Equilibrium Temperature Calculator

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Mass of Substance 1 (kg):

Specific Heat Capacity 1 (J/kg·°C):

Initial Temperature 1 (°C):

Mass of Substance 2 (kg):

Specific Heat Capacity 2 (J/kg·°C):

Initial Temperature 2 (°C):

Equilibrium Temperature (°C):

The Equilibrium Temperature Calculator helps you find the final temperature when two substances at different temperatures are mixed together and allow to exchange heat. This tool is useful in science labs, engineering applications, cooking, and daily life scenarios where materials interact thermally without losing heat to the surroundings.

It assumes that no heat is loss to the environment and both substances stay in the same phase (no melting or boiling).

Formula of Equilibrium Temperature Calculator

Tₑ = (m₁ × c₁ × T₁ + m₂ × c₂ × T₂) / (m₁ × c₁ + m₂ × c₂)

Detailed Breakdown:

Tₑ = Equilibrium temperature (in °C or K)
m₁, m₂ = Mass of each substance (kg or g)
c₁, c₂ = Specific heat capacities (J/kg·°C or J/g·°C)
T₁, T₂ = Initial temperatures of the substances (°C or K)

Assumptions:

The system is perfectly insulated (no heat loss)
No phase changes occur (e.g., solid to liquid)
Units must match (mass and heat capacity)

This formula comes from the principle of conservation of energy—heat lost by the hotter object is equal to the heat gained by the cooler one.

Common Reference Table

Mass 1 (g)	Temp 1 (°C)	Mass 2 (g)	Temp 2 (°C)	c₁ = c₂ (J/g·°C)	Equilibrium Temp (°C)
100	80	100	20	4.18	50
200	60	100	30	4.18	50
150	90	150	10	4.18	50
100	100	300	0	4.18	25

This table assumes water-like heat capacity for both substances.

Example of Equilibrium Temperature Calculator

Suppose you mix 100 grams of hot water at 80°C with 200 grams of cold water at 30°C. Assume both have the same specific heat of 4.18 J/g·°C.

Using the formula:

Tₑ = (100 × 4.18 × 80 + 200 × 4.18 × 30) / (100 × 4.18 + 200 × 4.18)

Most Common FAQs

What does equilibrium temperature mean?

It is the final temperature reached when two substances exchange heat and no more temperature change occurs.

Can different materials reach the same final temperature?

Yes, the calculator works for any two materials as long as their heat capacities are known.

Is it important to use the same units?

Yes, always use consistent units for mass and specific heat, like both in grams and J/g·°C or kg and J/kg·°C.