Drop a hot metal block into cold water and both end up at the same temperature. Energy conservation gives that final temperature – a classic way to measure specific heats.
How to use the Thermal Equilibrium Calculator
- Body 1 material
- Body 1 specific heat
- Body 1 mass
- Body 1 temperature
- Body 2 material
- Body 2 specific heat
- Body 2 mass
- Body 2 temperature
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the materials, enter the masses and starting temperatures. Phase changes are not included.
Tips
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.
Common mistakes to avoid
- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).
Inputs explained
| Field | What to enter |
|---|---|
| Body 1 material | Choose one: Water, Ice, Steam, Air … |
| Body 1 specific heat | Units: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C) |
| Body 1 mass | Units: kg, g, mg, t, lb, oz |
| Body 1 temperature | Units: °C, °F, K |
| Body 2 material | Choose one: Water, Ice, Steam, Air … |
| Body 2 specific heat | Units: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C) |
| Body 2 mass | Units: kg, g, mg, t, lb, oz |
| Body 2 temperature | Units: °C, °F, K |
What each result means
- Final temperature = ([C1]×[Body 1 temperature] + [C2]×[Body 2 temperature])÷([C1] + [C2])
- Heat transferred = abs([C1]×([Body 1 temperature] – ([C1]×[Body 1 temperature] + [C2]×[Body 2 temperature])÷([C1] + [C2])))
Example values
How the main result changes when Body 1 specific heat changes and everything else stays at the example values above:
| Body 1 specific heat (J/(kg·K)) | Final temperature (°C) |
|---|---|
| 450 | 27.7486 |
| 675 | 27.7486 |
| 900 | 27.7486 |
| 1,125 | 27.7486 |
| 1,350 | 27.7486 |
| 1,800 | 27.7486 |
Formula
T_f = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂)Worked example
Inputs — Body 1 material: Aluminium; Body 1 mass: 0.5 kg; Body 1 temperature: 100 °C; Body 2 material: Water; Body 2 mass: 1 kg; Body 2 temperature: 20 °C.
Results — Final temperature = 27.7486 °C; Heat transferred = 32,404.74247 J.
Key terms
- Zeroth law
- Basis for defining temperature.
Frequently asked questions
What is thermal equilibrium?
When two bodies in contact reach the same temperature and no net heat flows.
Why is the final temperature closer to the water's?
Water has a much larger heat capacity.
What is the zeroth law of thermodynamics?
Bodies in equilibrium with a third are in equilibrium with each other.
What about heat lost to the surroundings?
Real experiments need insulation or corrections.
What formula does the Thermal Equilibrium Calculator use?
T_f = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂).