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. D

    How Many Sprints to Burn 500 Calories at 4.5 m/s?

    Homework Statement Please help with this problem! How many sprints from rest to a speed of 4.5 m/s would a 59 kg woman have to complete in order to burn off 5.0 x 102 Calories? (Assume 100% efficiency in converting food energy to mechanical energy.) Homework Equations...
  2. A

    Internal energy enthelpy problem

    hello happy new year i'm a little confused here after i saw this U= KE + PE + H(enthalpy)----------------------1 while it is known that H=U+PV------------------2 i'm sure that eqn 2 is true but do you think with m that 1 is not true ?? the problem is that my instructor use...
  3. M

    Is Heat Flowing Into or Out of the System?

    Homework Statement The internal energy of a system increases by 200 J while 900 J of work are performed on it. What was the magnitude of the heat flow into or out of the system? Does the heat flow "out of" or "into" the system? Homework Equations Don't really need. The Attempt...
  4. S

    Adiabatic process-how is internal energy mcv(t2-t1)

    In polytropic process internal energy change is=mCv(T2-T1)? why is it not mCp(T2-T1)? Why are we not taking specific heat at constant pressure?
  5. Valour549

    Difference between Internal Energy and Enthelpy

    \Delta U = Q - W = Q - PV (where PV is the work done BY the system). \Delta H = \Delta U + PV (where PV is work done BY the system). 1) Above I defined PV in both equations as work done BY the system. I think this must be correct to show that when P is constant we can have \Delta H = Q...
  6. S

    Change in internal energy in air

    If we apply 300 kJ of heat to 2500 moles of air at constant pressure, what is the change in internal energy? So far i think I use the equation: (f/x)nkT, but I don't know how to calculate the degrees of freedom and whether I do or not, and whether or not to calculate the number of moles by...
  7. Y

    When are work and heat calculated by differences in enthelpy or internal energy

    Hi, This is not exactly homework, but I'm not sure it belongs in any other section either. I've been reading through Applied Thermodynamics for Engineering Technologists by Eastop & McConkey. In general it's pretty good I think. However, in the first few chapters, it explained that Q+W =...
  8. F

    Why is Cv used instead of Cp for calculating the internal energy of a gas?

    internal energy of a gas :( Hi all! I have a problem with this equation ΔU=mCvΔT, where ΔU=change in internal energy, m=mass, Cv=specific heat of air/gas at constant volume,ΔT=change in temp. Although this expression is true for all processes which can be applied to a gas e.g polytropic...
  9. R

    The Molar Specific Heat (internal energy)

    Homework Statement One mole of an ideal diatomic gas undergoes a transition from. a to c along the diagonal path What is the change in internal energy? Homework Equations The Attempt at a Solution I've tried to use the two other paths since the internal energy is the same both...
  10. P

    Internal Energy During Phase Changes

    I know that phase changes, such as the melting of ice, occur at constant temperature. Doesn't this imply that the change in internal energy during the phase change is zero, since the temperature remains the same? I thought that in all isothermal processes this was the case, so that the First Law...
  11. J

    Calculating Change in Internal Energy: A Steam Engine's Performance

    A steam engine of 1kg pulls 8 cars of 1kg each. The velocity of the engine is 0m/s initially then gets up to 4m/s in a time of 4 s while moving a distance of 5.3 meters. During that time, the engine takes in 134J of heat. What is the change in internal energy? Ok so i know that: internal...
  12. P

    The Internal Energy of Neon Gas

    Homework Statement The internal energy of a monoatomic ideal gas such as neon is simply the total kinetic energy of all its atoms. What is the internal energy of 2 liters of neon at a temperature of 200 K and pressure of 0.7 atm? Homework Equations PV = nRT KE(ave) = 3/2kT U =...
  13. N

    Thermodynamics: Internal Energy

    Homework Statement I need some help on these problems, i got most of the other problems right, but these ones I am not sure what to do with. I don't even know if those are the right equations for it. Someone please help. 1. A cylinder-and-piston containing an ideal gas is placed in...
  14. H

    Internal Energy and kinetic friction

    Homework Statement Please help, I've been struggling with this question for so long! We haven't done internal energy so I am not sure even where to really begin? A 10.0 kg block is dragged over a rough, horizontal surface by a 76.0 N force acting at 20.0° above the horizontal. The block...
  15. W

    Internal Energy - Is there a maximum value?

