Enter the mass, specific heat, and initial temperature of two objects into the calculator to determine the equilibrium temperature (assuming no heat loss to the surroundings and no phase change).

Equilibrium Temperature Calculator

Main (solve for 1 variable)
Mixing (Teq only)

Enter any 6 values to calculate the missing variable.

Equilibrium Temperature Formula

The following formula is used to calculate the equilibrium temperature for two objects in thermal contact (assuming no heat loss and no phase change). 

T_{eq} = \frac{m_1 \cdot c_1 \cdot T_1 + m_2 \cdot c_2 \cdot T_2}{m_1 \cdot c_1 + m_2 \cdot c_2}

Variables:

  • Teq is the equilibrium temperature
  • m1 is the mass of object 1
  • c1 is the specific heat of object 1
  • T1 is the initial temperature of object 1
  • m2 is the mass of object 2
  • c2 is the specific heat of object 2
  • T2 is the initial temperature of object 2

To calculate the equilibrium temperature, sum the products of mass, specific heat, and initial temperature for both objects, then divide by the sum of the products of mass and specific heat for both objects.

What is Equilibrium Temperature?

Equilibrium temperature is the temperature at which two objects in thermal contact no longer exchange heat energy. At this point, the objects have reached a state of thermal equilibrium, meaning their temperatures are equal and stable. This concept is crucial in thermodynamics and helps in understanding heat transfer processes. In the idealized no-heat-loss case, the equilibrium temperature depends on the initial temperatures, masses, and specific heat capacities of the objects involved.

How to Calculate Equilibrium Temperature?

The following steps outline how to calculate the Equilibrium Temperature.

  1. First, determine the mass (m), specific heat (c), and initial temperature (T) of both objects.
  2. Next, use the formula Teq = (m1c1T1 + m2c2T2) / (m1c1 + m2c2) to calculate the equilibrium temperature.
  3. Insert the values into the formula and solve for Teq.
  4. Finally, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Initial Temperature of Object 1 (T1) = 50 °C

Mass of Object 1 (m1) = 2 kg

Specific Heat of Object 1 (c1) = 1000 J/kg°C

Initial Temperature of Object 2 (T2) = 20 °C

Mass of Object 2 (m2) = 1.5 kg

Specific Heat of Object 2 (c2) = 800 J/kg°C

Equilibrium Temperature (Teq) ≈ 38.75 °C