Heat Transfer and Thermal Equilibrium: Study Guide (Chemistry 6.3)

What temperature means for particles

In Topic 6.1 you saw that heat is one way energy moves between a system and its surroundings. This topic asks how that happens, particle by particle.

Start with what you know from the kinetic molecular theory (Topic 3.5):

• The particles in any sample of matter are always moving: flying around in a gas, sliding past each other in a liquid, vibrating about fixed positions in a solid.
• A moving particle has kinetic energy, KE = ½mv², where m is its mass and v its speed.
• At any moment the particles in a sample have a spread of kinetic energies. Some are fast, most are medium, a few are slow. (The Maxwell–Boltzmann distribution shows this spread for a gas.)
• The Kelvin temperature of a sample is proportional to the average kinetic energy of its particles.

So a thermometer reading is a measure of how energetic the particles are on average. This gives the first key idea of the topic:

The particles in a warmer body have a greater average kinetic energy than the particles in a cooler body.

Notice the word average. In a cup of warm water, some molecules are moving more slowly than some molecules in a cup of cold water. It is the average across the whole sample that is higher.

Statement	True?
The average kinetic energy of the particles in the warmer body is greater.	Yes
Every particle in the warmer body is faster than every particle in the cooler body.	No: the two spreads overlap
The warmer body always has more total energy.	No: a large cool lake has far more total energy than a hot cup of tea

How collisions move energy

Now put a warmer body in contact with a cooler body. This is called thermal contact: their particles can touch and collide, for example where a hot metal pan sits on a cold worktop, or where hot water meets the glass wall of a cold bottle.

At the surface where they meet, particles from the two bodies collide. In a collision between a faster particle and a slower particle, energy is usually passed from the faster one to the slower one. The faster particle comes away a little slower; the slower particle comes away a little faster.

Not every single collision sends energy the same way. Sometimes a fast particle from the cooler body hits a slow particle from the warmer body. But because the warmer body’s particles are more energetic on average, far more energy moves from warm to cool than from cool to warm. The net result is a flow of energy from the warmer body to the cooler body.

Inside each body, the particles keep colliding with their neighbours, so the energy gained at the boundary spreads through the cooler body, and the energy lost at the boundary is shared out across the warmer body.

This collision process has three names that mean the same thing: heat transfer, heat exchange and transfer of energy as heat. The amount of energy moved is given the symbol q. Two points about the word “heat”:

• Heat is energy on the move because of a temperature difference. Once it has arrived, it is just part of the energy of the body that received it.
• Heat always flows, on its own, from the warmer body to the cooler body. Nothing called “cold” ever moves.

Reaching thermal equilibrium

What happens as heat transfer continues?

1. The warmer body loses energy, so the average kinetic energy of its particles falls. Its temperature drops.
2. The cooler body gains energy, so the average kinetic energy of its particles rises. Its temperature rises.
3. The gap between the two average kinetic energies gets smaller. Collisions at the boundary now pass energy both ways in more similar amounts, so the net transfer becomes slower and slower.
4. Eventually the average kinetic energies of the two bodies become equal. Their temperatures are then equal too.

This final state is thermal equilibrium. It is a dynamic state:

• The particles do not stop moving, and they do not stop colliding.
• Energy still passes across the boundary in individual collisions, but the amount moving one way equals the amount moving the other way.
• So there is no net transfer of energy, and neither temperature changes any more.

Figure 2 shows what this looks like on a graph, using the data from Worked example 3. The warmer body cools and the cooler body warms; both curves level off at the same temperature, between the two starting temperatures.

Energy is conserved during heat transfer

If the two bodies are insulated from everything else, no energy escapes. Every joule the warmer body loses is gained by the cooler body:

energy lost by the warmer body = energy gained by the cooler body

That is why the equilibrium temperature always lies between the two starting temperatures. It is not always halfway. In Figure 2 the block falls 36.0 °C but the water rises only 16.0 °C, because the two bodies need different amounts of energy to change temperature by 1 °C. Topic 6.4 turns this into a calculation.

Same temperature, different particles

Thermal equilibrium means equal average kinetic energy. It does not mean equal speed, and it does not mean equal total energy.

• Speed. KE = ½mv². If two kinds of particle have the same average kinetic energy, the lighter ones must move faster on average. In a mixture of helium and argon at one temperature, the average kinetic energies are equal, but helium atoms (about one-tenth of the mass) move about 3.2 times faster on average.
• Total energy. A full swimming pool and a glass of water at the same temperature have the same average kinetic energy per particle. The pool has vastly more particles, so it has vastly more total energy. If you put them in contact, no net energy moves, because their particles are equally energetic on average.

This is the link between the two scales: temperature, a macroscopic reading on a thermometer, reports the average behaviour of the particles, not their total energy.

