Heat transfer is the physical process by which thermal energy moves between objects or regions at different temperatures. Three mechanisms govern it: conduction (direct contact), convection (fluid motion), and radiation (electromagnetic waves). This calculator covers the quantitative laws governing conduction and the temperature change of objects — the foundation for engineering calculations in building insulation, HVAC design, materials processing, food safety, and electronics cooling.

Specific Heat: Why Some Materials Heat Faster Than Others

The specific heat capacity c of a material tells you how much energy is needed to change its temperature: Q = mcΔT. Materials with high specific heat (like water at 4,186 J/kg·K) require more energy per degree of temperature change, which makes them excellent thermal buffers — they absorb large amounts of heat with little temperature rise. This is why water is used in car cooling systems, industrial heat exchangers, and why the ocean moderates coastal climate. Materials with low specific heat (like metals: iron at 450, copper at 385 J/kg·K) heat and cool quickly, which is why metal baking pans heat faster than ceramic ones in an oven but also why the ocean doesn't form near a steel plate. The joule is the SI unit of energy: 1 J = 1 kg·m²/s². A 100 W heater produces 100 joules per second; the time to raise 1 kg of water from 20°C to 100°C is (1 × 4,186 × 80) / 100 = 3,349 seconds ≈ 56 minutes — consistent with kitchen experience.

Fourier's Law: Predicting Heat Flow Through Materials

Fourier's law states that heat flows through a material at a rate proportional to the temperature gradient and to the material's thermal conductivity. For a flat slab: Power = k × A × ΔT / d. Three factors control conduction rate: the material (k — copper conducts 10,000× better than fiberglass insulation), the geometry (thicker walls slow heat flow; larger area increases it), and the temperature difference (ΔT — the driving force). Building insulation design directly applies this formula. Adding fiberglass batt insulation (k = 0.04 W/m·K) to a wall creates a thermal resistance layer that dramatically reduces heat flow. The thermal resistance R = d/(k×A) adds in series with the wall structure's resistance — this is the physical basis of the R-value system used in building codes. A wall with R-13 insulation (in imperial units, ≈ 2.3 m²·K/W) reduces heat loss by a factor proportional to the total R-value. Engineers choose materials by balancing thermal resistance (low k, high d) against structural requirements, cost, and moisture management.

Newton's Law of Cooling: Exponential Temperature Decay

When a hot object is placed in a cooler environment, it loses heat at a rate proportional to the temperature difference between the object and the environment. This produces exponential decay: T(t) = T_env + (T₀ − T_env) × e^(−kt). The cooling constant k captures how quickly the specific object-environment system exchanges heat — it depends on the surface area, material conductivity, fluid convection characteristics, and emissivity for radiation. High k means rapid cooling (a metal spoon in cold water); low k means slow cooling (a well-insulated thermos). The exponential form means the temperature difference halves every t₁/₂ = ln(2)/k seconds. Practical applications include: food safety (how quickly does a cooked chicken cool from 165°F to the danger zone?), forensic temperature-of-death estimation, industrial quenching processes, and electronics thermal management. The law is an approximation valid when the temperature difference is not too large — at very large ΔT, radiation (which scales with T⁴) becomes significant and the simple linear cooling model breaks down.