6.3 Heat Transfer

Heat Transfer & Thermal Equilibrium

Mix two substances at different temperatures and watch particles slow or speed up as heat flows between them. Computes T_final live, confirming q_lost = q_gained.

q = mcΔTThermal Equilibrium4 MaterialsParticle Animation
Topic 6.3

Heat Transfer and Thermal Equilibrium

Explain the relationship between the transfer of thermal energy and molecular collisions.

The particles in a warmer body have a greater average kinetic energy than those in a cooler body. That is the entire definition of "warmer" at the particulate level.

Collisions between particles in thermal contact can transfer energy. This process is called heat transfer, heat exchange, or transfer of energy as heat. When a fast-moving particle collides with a slow-moving one, energy passes from fast to slow — statistically, always net from hot to cold.

Eventually thermal equilibrium is reached as the particles continue to collide. At thermal equilibrium the average kinetic energy of both bodies is the same, and hence their temperatures are the same.

Three points the AP Exam tests around this:

  • Collisions never stop at equilibrium. Energy continues to be exchanged in both directions; the net transfer is zero. (Compare the dynamic nature of chemical equilibrium in Unit 7.)
  • Equal temperature does not mean equal energy. A swimming pool and a cup of coffee at the same temperature have the same average kinetic energy per particle but vastly different total energies, because the pool has vastly more particles.
  • Energy is conserved (the first law): q lost by the hot body = −q gained by the cold body, provided the system is insulated. This is the equation behind every calorimetry calculation.

The role of heat capacity. Two objects exchanging the same amount of energy will not undergo the same temperature change if their masses or specific heat capacities differ. Water's unusually high specific heat capacity (4.18 J·g⁻¹·°C⁻¹) means it resists temperature change — which is why it is used as the working fluid in calorimeters and radiators.

Key points

  • Temperature measures average kinetic energy per particle, not total energy.
  • Heat transfer is energy passed by particle collisions, net from hot to cold.
  • At thermal equilibrium average kinetic energies are equal and net transfer is zero — but collisions continue.
  • qlost = −qgained is the conservation statement behind all calorimetry.

Equations

  • not on the sheetFirst law of thermodynamics applied to an insulated system.

Common mistakes

  • "Cold flows into the hot object." Only energy is transferred, and it moves from hot to cold.
  • Equating temperature with total energy. They are different quantities.
  • Thinking transfer stops at equilibrium. Only the net transfer is zero.
  • Assuming equal temperature changes. ΔT depends on mass and specific heat capacity.

Worked example

A 50.0 g block of iron (c = 0.449 J·g⁻¹·°C⁻¹) at 95.0 °C is dropped into 100.0 g of water (c = 4.18 J·g⁻¹·°C⁻¹) at 22.0 °C in an insulated container. Find the final temperature, and explain why it is much closer to the initial temperature of the water.

Set up conservation: qiron = −qwater

(50.0)(0.449)(Tf − 95.0) = −(100.0)(4.18)(Tf − 22.0)

22.45(Tf − 95.0) = −418(Tf − 22.0)
22.45 Tf − 2132.75 = −418 Tf + 9196
440.45 Tf = 11328.75
Tf = 25.7 °C

Why so close to the water's starting temperature: the product m × c is the object's total heat capacity — 22.45 J/°C for the iron but 418 J/°C for the water, nearly 19 times greater. Because the water can absorb far more energy per degree of temperature change, the same quantity of energy transferred produces a large temperature drop in the iron and only a small rise in the water. The final temperature therefore lands near the water's starting value.

Full notes for topic 6.3 →