Temperature and Translational Kinetic Energy
Equipartition assigns (1/2)k_BT to each independent quadratic translational coordinate, so every ideal-gas molecule has mean translational energy (3/2)k_BT.
Why this shows up in the exam
Comparing gases at the same temperature · Converting energy per molecule to temperature · Testing kinetic-theory statements
Learn the idea
Absolute temperature measures average translational kinetic energy, independent of molecular identity. At equilibrium, light and heavy molecules have the same average translational energy, although the lighter ones move faster.
🧠 Memory hook: Same T means same average translational energy, not same speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- <K_trans> = (3/2) k_B T — mean translational energy per molecule at thermal equilibrium
- K_trans,total = (3/2) nRT = (3/2)PV — total translational energy of n moles of an ideal gas
How to approach it
- 1Convert temperature to kelvin
- 2Decide per molecule or whole sample
- 3Use k_B or R consistently
Common slip-ups that cost marks
- •Making average kinetic energy depend on molar mass
- •Using Celsius as proportional temperature
- •Counting rotational energy as wall-pressure energy
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas has rms molecular speed 300 m/s at 300 K. What is its rms speed at 1200 K, assuming ideal behavior?
More from Kinetic Theory of Gases
Ideal gas law and gas laws
The ideal gas law and related gas laws describe the relationships between pressure, volume, temperature, and number of moles for ideal gases.
Degrees of freedom and thermal properties
Degrees of freedom determine the distribution of energy among molecules, affecting internal energy, specific heats, and the ratio of specific heats (γ).
Kinetic theory and molecular motion
The kinetic theory explains the behavior of gases in terms of the motion and collisions of their molecules, relating properties like pressure, temperature, and kinetic energy.
RMS speed and temperature dependence
The root mean square (rms) speed of gas molecules depends on temperature and molar mass, and is a key measure of molecular motion in gases.
Mean free path and collisions
Mean free path is the average distance a molecule travels between collisions, and depends on molecular size and number density.
Ideal-Gas Equation and Molecular Form
For a dilute ideal gas in thermal equilibrium, the state variables satisfy PV = nRT = Nk_B T, where intermolecular potential energy and molecular volume are neglected.