat and Work Relationships

    Can some one check my work, I'm not sure if I am understanding how internal energy heat and work are related. Work is defined to be positive if the system does work on the environment. Q=\Delta U +W I am showing if the process is positive, negative or 0. Also this is suppose to be an ideal gas
  2. W

    Factors affecting the internal energy

    does the identity of molecules affect the internal energy, besides the temperature and volume?
  3. G

    Constant internal energy with volume change?

    Constant internal energy with volume change?? My book says that you can change the temperature of a substance at constant internal energy by changing only the volume. how can this happen? since the internal Energy E is this: \Delta E = q + w = q - P\DeltaV where q is heat, w is...
  4. G

    Phase Changes and internal energy

    The internal Energy E is this: \Delta E = q + w = q - P\DeltaV where q is heat, w is work, and V is volume Phase changes occur when you change internal energy of the system, right? I am assuming that this means when you go from gas to liquid to solid, you must decrease the internal...
  5. G

    Magneto Caloric Effect: Exploring Internal Energy Change

    In magneto caloric effect, we see that when a substance in an adiabetic closure is exposed to external magnetic field, its temperature increases. But the internal energy of the substance has to be constant so this implies decrease in internal potential energy. However the application of magnetic...
  6. L

    Deriving an expression for internal energy.

    Homework Statement Show that the change in internal energy of a simple system between states (V1, T1) and (V2, T2) is given by ∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dVHomework Equations dU=dQ-pdVThe Attempt at a Solution As U is a function of...
  7. Telemachus

    Conceptual question about internal energy

    Hi there. Here is the deal, today morning in my thermodynamic class we were making some exercises of stability, and then surged a question about internal energy. The thing is I thought that the internal energy should be always positive in sign. This doesn't mean that the variation must be...
  8. S

    False: Internal Energy of A & B is Not Determined by T Alone

    Homework Statement Why is this false? "if systems A and B each consist of pure liquid water at 1 bar pressure and if TA>TB, then the internal energy of system A must be greater than that of B" Homework Equations The Attempt at a Solution It seems true to me. Could it be that B...
  9. A

    NON-monatomic gas expansion, find internal energy change

    Homework Statement A NON-monatomic gas expands from I to F in the Figure (Since it is not monatomic U=3/2nRT does not give you the internal energy, this only works for monatomic gases, instead you must use the first law). The energy added to the gas by heat is 424 J when the gas goes from I to...
  10. C

    Thermodynamics - internal energy change question

    Homework Statement Assume ideal gas conditions. Cp=(7/2)R, Cv=(5/2)R 15 moles of airis contained in a cylinder and prevented from escaping by a frictionless piston initial conditions are 1.5 bar, gas volume 0.2m^3 final conditions required are 10 bar t 27 degrees celsius calculate...
  11. P

    Change in internal energy when ice melts to water at 0C

    If we melt ice at 0'C to water at 0C, what is the change in the internal energy of the ice-water system? As per the first law of thermodynamics, ΔU = ΔQ +ΔW where they are increase in internal energy, heat flow to the system and work done on the system respectively. If we melt ice at 0C, we...
  12. T

    Help Internal Energy of a Liquid

    In thermodynamics Change in Internal Energy = Heat - Work (\DeltaU=Q-W) During vaporization my Heat is mass*Latent Heat (Q=mL) and Work is Pressure*change in volume (W=P\DeltaV), so \DeltaU=mL-P\DeltaV. Let's take any of the natural monoatomic gases, Neon in this case. \Delta = Volume...
  13. S

    Internal energy and thermodynamic entropy

    As a practical matter, the internal energy of a system is treated as a state function of a the system and is concerned only with the kinetic energy of particles, not the potential energy. So for thermodynamic entropy, S=E/T, (S=entropy, T= absolute temperature) I'm considering E to be kinetic...
  14. N

    Thermodynamics question; internal energy and heat?

