How To Calculate Equilibrium Temperature

Equilibrium Temperature Equation:

\[ T_{eq} = \frac{T_1 m_1 c_1 + T_2 m_2 c_2}{m_1 c_1 + m_2 c_2} \]

Temperature 1 (T1):

°C

Mass 1 (m1):

Specific Heat 1 (c1):

J/kg·°C

Temperature 2 (T2):

°C

Mass 2 (m2):

Specific Heat 2 (c2):

J/kg·°C

Equilibrium Temperature (T_eq):

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1. What is Equilibrium Temperature?

The equilibrium temperature is the final temperature reached when two substances at different temperatures come into thermal contact and exchange heat until they reach the same temperature. This principle is fundamental in thermodynamics and heat transfer calculations.

2. How Does the Calculator Work?

The calculator uses the equilibrium temperature equation:

\[ T_{eq} = \frac{T_1 m_1 c_1 + T_2 m_2 c_2}{m_1 c_1 + m_2 c_2} \]

Where:

\( T_{eq} \) — Equilibrium temperature (°C)
\( T_1 \) — Temperature of first substance (°C)
\( m_1 \) — Mass of first substance (kg)
\( c_1 \) — Specific heat capacity of first substance (J/kg·°C)
\( T_2 \) — Temperature of second substance (°C)
\( m_2 \) — Mass of second substance (kg)
\( c_2 \) — Specific heat capacity of second substance (J/kg·°C)

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

3. Importance of Equilibrium Temperature

Details: Calculating equilibrium temperature is essential in various applications including thermal system design, materials science, environmental studies, and industrial processes where heat transfer occurs between different materials.

4. Using the Calculator

Tips: Enter all temperatures in Celsius, masses in kilograms, and specific heat capacities in J/kg·°C. Ensure all mass and specific heat values are positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if the substances are at the same initial temperature?
A: If T1 = T2, the equilibrium temperature will be the same as the initial temperature (no heat transfer occurs).

Q2: How does specific heat affect the equilibrium temperature?
A: Substances with higher specific heat capacities have greater influence on the final equilibrium temperature as they can absorb or release more heat per unit mass.

Q3: Can this be used for more than two substances?
A: The equation can be extended to multiple substances by adding more terms to the numerator and denominator.

Q4: What assumptions does this calculation make?
A: It assumes perfect thermal contact, no heat loss to surroundings, and constant specific heat capacities over the temperature range.

Q5: How does mass affect the equilibrium temperature?
A: Larger masses have greater influence on the final temperature as they contain more thermal energy.