300
J
0.3
kJ
-200
J
-202.65
J
0
J
300
J
0.3
kJ
-200
J
-202.65
J
0
J
The Internal Energy Calculator computes the change in internal energy (ΔU) of a thermodynamic system using the first law of thermodynamics. Internal energy encompasses all kinetic and potential energy of molecules within a system, including translational, rotational, vibrational, and electronic energy. This calculator supports two modes: direct input of heat and work (ΔU = q + w), or calculation using pressure-volume work (ΔU = q − PΔV). Understanding internal energy is fundamental to thermodynamics, engine design, chemical engineering, and the analysis of any energy transformation process.
The first law of thermodynamics states:
$$\Delta U = q + w$$
where q is heat added to the system and w is work done on the system. For expansion/compression work against constant external pressure:
$$w = -P_{ext} \Delta V$$
Therefore:
$$\Delta U = q - P\Delta V$$
The enthalpy change is related by:
$$\Delta H = \Delta U + P\Delta V = q \quad (\text{at constant pressure})$$
Sign conventions: q > 0 means heat absorbed by system, w > 0 means work done on system (compression), w < 0 means work done by system (expansion).
Positive ΔU means the internal energy increased — the system gained energy from heat or work input. Negative ΔU means energy was lost. The work term shows how much energy went into expansion/compression. At constant volume (ΔV = 0), ΔU = q (heat at constant volume). At constant pressure, q = ΔH, and ΔU = ΔH − PΔV.
Inputs
Results
w = −PΔV = −101325 × 0.005 = −506.6 J. ΔU = 1000 + (−506.6) = 493.4 J. Of the 1000 J heat absorbed, 506.6 J went to expansion work, leaving 493.4 J as increased internal energy.
Inputs
Results
No heat exchanged (adiabatic-like). 3000 J of work done on the gas (compression). All work increases internal energy: ΔU = 0 + 3000 = 3000 J.
Internal energy (U) is the total microscopic energy of a system — the sum of all kinetic and potential energies of its molecules. It includes translational, rotational, vibrational, and electronic contributions but excludes bulk kinetic and potential energy.
The first law states that energy is conserved: ΔU = q + w. The change in internal energy equals the heat added to the system plus the work done on the system.
In the IUPAC convention: work done on the system is positive (w > 0), work done by the system is negative (w < 0). For PV work: w = −PextΔV, so expansion (ΔV > 0) gives negative work.
ΔH = ΔU + Δ(PV). At constant pressure, ΔH = qP. At constant volume, ΔU = qV. For reactions involving gases, ΔH ≠ ΔU due to PV work.
When no work is done (w = 0), typically at constant volume with no other forms of work. This is the basis of bomb calorimetry.
No, we can only measure changes in internal energy (ΔU). The absolute internal energy of a system is not directly measurable, but changes are well-defined through the first law.
An adiabatic process has q = 0 (no heat exchange). Therefore ΔU = w: all energy change comes from work. Rapid compression/expansion and insulated systems approximate adiabatic conditions.
For an ideal gas, U depends only on temperature: ΔU = nCvΔT, where Cv is the molar heat capacity at constant volume. For real substances, U also depends on intermolecular interactions.
Internal energy is measured in joules (J) or kilojoules (kJ) in SI units. The calorie (1 cal = 4.184 J) is still used in some contexts.
ΔU is directly measured in bomb calorimetry (constant volume). It connects to ΔH by: ΔH = ΔU + ΔnRT for ideal gas reactions, where Δn is the change in moles of gas.
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