    Hi, I am going to teach a class of year 9 students on the topic "Thermal Properties of Matter" and the concept of Internal Energy is mentioned inside. As I was trying to anticipate the types of questions that will be asked by them, this question suddenly struck me: Is there a limit to the...
  16. G

    Help with change in internal energy for a real system.

    Homework Statement Tarzan, whose mass is 110 kg, is hanging at rest from a tree limb. Then he let's go and falls to the ground. Just before he let's go, his center of mass is at a height 3.0 m above the ground and the bottom of his dangling feet are at a height 2.0 above the ground. When he...
  17. T

    Relation between heat capacity and internal energy

    The task is to derive an expression for the heat capacity of a system at constant volume and show that at high temperatures it is inversely proportional to the square of temperature. As far as I'm concerned the relation between internal energy and heat capacity is: Cv=dE/dT However with...
  18. N

    Determine the change in internal energy, of the gas during this process

    Homework Statement A gas sample heated in a cylinder used 650 kJ of heat. A piston that compresses the gas does 800 kJ of work. What is the change in internal energy, ΔE, of the gas during this process Homework Equations ΔE = q + w The Attempt at a Solution ΔE = q + w ΔE =...
  19. M

    Internal energy present, is there conservation of energy?

    Hmm. This is another thing I'm unsure abt. When some mechanical energy is converted to internal energy, can we still say that energy is conserved? Can the internal energy be negative? Thanks for answering my qns :)
  20. W

    Combining Differently-Tempered Gases: Calculating Internal Energy Change

    How do you combine two separate volumes of an ideal gas which are at different temperatures pressures and volumes and then work out the change in internal energy? I have been trying to get my head around this without success.
  21. Q

    Finding the equation of state and internal energy of a given gas.

    Consider a gas contained in volume V at temperature T. The gas is composed of N distinguishable particles at zero rest mass, so that the energy E and momentum p are related by E = pc. The number of single-particle energy states in the range p to p + dp is 4\pi Vp^2 dp . Find the equation of...
  22. K

    Using Constant-Volume Specific Heat for Calculating Change of Internal Energy?

    I note that in many case, we always use the constant-volume specific heat to calculate the change of internal energy. For example, in a adiabatic process (P1, V1, T1) to (P2, V2, T2), since internal energy is state variable, we always like to build a fictitious isochoric process from (P1...
  23. J

    Does the internal energy of the combined system change when ice melts?

    PROBLEM: Some warm water is mixed with ice and the ice melts. Assume that the entire process happens in an insulated box. Does the internal energy of the combined (ice+water) system change? Does the entropy of the combined system change? Considering that the ice and water as separate...
  24. 6

    Change in internal energy of a gas

    Homework Statement Two moles of carbon monoxide (CO) start at a pressure of 1.2 atm and a volume of 30 liters. The gas is then compressed adiabatically to 1/3 this volume. Assume that the gas may be treated as ideal. What is the change in the internal energy of the gas? n = 1.2 atm V2...
  25. J

    Conceptual question about internal energy

    Homework Statement From the beginning of chapter 21 Haliday, Resnick and Walker: `Suppose that you return to your chilly dwelling after snowshoeing through the woods on a cold winter day. Your first thought is to light a stove. But why, exactly, would you do that? Is it because the stove...
  26. L

    Internal Energy Homework: Compare & Rank H2 Molecules in Containers

    Homework Statement Compare the Internal (or Thermal) energies of the different containers sketched below. Choose the correct ranking of the internal energies provided. Each container contains H2 molecules with the shown amount (the number of molecules) at the same temperature. a) A=B=C=D...
  27. A

    Heat and Internal Energy and Heat and Temperature Change: Specific Heat Capacity

    Homework Statement When you take a bath, how many kilograms of hot water (49°C) must you mix with cold water (12°C) so that the temperature of the bath is 36°C? The total mass of water (hot plus cold) is 191 kg. Ignore any heat flow between the water and its external surroundings. Temperature...
  28. P

    What Happens to dU, dQ, and dW During Boiling?

