Thermal Equilibrium Calculator
Calculate the final temperature when two objects or systems exchange heat until thermal equilibrium
Calculate Thermal Equilibrium
Choose whether to include latent heat for phase transitions (melting, freezing, vaporization)
Object 1 (Lower Temperature)
Specific Heat: 4,181.3 J/(kg·K)
Object 2 (Higher Temperature)
Specific Heat: 4,181.3 J/(kg·K)
Thermal Equilibrium Results
Should be close to zero for energy conservation (Q₁ + Q₂ = 0)
Formula used:
T_final = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂)
Q = mcΔT
Equilibrium Analysis
Example Calculation
Ice and Hot Water Mixing
Object 1: 100 g ice at 0°C
Object 2: 500 g water at 20°C
Specific heat of water: 4,181.3 J/(kg·K)
Latent heat of fusion: 334,000 J/kg
Solution
Without phase change: T_f = (0.1×4181×0 + 0.5×4181×20)/(0.1×4181 + 0.5×4181)
T_f = (0 + 41,810)/(418.1 + 2090.5) = 41,810/2508.6 = 16.67°C
With melting: Ice melts first (334 kJ), then heats to final temperature
Result: Approximately 13.3°C (accounting for melting energy)
Zeroth Law of Thermodynamics
Thermal Equilibrium
Objects at same temperature = no heat transfer
Transitive Property
If A=B and B=C in temperature, then A=C
Temperature Scale
Establishes basis for temperature measurement
Heat Transfer Mechanisms
Heat flows from high to low temperature until equilibrium
Physics Tips
Final temperature is always between initial temperatures
Energy is conserved: Q₁ + Q₂ = 0
Higher specific heat = more energy to change temperature
Phase changes require additional latent heat energy
Understanding Thermal Equilibrium
What is Thermal Equilibrium?
Thermal equilibrium occurs when two or more objects reach the same temperature and no longer exchange heat. This fundamental concept is described by the zeroth law of thermodynamics and forms the basis for temperature measurement.
Heat Transfer Process
- •Heat flows from high to low temperature objects
- •Rate depends on temperature difference and materials
- •Process continues until temperatures equalize
- •Total energy is conserved throughout the process
Mathematical Framework
Q = mcΔT
Q₁ + Q₂ = 0
T_f = (m₁c₁T₁ + m₂c₂T₂)/(m₁c₁ + m₂c₂)
- Q: Heat transferred (Joules)
- m: Mass of object (kg)
- c: Specific heat capacity (J/kg·K)
- ΔT: Temperature change (K or °C)
- T_f: Final equilibrium temperature
Note: For phase changes, add latent heat: Q = mL
Phase Changes and Latent Heat
When substances undergo phase transitions (melting, freezing, vaporization, condensation), additional energy called latent heat is required. This energy doesn't change temperature but changes the molecular structure of the material.
Melting/Freezing
Latent heat of fusion
Water: 334 kJ/kg
Vaporization/Condensation
Latent heat of vaporization
Water: 2,260 kJ/kg
Total Energy
Q_total = Q_sensible + Q_latent
Q = mcΔT + mL