Internal energy
| English | Chinese | Pinyin |
|---|---|---|
| molecule | 分子 | fèn zǐ |
| internal energy | 内能 | nèi néng |
| ideal gas | 理想气体 | lǐ xiǎng qì tǐ |
| intermolecular | 分子间 | fèn zǐ jiān |
| phase change | 相变 | xiāng biàn |
The hidden energy inside
- A still cup of hot tea isn't moving — yet it holds lots of energy.
- That energy is in its jiggling molecules 分子, not in the cup's motion.
- We call it the internal energy 内能.
What internal energy is
- $U$ = the random kinetic energy of all the molecules + the potential energy from forces between them.
- It is the energy of the random motion — not the object moving as a whole.
A steam turbine does work as expanding steam pushes its blades around
The spread of molecular energies
Internal energy is the total random kinetic + potential energy of the molecules. Heat the gas and the whole speed distribution shifts to higher energy.
Internal energy is the sum of which energies?
Internal energy = random molecular KE + intermolecular PE. The object's overall motion (bulk KE) is separate.
It depends only on the state
- $U$ is fixed by the state (temperature, pressure, volume, amount) — not the path taken.
- A train rushing along has bulk kinetic energy, but that is separate from $U$.
Internal energy is the random motion of molecules inside the cup — not the cup's bulk motion. A moving train has bulk KE, but that is separate from $U$.
A moving train's bulk kinetic energy counts as part of its internal energy.
No — internal energy is the energy of the random molecular motion, not the whole object moving along.
Internal energy depends only on the state of the system, not on the path taken to reach it.
Yes — $U$ is a function of state (T, p, V, amount); two routes to the same state give the same $U$.
Internal energy of an ideal gas 理想气体
- An ideal gas has no intermolecular 分子间 PE, so $U$ is purely kinetic: $U = \tfrac{3}{2}nRT$.
- So $U$ is proportional to temperature — double $T$, double $U$ (ideal gas only).
A gas pushing a piston of area A out by Delta x does work W = p Delta V
For an ideal gas, the internal energy is:
No intermolecular PE, so $U$ is all kinetic: $U = \tfrac{3}{2}NkT = \tfrac{3}{2}nRT$.
For an ideal gas, if the absolute temperature doubles, the internal energy multiplies by:
$U = \tfrac{3}{2}nRT \propto T$, so doubling $T$ doubles $U$.
During a phase change 相变
- When ice melts or water boils, the temperature stays constant.
- But $U$ still rises: the energy breaks the bonds, raising the molecular potential energy.
While water boils at constant temperature, its internal energy:
The temperature (and so KE) is unchanged, but energy goes into breaking bonds — raising the molecular PE, so $U$ rises.
You've got it
- internal energy $U$ = random molecular KE + PE (not the object's bulk motion)
- $U$ depends only on the state, not the path
- ideal gas: $U = \tfrac{3}{2}nRT$ (∝ $T$); a phase change raises $U$ at constant $T$