AP Chemistry 6.2: Heat Transfer and Thermal Equilibrium

When two objects at different temperatures come into contact, energy is transferred between them as heat.

• The warmer object's particles have greater average kinetic energy than the cooler object's particles. Collisions between particles transfer energy from the hotter material to the colder material.
• Therefore:
• heat naturally flows from hot → cold
• This continues until the two objects reach the same temperature. Khan Academy's current Unit 6 describes thermal equilibrium in terms of this heat transfer and equal final temperature.

Thermal equilibrium occurs when objects in thermal contact reach the same temperature and there is no longer a net transfer of heat between them.

• For example, suppose a piece of metal at 90°C is placed into water at 20°C.
• Initially:
• metal is hotter than water.
• Energy transfers:
• metal → water
• The metal cools while the water warms.
• Eventually both may reach, for example:
• 30°C.
• At that point they are at the same temperature, so they have reached thermal equilibrium.

If the setup is thermally isolated so that no significant energy escapes:

• heat lost by hot object + heat gained by cold object = 0
• or:
• qhot + qcold = 0
• Therefore:
• qhot = −qcold
• This relationship becomes the foundation of calorimetry.
• Suppose the hot metal loses 2,000 J.
• Then:
• qmetal = −2000 J
• The water must gain approximately 2,000 J:
• qwater = +2000 J
• The signs are opposite because energy lost by one part is gained by another.

The final equilibrium temperature must normally lie between the initial temperatures of the objects.

• If one material begins at 80°C and the other at 20°C, an isolated system cannot normally reach a final equilibrium temperature of 95°C or 5°C without another energy source or sink.

However, the final temperature is not necessarily halfway between the two initial temperatures.

• Why?

Different samples can have different:

• masses
• specific heat capacities
• A large amount of water may experience only a small temperature change while a small piece of metal experiences a much larger temperature change.

Suppose a hot metal block contacts a cooler metal block.

• Particles in the hotter block have greater average kinetic energy. Collisions at the boundary transfer energy to particles in the cooler block.
• As the hot block loses energy, its particle motion decreases.
• As the cool block gains energy, its particle motion increases.
• Eventually the average kinetic energies associated with the temperatures become equal, so both objects reach the same temperature.

Temperature itself does not “flow.”

• Energy flows as heat.

Temperature tells us about the average kinetic energy of particles and determines the direction in which heat is transferred.

Do not assume objects contain equal amounts of thermal energy just because they have the same temperature.

Do not assume the final temperature must be exactly halfway between the two starting temperatures.

Do not say cold “flows” from one object to another. Energy transfers from the hotter object to the cooler one.

In an isolated heat-transfer problem:

• energy lost = energy gained
• or:
• qlost + qgained = 0