Worked example 1: explaining heat transfer at the particle level

Question. A sealed glass bottle of juice at 5 °C is placed in a bowl of water at 40 °C. Explain, in terms of particles, why the juice warms and the water cools, and why both temperatures eventually stop changing.

1. Compare average kinetic energies. The water is warmer, so its molecules have a greater average kinetic energy than the particles of the glass and the juice.
2. Describe the collisions. Water molecules collide with the particles of the outside of the glass. On average, energy passes from the faster water molecules to the slower glass particles. The glass particles pass energy on, by collisions, to the juice particles inside.
3. State the net direction. Energy moves from the water, through the glass, into the juice. This is heat transfer. The average kinetic energy of the juice particles rises (temperature rises); that of the water molecules falls (temperature falls).
4. Explain the end point. As the gap in average kinetic energy narrows, the net transfer slows. When the average kinetic energies are equal, the temperatures are equal. Collisions continue, but energy passed each way is equal, so there is no net transfer: thermal equilibrium.

Point to notice. A full answer names the particles, says “average kinetic energy”, says which way energy moves, and says that collisions continue at equilibrium.

Worked example 2: comparing average kinetic energies

Question. A sample of nitrogen gas is warmed from 25 °C to 323 °C. (a) By what factor does the average kinetic energy of the molecules change? (b) A student says the factor is about 13. Explain the error.

1. Convert to kelvin. Average kinetic energy is proportional to the Kelvin temperature.
   • T₁ = 25 + 273.15 = 298.15 K
   • T₂ = 323 + 273.15 = 596.15 K
2. Form the ratio. KE₂ / KE₁ = T₂ / T₁ = 596.15 / 298.15 = 1.9995.

Answer (a). The average kinetic energy doubles (factor 2.00).

(b) The student divided the Celsius values: 323 / 25 = 12.9. The Celsius scale has its zero at the freezing point of water, not at zero kinetic energy, so ratios of Celsius temperatures have no physical meaning. Only the Kelvin scale starts from zero average kinetic energy.

Check. To halve the average kinetic energy from 25 °C, you would need 298.15 ÷ 2 ≈ 149.1 K, which is about −124 °C, not 12.5 °C.

Worked example 3: reading a heating–cooling record

Question. A hot metal block is placed in water in an insulated container. Both temperatures are recorded (thermometers read to ±0.1 °C). The data are fictional.

Time (min)	0	1	2	3	4	6	8	10
Block (°C)	70.0	50.2	41.3	37.3	35.5	34.3	34.1	34.0
Water (°C)	18.0	26.8	30.8	32.5	33.3	33.9	34.0	34.0

(a) In which direction does energy move? (b) When is thermal equilibrium reached? (c) Explain why the temperatures change quickly at first and slowly later.

1. (a) The block’s temperature falls and the water’s rises, so energy moves from the block to the water. The block’s particles start with the greater average kinetic energy.
2. (b) At 8 min the readings differ by 0.1 °C, which is within the ±0.1 °C precision of the thermometers. By 10 min both read 34.0 °C. Thermal equilibrium is reached at about 8 to 10 min, at 34.0 °C.
3. (c) At the start the temperature gap is 52.0 °C, so the difference in average kinetic energy is large and much more energy passes from block to water than back. In the first minute the block falls 19.8 °C. Between 3 and 4 min the gap is under 5 °C, the two-way transfers are much closer in size, and the block falls only 1.8 °C, about 11 times less.

Interpretation. The record matches Figure 2: both curves flatten towards the same temperature, and that temperature lies between 18.0 °C and 70.0 °C.

Common misconceptions

• “Cold flows from the cold object into the warm one.” Only energy moves, and it moves from warmer to cooler.
• “An object contains heat.” An object has energy and a temperature. Heat is the name for energy while it is being transferred because of a temperature difference.
• “At thermal equilibrium the particles stop moving.” They keep moving and colliding. Only the net transfer stops.
• “At equilibrium the particles in both bodies have the same speed.” They have the same average kinetic energy. Lighter particles move faster on average.
• “Every particle in the hotter body is faster than every particle in the colder body.” The spreads overlap; only the averages differ.
• “A bigger object at the same temperature will give energy to a smaller one.” Equal temperatures mean equal average kinetic energy, so there is no net transfer, whatever the sizes.
• “The final temperature is always halfway between the two.” It is always between them, but where depends on how much of each substance there is and what it is (Topic 6.4).
• Using °C in a kinetic energy ratio. Average kinetic energy is proportional to the Kelvin temperature. Convert first.

Where this leads

Next, Topic 6.4 puts numbers on heat transfer with q = mcΔT and uses the idea “energy lost = energy gained” to analyse calorimetry experiments. Thermal equilibrium is also the assumption behind every final temperature you read in a calorimeter. Try the practice questions now, then use the revision notes and the checklist to consolidate.