Specific heat and thermal conductivity

The energy required to change a material's temperature depends on three factors: the mass of the sample, the temperature change desired, and the material's specific heat.

Q = mcΔT Q = energy transferred, m = mass, c = specific heat, ΔT = temperature change

Specific Heat

• Specific heat is an intrinsic property — it reflects how atoms are arranged and interact within the material, not how much material is present
• Materials with low specific heats warm and cool rapidly for a given energy input
• Materials with high specific heats resist temperature changes for the same energy input

When two objects reach thermal equilibrium in an isolated system, conservation of energy determines the final temperature: the energy lost by the hotter object equals the energy gained by the cooler one.

Thermal Conductivity

The rate at which energy conducts through a material depends on the thermal conductivity, the cross-sectional area, the thickness, and the temperature difference across the material. The rate increases with thermal conductivity, area, and temperature difference, and decreases as the material gets thicker.

ΔQ/Δt = kAΔT / L k = thermal conductivity, A = cross-sectional area, ΔT = temperature difference, L = thickness

• Thermal conductivity, like specific heat, is intrinsic — it depends on atomic arrangement and interactions
• Metals conduct energy rapidly because of free electrons
• Insulators conduct energy slowly

On the AP exam, both specific heat and conduction questions reward careful attention to proportionality reasoning: knowing how the rate or energy changes when one variable doubles is just as important as plugging numbers into a formula.