    Homework Statement A helium balloon with a volume of 1m^3 and temperature of 27 deg c is placed in liquid nitrogen in an open container and cools to a temperature of 77 K. Assume that helium behaves like an ideal gas at constant atmospheric pressure and find the new volume of the gas in the...
  15. D

    What is the Internal Energy of an Ideal Gas at Given Conditions?

    Homework Statement A container of volume 0.72 m^3 contains 1.4 mol of argon gas at 24 degrees C. Assuming argon behaves as an ideal gas, find the total internal energy of this gas. The value of gas constant is 8.31451 J/mol x K. Answer in units of J. Homework Equations PV=nRT...
  16. P

    Calculating Internal Energy Absorbed in Truck Cab After Collision

    How to calculate Energy absobed by the components of a Truck Cab after crash test?? Hi, I have a question regarding the calculation of internal energy of components after collision. In conducting the frontal impact test as per the ECE R29 regulation, a swing bob has to hit the front of...
  17. A

    Thermodynamics: Internal Energy of a Gas

    Homework Statement Helium (He), a monatomic gas, fills a 0.010-m^3 container. The pressure of the gas is 6.2 multiplied by 10^5 Pa. How long would a 0.38-hp engine have to run (1 hp = 746 W) to produce an amount of energy equal to the internal energy of this gas? Homework Equations...
  18. S

    Is Internal Energy of Ideal Gas Really Only Dependent on Temperature?

    We known U=3/2nRT (monatomic ideal gas), just depends on temperature. Most texts assert connecting U and Q with constant volume condition and say"\Delta U = nCv\Delta T for any process because of internal energy only depends on temp". I think that statement is very strange. Deriving...
  19. R

    Internal energy after evaporation?

    Homework Statement Two grams of water are sealed in a rigid con- tainer; then the water is vaporized by heating. 1664 cal of heat is needed for vaporization. What is the change in internal energy of the water? Answer in units of J. Homework Equations 1 kcal= 4,186 J The Attempt...
  20. C

    Internal Energy: Evaporation & 1st Law of Thermodynamics

    hi, Can anybody explain the phenomenon behind internal energy? and what is the change in internal energy when water evaporates. Please do give reference to first law of thermodynamics. Thanks in advance.
  21. B

    Thermal Physics - Internal Energy

    Homework Statement A gas obeys the equation p(V-b) = RT and has cv independent of temperature. Show: (a) the internal energy is a function of temperature only (b) the ratio cp/cv is independent of temperature and pressure (c) the equation of an adiabatic change has the form p(V-b)^gamma...
  22. K

    Julie's Jump: Solving Kinetic Energy & Internal Energy Problems

    Homework Statement Julie has a mass of 60 kg. In an experiment she crouched down, then jumped straight up. Her lab partners measured the height of her center of mass above the floor at three instants: 1) 0.43 m when crouched down; 2) 1.02 m just as her feet were leaving the floor; 3) the...
  23. K

    Show that the Internal Energy of an Ideal gas is a Function of T only

    Homework Statement Show that internal energy U = U(T) only for an ideal gas who'se equation of state is: P(V-b) = RT (the claussius equation for n moles of gas) Homework Equations Thermodynamic Equation of state: \left(\frac{\partial U}{\partial V}\right)_T =...
  24. K

    Thermodynamic Potentials - Internal energy problem.

    Homework Statement For Cyclohexane Boiling point T_b = 80.1°C P = 1atm \Delta H_{vap} = 30.1 kJ/mol Determine at phase change liquid to vapour, Changes in: a)Entropy per mole b)Gibbs free energy per mole c)Internal energy per mole assume ideal gas behaviour for the vapour...
  25. A

    Micro and macro internal energy approach

    Why is internal energy not sufficient to compare states? Thank you for your answer.
  26. T

    Thermo(concept Q, pic included)- How does internal energy increase but

    Homework Statement http://img694.imageshack.us/img694/9990/fig24a.jpg" The scenario is, the water in the beaker = system 1. Everything else, including walls = system 2. The bunsen burner heats the water in the beaker. dU or the change in internal energy of system 2 decreases. dT or the...
  27. A

    Quick Internal Energy Question

    Is the internal energy for a closed cycle always zero?
  28. K

    Constant volume Specific heat and internal energy relationship in nonideal gas.

