internal energy
Summary
Internal energy (U) is the total kinetic and potential energy of a system's particles, and it is a state function. Its change follows the first law, ΔU = q + w (w is work on the system; physics texts write Q − W with W by the system). For an ideal gas, U depends only on temperature.
Detail
Meaning: Internal energy, U, is the total microscopic energy of a system: particle kinetic energy plus the potential energy of bonds and intermolecular attractions, excluding the motion or height of the system as a whole. U is a state function, so ΔU depends only on the initial and final states.
Equation: ΔU = q + w, where q is heat added to the system (J) and w is work done on the system (J). Physics texts write ΔU = Q − W, with W the work done by the system. For an ideal gas, ΔU = nCvΔT, where n is moles (mol), Cv is molar heat capacity at constant volume (J/(mol·K)) and ΔT is the temperature change (K).
On the MCAT: Questions ask for the signs of ΔU, q and w. Isothermal ideal gas: ΔU = 0, so q = −w. Adiabatic: q = 0, so ΔU = w; compression warms a gas. Constant volume: w = 0, so ΔU = q.
Common confusion: Heat and work are path-dependent energy transfers, not stored forms of energy. ΔU also differs from ΔH, which equals q at constant pressure: ΔH = ΔU + PΔV, a gap that matters mostly when the moles of gas change.
Sources
- Chemistry: The Central Science
- General Chemistry: Principles and Modern Applications
- Physical Chemistry
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.