Thermal Equilibrium Calculator
Find the heat transferred between two bodies reaching equilibrium.
Two objects in contact exchange heat until they reach the same temperature.
How the Math Works
The Thermal Equilibrium Calculator uses the principle of conservation of energy to determine the final equilibrium temperature when two objects exchange heat. The formula T_f = (m₁c₁T₁ + m₂c₂T₂)/(m₁c₁ + m₂c₂) calculates the weighted average temperature based on each object's mass (m) and specific heat capacity (c). The heat transferred (Q) is then found using Q = m₁c₁(T₁ − T_f), which represents the energy change for the first object as it moves toward the equilibrium state.
Practical Applications
To use this calculator practically, input the mass and specific heat capacity of each substance along with their initial temperatures. For example, when mixing hot water and cold water in a container, enter the mass of each water portion and their respective temperatures. The calculator will output the final equilibrium temperature and the amount of heat transferred, helping you predict whether you'll achieve your desired temperature without guesswork.
Day-to-Day Use
This calculation helps in everyday cooking, such as determining how much hot water from a kettle is needed to fill a container with a specific temperature, or how long it takes for a casserole to reach serving temperature. It's also useful for practical scenarios like mixing drinks at a party, adjusting the temperature of baby formula, or understanding why metal feels hot while plastic containers don't, making temperature management in daily activities more intuitive and efficient.
Worked example
1 kg metal at 200 °C in 3 kg water at 20 °C → about 32.6 °C.
FAQ
Why does the metal cool more than the water warms?
Water's high specific heat resists temperature change.