Compute the final equilibrium temperature of two substances based on heat exchange: Qlost = Qgained. Includes intuitive bar chart & heat flow analysis.
The Law of Energy Conservation governs thermal interactions: when two bodies at different temperatures are brought into thermal contact, energy flows as heat from the warmer object to the cooler one until both reach a common equilibrium temperature. This principle is the foundation of calorimetry and thermodynamic analysis.
? Fundamental Equation:
m₁·c₁·(T₁ − Tf) + m₂·c₂·(T₂ − Tf) = 0
Which rearranges to:
Tf = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂)
Where: m = mass (g), c = specific heat capacity (J/g·°C), T = temperature (°C). The expression assumes no heat loss to surroundings and no phase change.
Water's high specific heat (4.184 J/g°C) means it requires more energy to change temperature than metals like copper (0.385 J/g°C). This explains why oceans moderate climate and why metal spoons heat up quickly in hot coffee. Our calculator automatically accounts for these variations, letting you explore realistic material interactions.
A barista pours 180 g of black coffee (c ≈ 4.18 J/g°C) at 85°C into a cup, then adds 40 g of cold milk (c ≈ 3.93 J/g°C) at 5°C. Using our calculator, the final temperature drops to ≈ 71.2°C, achieving drinkable warmth without scalding. This demonstrates instantaneous heat exchange – essential for food science and catering.
In heat treatment, a steel part (mass 2 kg, c = 0.49 J/g°C) at 850°C is quenched in 10 L of oil (c ≈ 2.0 J/g°C) at 30°C. The equilibrium final temperature can be calculated to prevent thermal shock and predict oil bath temperature rise. Engineers rely on these principles for process design.
Starting from energy conservation: heat lost by hot substance = heat gained by cold substance. Considering signs, Q₁ + Q₂ = 0 → m₁c₁(Tf − T₁) + m₂c₂(Tf − T₂) = 0. Solve for Tf yields the weighted average formula. If m₁c₁ dominates, Tf leans toward T₁. Our interactive tool solves instantly, eliminating algebraic errors.