    Boiling Internal Energy - URGENT A quick question: dU = dQ - dW What are dU, dQ and dW during Boiling? I thought: -the particles do work, hence dW is + -dU increases as particles gain more energy so dQ = dU + dW - showing that heat flows in. Which made sense to me. Or is...
  29. F

    Simple BCS theory: question about the internal energy

    Hi all, I'm am reading chapter 3 of Tinkham's "Introduction to superconductivity". At some point several thermodynamic quantities are considered (sec. 3.6.3). In particular fig. 3 compares the internal energies of the superconducting and normal states, showing that they are different below...
  30. P

    Internal energy does or does not depend on volume of molecules?

    I am kind of confused by the conflict of the following two concepts. If I understood correctly, internal energy of a system is independent of the volume occupied by the gas molecules. This is because the gas molecules are assumed to be ideal and therefore have no intermolecular interactions...
  31. N

    Exploring the Relationship Between Kinetic and Potential Energy in Gases

    [SOLVED] Internal energy of a gas Is the internal energy of a gas simply the total kinetic energy possesed by the particles? I ask this, since I have read this to be the case, however I have also read that when changing state, eg. from liquid to gas, the latent heat is the energy required to...
  32. T

    Internal Energy of an ideal gas

    [SOLVED] Internal Energy of an ideal gas Homework Statement The temperature of 0.158 mol of an ideal gas is held constant at 67.0 degrees Celsius while its volume is reduced to a fraction of 20.0 % of its initial volume. The initial pressure of the gas is 1.19 atm. What is the change in...
  33. C

    How Much Warmer Could Water Get After a 50 Meter Fall?

    Homework Statement On his honeymoon, James Joule tested the conversion of mechanical energy into internal energy by measuring temperatures of falling water. If water at the top of a Swiss waterfall has a temperature of 10.0 degrees Celsius and then falls 50.0 m, what maximum temperature at the...
  34. C

    [Thermo] Equation of State Given, Find Internal Energy and Specific Heat

    Homework Statement P=RT/(v-b) - a/(T(V+c)^2) Homework Equations u2-u1= Integral ( Cv dT) + Integral ( T * (dP/dT)v - P) dV The Attempt at a Solution I've differentiated P with respect to T to get R/(v-b)+a/(T^2(V+C)^2 and plugged the relevants back into the equation for...
  35. D

    Does the Potential Energy Stay the Same When an Object's Temperature Increases?

    I know that molecules have kinetic and potential energy to make up internal energy. When the temperature of an object increases, the internal energy increases. When the kinetic energy doubles, the temperature doubles as KE is directly proportional to the kelvin temperature. Does this mean...
  36. R

    How Much Energy is Needed to Heat LNG from -165°C to 5°C?

    Homework Statement I have liquid natural gas, or LNG, at -165degrees Celsius. I want to know the total energy required to heat the gas up 50ml to 5 degrees Celsius. Homework Equations Not sure. Im assuming I need information regarding specific heat etc. Heat of vaporization maybe...
  37. T

    Thermodynamics-Finding Internal energy

    I am going over this example 0.5 kg of air undergoes a Carnot cycle with η = 0.5. Given the initial pressure p1 = 700 kPa, initial volume V1 = 0.12 m3 and heat transfer during the isothermal expansion process Q12 = 40 kJ, Find the highest and the lowest temperatures in the...
  38. M

    How Does Internal Energy Change at Constant Temperature?

