Blank: temperature is a measure of the average kinetic energy of particles in an object (their random thermal motion).
In physics, “temperature” quantifies how energetic the microscopic, random motion of particles is on average. Faster random motion corresponds to higher temperature.
Step 1: Identify what “particle motion” means
Matter is made of atoms and molecules that are always in motion. The type of motion depends on the state:
| State of matter | Dominant microscopic motion | How higher temperature appears microscopically |
|---|---|---|
| Solid | Vibrations about fixed lattice positions | Vibrations have larger amplitude and energy |
| Liquid | Vibrations + short-range rearrangements (diffusive motion) | More vigorous motion and faster molecular rearrangements |
| Gas | Random translational motion between collisions | Higher average speeds of molecules |
Step 2: Connect temperature to average kinetic energy (kinetic theory)
For an ideal monatomic gas, kinetic theory gives a direct quantitative link between temperature and the average translational kinetic energy per molecule:
\[ \langle K_{\text{trans}} \rangle = \frac{3}{2} k_B T \]Here, \(k_B\) is Boltzmann’s constant, \(T\) is the absolute temperature in kelvins, and \(\langle \cdot \rangle\) denotes an average over many molecules.
The key word is average: temperature does not measure the kinetic energy of one specific particle and does not measure the total kinetic energy of all particles. It measures the typical (mean) energy per particle associated with random thermal motion.
Step 3: Distinguish temperature from heat and internal energy
Several quantities sound similar but are conceptually different:
| Quantity | What it means | Depends on amount of substance? |
|---|---|---|
| Temperature \(T\) | Measure of average microscopic kinetic energy (thermal motion) | No (intensive) |
| Heat \(Q\) | Energy transferred due to a temperature difference | Yes (transfer amount depends on system/process) |
| Internal energy \(U\) | Total microscopic energy (kinetic + potential at molecular level) | Yes (extensive) |
Step 4: Why “average kinetic energy” is the best completion
Temperature is defined operationally through thermal equilibrium (zeroth law): systems in mutual thermal equilibrium share the same temperature. Microscopically, thermal equilibrium corresponds to a stable energy distribution of particles. The distribution changes with temperature, but its “center” (typical kinetic energy) is captured by an average value.
Step 5: Final completion and interpretation
The blank is completed by average kinetic energy. Temperature is a macroscopic indicator of microscopic random motion: higher \(T\) means particles have, on average, more kinetic energy (more vigorous thermal motion), consistent with thermal equilibrium and kinetic theory.