1. What is Thermal Equilibrium?

Thermal equilibrium occurs when two substances reach the same temperature after exchanging heat energy. This calculator determines the final equilibrium temperature when two objects with different temperatures come into thermal contact.

2. How Does the Calculator Work?

The calculator uses the thermal equilibrium equation:

Where:

• \( T_{eq} \) — Equilibrium temperature (°C)
• \( m_1, m_2 \) — Masses of the two objects (kg)
• \( c_1, c_2 \) — Specific heat capacities (J/kg·°C)
• \( T_1, T_2 \) — Initial temperatures (°C)

Explanation: The equation balances the heat lost by the hotter object with the heat gained by the cooler object to find the final equilibrium temperature.

3. Importance of Thermal Equilibrium Calculation

Details: Calculating equilibrium temperature is essential in thermodynamics, heat transfer analysis, engineering systems, and understanding energy conservation in thermal processes.

4. Using the Calculator

Tips: Enter all values in consistent units (kg for mass, J/kg·°C for specific heat, °C for temperature). All mass and specific heat values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What if the objects have the same specific heat?
A: The equation simplifies to a weighted average based on masses: \( T_{eq} = (m_1 T_1 + m_2 T_2)/(m_1 + m_2) \).

Q2: Does this account for phase changes?
A: No, this assumes no phase change occurs. For phase changes, latent heat must be considered separately.

Q3: What are typical specific heat values?
A: Water: ~4186 J/kg·°C, Iron: ~450 J/kg·°C, Aluminum: ~900 J/kg·°C, Air: ~1005 J/kg·°C.

Q4: Can this be used for more than two objects?
A: Yes, by extending the numerator and denominator to include additional terms for each object.

Q5: What if heat is lost to the environment?
A: This assumes an isolated system. For open systems, heat loss terms would need to be included.