    Hi, 1. \color{blue}dq=dU+PdV so C_V = \left(\frac {\partial q}{\partial T}\right)_V= \left(\frac {\partial U}{\partial T}\right)_V leads to dU=C_{V}dT so \color{red}\left(\frac {\partial U}{\partial V}\right)_T = 0 meaning that internal energy of NONideal gas is a sole function of T? 2. As...
  29. M

    Heat and internal energy of water temperature

    Homework Statement Water at the top of Niagara Falls has a temperature of 10.0degrees celsius. If it falls a distance of 50.0m and all of its potential energy goes into heating the water, calculate the temperature of the water at the bottom of the falls. Homework Equations W = change...
  30. A

    Change in internal energy => change in rest mass

    Consider the following situation. Two particles are initially separated by some distance and are then pulled further apart, thus increasing the potential energy of the system (due to the gravitational force of attraction between them). If I am correct in understanding special relativity, then...
  31. C

    Internal energy and pv diagrams

    http://img689.imageshack.us/img689/511/pistonquerstion.jpg This is my part attempt... [PLAIN][PLAIN]http://img830.imageshack.us/img830/7342/internalenergyanswer.jpg And ideas on how I can do the rest of it?
  32. K

    Enthelpy vs. Internal Energy (Thermodynamics)

    Hello! First post here :-) Hope this isn't too simple for this forum...if so, by all means give me a pointer... I'm wondering about some basic thermod. concepts. Could somebody please shed a little light on these? Internal Energy and Enthalpy (both from macroscopic viewpoint) Does...
  33. T

    Finding internal energy change in a adiabatic compression process.

    Can you help me with this problem? An ideal gas is compressed adiabatically. The work done over it is 200 J. How much will the internal energy change? A) 200 J B) 100 J C) -200 J D) 0 J Which formula do you use to solve it? Thanks in advance!
  34. T

    Thermodynamics change in internal energy

    1. A gas bottle with a volume of 0.1 m3 contains 0.4 kg of a gas at a pressure of 7 MN/m2 and a temperature of 150 ºC. For this gas Cp = 10.54 kJ/kg K. Calculate the changes in internal energy when temperature is raised to 500K Given answer: 362 kJ 2. pV=mRT pv=RT...
  35. M

    Thermodynamics- validity of change of internal energy equation

    Just had a thermodynamics exam, and one of the questions was For an ideal gas, is the relation \DeltaU = mC_{}v\DeltaT restricted to constant volume processes only? Why? I wrote that it was only valid for constant volume processes, because this is what C_{}V is defined as, however now I'm...
  36. C

    Debye internal energy for heat capacity

    I'm working from Feynman's definition of internal energy for the Debye theory of heat capacity. I'm trying to use that to derive the normal definition of heat capacity that I've seen. But I'm running into a problem. Note, in the following V_0 is frequency, whereas V is volume (that's how Feynman...
  37. T

    Difference between enthelpy and internal energy

    What's the difference between enthalpy and internal energy? Internal energy is the average of the kinetic energy (linear and angular) of the particles of the body (or system), right? Could someone explain me this clearly? Thank you
  38. C

    Finding Velocity After Sliding with Work-Energy Equations

    Homework Statement A 15.0 kg block is sliding across the floor. Initially, it is moving at 1.2 m/s. However, after sliding 20.0 meters, =7.5 J of work are done on it by friction. What is the block's velocity after sliding 20.0 meters? Homework Equations KE=.5v2 lw-l=F\DeltaXcos\theta...
  39. R

