Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- Two systems are in thermal contact if energy can move between them by thermal processes.
- Heating moves energy into a system; cooling moves energy out. Both are transfers, not contents.
- The three thermal processes are conduction, convection and radiation.
- Atoms in a hotter system have a larger average kinetic energy. In a collision, energy is most likely, but not certain, to pass from the higher-energy atom to the lower-energy one.
- After very many collisions, the most probable state is equal temperatures.
- Thermal equilibrium: no net energy transfer by thermal processes between systems in contact.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| K_avg = (3/2)k_B T | k_B = 1.38 × 10⁻²³ J/K, T in K | link temperature to atomic energy |
| Energy lost by hot system = energy gained by cold system | J; isolated pair of systems | check a transfer |
| T_f = (N₁T₁ + N₂T₂)/(N₁ + N₂) | same monatomic ideal gas, rigid insulated boxes | find a final temperature |
| Process | Carrier | Needs matter? |
|---|---|---|
| Conduction | collisions between neighbouring particles | yes |
| Convection | bulk movement of a fluid | yes, a fluid |
| Radiation | electromagnetic waves | no |
Assumptions behind the numbers
- The pair of systems is isolated: no energy leaks to the surroundings.
- For gas samples: ideal, monatomic, in rigid boxes (no work done).
- Temperatures are in kelvin when you use K_avg = (3/2)k_B T.
Mistakes to avoid
- “Cold flows in.” Only energy flows.
- Internal energy decides the direction. Temperature decides it.
- “Every collision goes hot to cold.” It is the most likely result, not a certainty.
- “Equilibrium means atoms stop.” Exchange continues; the net is zero.
- Simple average for T_f. Weight by the number of atoms.
- Convection in a solid. Solids conduct; only fluids convect.
Quick self-check
- A small iron nail at 90 °C is dropped into a large tank of water at 20 °C. Which way does net energy flow? (Nail to water: the nail is at the higher temperature, even though the water has more internal energy.)
- Which thermal process can cross a vacuum? (Radiation only.)
- Equal numbers of atoms of the same gas at 300 K and 500 K reach equilibrium in insulated rigid boxes. Final temperature? (400 K.)
- What is the average kinetic energy of a gas atom at 300 K? (6.21 × 10⁻²¹ J.)
Next: practice questions.