    [SOLVED] Internal Energy and Heat Homework Statement Ten joules of heat energy are transferred to a sample of an ideal gas at constant temperature. As a result, the internal energy of the gas: a) increases by 10 J b) increases by less than 10 J c) increases by more than 10 J d) remains...
  39. N

    Internal energy, thermodynamics

    [SOLVED] Internal energy, thermodynamics Homework Statement I have the equation for the internal energy: U = (f/2) * N * k * T, where f is the degrees of freedom, N is the number of molecules, k is Bolzmann's constant and T is the temperature in Kelvin. This can be written as U = (f/2)*p*V...
  40. B

    How to Calculate Heat Required to Double Internal Energy of Helium Gas?

    [SOLVED] Internal Energy Problem Homework Statement Given .15meters cubed of Helium gas at 300K and 3Pa in a chamber with a frictionless piston. How much heat is required to double the internal energy of the gas at constant pressure? Homework Equations I really don't know what equations...
  41. A

    Heat and internal energy of gas

    One mole of an ideal diatomic gas at room temperature undergoes a transition from a to c along the diagonal path in Figure 19-23. (a) During the transition, what is the change in internal energy of the gas? -4987 J (b) How much energy is added to the gas as heat? ____ J (c) How much heat is...
  42. J

    Is Internal Energy Always Proportional to Temperature?

    Internal energy vs temperature(q37) For this question: http://tinyurl.com/3ymlnj The answer to this question is c. But according to my understanding, increasing of internal energy means increasing of temperature. Hence is isothermal situation, the change of internal energy is 0. With...
  43. A

    How Do You Calculate the Change in Internal Energy for Hydrogen Gas?

    Homework Statement One mole of hydrogen gas is heated from 278 K to 390 K at constant pressure. Hydrogen has a specific heat of 43.6 J/mol*K. The universal gas constant is 8.31451 J/K mol. Calculate the change in the internal energy of the gas. Answer in units of J Homework Equations...
  44. T

    Relating internal energy to highest temp

    Homework Statement one mole of He, H2, CO2 goes through a process such that the change in their internal energies are the same. WHich of the gases has a higher temp change? Homework Equations Eint=3/2nRdeltaT=nCvdeltaT (for monatomic gases) Eint=5/2nRT (diatomic gases) polytamoic gases...
  45. N

    Specific Heat Capacity and Change in Internal Energy

    Homework Statement I'm having trouble with the following two problems: 1. A jar of tea is placed in the sunlight until it reaches an equilibrium temperature of 32*C. In an attempt to cool the liquid, which has a mass of .180kg, .112 kg of ice at 0*C is added. At the time at which the...
  46. F

    Internal energy of the gas in a gasoline engine

    I am so lost with this question. Can anyone help? The internal energy of the gas in a gasoline engine's cylinder decreases by 176:7 J. If 67.0 J of work is done by the gas, how much energy is transferred as heat? Answer in units of J
  47. K

    Thermodynamic Changes in Phase Transitions

    Homework Statement Does the internal energy increase/decrease(U), quantity of heat released or supplied (Q), and work done by or on a system (W) when (a) water freezes to ice at constant temperature (b) ice melts to water at constant temperature (c) water evaporates at constant temperature...
  48. B

    Calculating Internal Energy Loss from Friction in Satellite Fall

    A 575 kg satellite is in a circular orbit at an altitude of 550 km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface, where it hits the ground with a speed of 2.10 km/s. How much energy was transformed to internal energy by means of...
  49. mbrmbrg

    Thermodynamics-work, heat, & internal energy

    Thermodynamics--work, heat, & internal energy Homework Statement When a system is taken from state i to state f along path iaf in Figure 18-41, Q = 60 cal and W = 20 cal. Along path ibf, Q = 51 cal. Fig. 18-41 (see attatched) (a) What is W along path ibf? (b) If W = -13 cal for the...
  50. S

    Temperature and internal energy question

    How can I find the temperature of something if I'm give the internal energy(U), volume(V), and number of moles(N). I thought it'd just be pv = nrt but I am not sure what to do with the internal energy or how to use it with pressure. Thanks.
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