    How Does Internal Energy and Temperature Determine the Phase of R134A?

    if you're given just the temperature and internal energy of R134A how do you determine the phase of the substance? If I was given the pressure instead of internal energy then i would just look in my tables to see if the pressure is above or below the saturated pressure and i would then know...
  40. C

    Multiple Choice problem (internal energy)

    What must be true for two objects of the same material to have the same internal energies? (Choose all that apply) a. The masses of both objects must be equal b. Both objects must have the same density c. The temperatures of both objects must be equal d. Separate objects cannot have...
  41. S

    How Is Energy Calculated in a Viscously Damped Spring-Mass System?

    Homework Statement Use your program for the viscously damped spring to solve this problem. Make sure you change the parameters as specified below. A mass m=7.1 kg is attached to the end of a spring with a spring constant of k=16.4 N/m. The mass moves through a viscous damping medium with...
  42. A

    Does Heating a Gas Under Constant Pressure or Volume Affect Its Internal Energy?

    Homework Statement I have two identical volumes of gas, and I heat them both to 100 C, one under constant pressure, one under constant volume. Which has more internal energy after the process? The attempt at a solution I believe that they both have the same as the extra heat you have...
  43. F

    Change in internal energy of an inelastic collision.

    Homework Statement A car of mass 2200 kg collides with a truck of mass 4500 kg, and just after the collision the car and truck slide along, stuck together, with no rotation. The car's velocity just before the collision was < 35, 0, 0 > m/s, and the truck's velocity just before the collision...
  44. T

    Internal Energy of an Expanding Gas

    Homework Statement 2 moles of a monatomic ideal gas expands from state A to state B. PA = PB = 600 N/m2, VA = 3.0 m3 and VB = 9.0 m3. i. Calculate the work done by the gas as it expands. ii. Calculate the change in internal energy of the gas as it expands. iii. Calculate the heat added to or...
  45. S

    Battery efficiency and internal energy

    Homework Statement One rechargeable battery of mass 15.0 g delivers to a CD player an average current of 15.5 mA at 1.00 V for 2.50 hr before the battery needs to be recharged. The recharger maintains a potential difference of 2.00 V across the battery and delivers a charging current of 10.0...
  46. S

    Internal energy of a hydrostatic system in a reversible adiabatic process

    Homework Statement A simple hydrostatic system is such that PV^k is constant in a reversible adiabatic process, where k > 0 is a given constant. Show that its internal energy has the form E=\frac{1}{k-1}PV+NF(\frac{PV^k}{N^k} where f is an arbitrary function. Hint: PV^k must be a function of...
  47. L

    Enthelpy vs Internal energy for first law

    U is internal energy, which is the sum of heat + work done. \DeltaU = q + w -----(1) where w = \Delta(PV) Enthalpy is the internal energy + work done \DeltaH = \DeltaU + P\DeltaV At constant pressure, \DeltaH = q - P\DeltaV + P\DeltaV \DeltaH = q_{p} Where q_{p} is used to...
  48. T

    What is the correct sign convention for the change in internal energy?

    In my book it says that the change in internal energy = Q -W Yet, my teacher says that its Q + W He says that it's reversible due to the signs... but i don't know what that means... can somebody give me an example?
  49. K

    What is the change in internal energy of the water

    Hi there, I have some serious problems with a couple of questions. Need help for exam revision. 1.1 Homework Statement A 2kg chunck of ice at -10Celsius is added to 5kg of water at 45Celsius. What is the final temperature of the system? 1.2 Relevant equations specific heat capacity of ice -...
  50. S

    Vaporization and change in internal energy

    Homework Statement Suppose 1 g of water vaporizes isobarically at atmosphere pressure (1.013 x 105 Pa). Its volume in the liquid state is Vi = 1 cm3, and its volume in the vapor state is Vf = 1671 cm3. Find the change in internal energyHomework Equations \Delta U = \Delta Q - \Delta W \Delta...
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