The Final Temperature Calculator is a reliable tool for students, engineers, and anyone working with heat and energy transfer. It calculates the final temperature when heat is exchanged between substances, when a gas is heated or cooled, or during special processes like adiabatic compression. By using this calculator, you save time and avoid mistakes when solving thermodynamics problems. This tool belongs to the Thermodynamics & Heat Transfer Calculators category.
Formula of Final Temperature Calculator
1. Heat Exchange Between Two Substances (No Heat Loss)
Formula:
Final Temperature (Tf) = (m₁ × c₁ × T₁ + m₂ × c₂ × T₂) / (m₁ × c₁ + m₂ × c₂)
Where:
- Tf = final equilibrium temperature (°C or K)
- m₁, m₂ = masses of the two substances (kg)
- c₁, c₂ = specific heat capacities (J/kg·K)
- T₁, T₂ = initial temperatures (°C or K)
2. Ideal Gas Heating or Cooling (Constant Pressure)
Formula:
Q = m × c_p × (Tf − Ti)
So,
Tf = Ti + (Q / (m × c_p))
Where:
- Q = heat added or removed (J)
- m = mass (kg)
- c_p = specific heat at constant pressure (J/kg·K)
- Ti = initial temperature (°C or K)
3. Adiabatic Process (No Heat Exchange, Ideal Gas)
Formula:
Tf = Ti × (V₁/V₂)^(γ − 1)
or
Tf = Ti × (P₂/P₁)^((γ − 1)/γ)
Where:
- Ti = initial temperature (K)
- V₁, V₂ = initial and final volumes
- P₁, P₂ = initial and final pressures
- γ = heat capacity ratio (c_p / c_v)
Quick Reference Table
| Scenario | Example Inputs | Approx. Final Temperature |
|---|---|---|
| Heat exchange | 2 kg water at 80°C + 1 kg water at 20°C | ~60°C |
| Heating gas | Add 5,000 J to 1 kg air at 25°C (c_p = 1005 J/kg·K) | ~30°C |
| Adiabatic compression | Air at 300 K, compressed from 2 m³ to 1 m³ (γ = 1.4) | ~379 K |
Example of Final Temperature Calculator
Problem:
Find the final temperature when 1 kg of hot water at 90°C is mixed with 2 kg of cold water at 30°C.
Solution:
Tf = (1 × 4184 × 90 + 2 × 4184 × 30) / (1 × 4184 + 2 × 4184)
= (376,560 + 250,080) / (12,552)
= 626,640 / 12,552
≈ 49.9°C
The final temperature will be about 49.9°C.
Most Common FAQs
Most basic calculators handle two substances. For multiple substances, repeat the process step by step, combining two at a time.
It works with either, but you must use the same unit for all inputs. For adiabatic or ideal gas formulas, Kelvin is safest.
No. This calculator assumes a perfectly insulated system with no heat lost. For real situations, small heat losses should be considered separately.