Thermal Equilibrium Calculator
Mix two objects or substances at different temperatures and find the final temperature they settle at once heat stops flowing between them.
What This Calculator Does
When two objects or substances at different temperatures are placed in contact and isolated from their surroundings, heat flows from the hotter one to the cooler one until both reach the same final temperature — thermal equilibrium. This calculator finds that final temperature.
The Formula
Assuming no heat is lost to the surroundings and no phase change occurs, conservation of energy means the heat lost by the warmer substance equals the heat gained by the cooler one: m₁c₁(T₂ − T₁) = −m₂c₂(T₂ − T₂init). Solving for the common final temperature T₂ gives T₂ = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂), where m is mass and c is specific heat capacity.
Note: This is an idealized calculation for general educational and planning purposes — it assumes a perfectly insulated system with no phase changes (melting/boiling) and no heat exchange with a container or the environment.