Final Temperature of Mixture Calculator

Final Temperature Formula:

\[ T_f = \frac{m_1 \times c_1 \times T_1 + m_2 \times c_2 \times T_2}{m_1 \times c_1 + m_2 \times c_2} \]

Mass 1 (m₁):

Specific Heat 1 (c₁):

J/kg°C

Temperature 1 (T₁):

°C

Mass 2 (m₂):

Specific Heat 2 (c₂):

J/kg°C

Temperature 2 (T₂):

°C

Final Temperature (T_f):

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1. What is the Final Temperature of Mixture?

The final temperature of a mixture is the equilibrium temperature reached when two substances at different temperatures are combined. This calculation is based on the principle of energy conservation, where heat lost by the hotter substance equals heat gained by the cooler substance.

2. How Does the Calculator Work?

The calculator uses the following equation:

\[ T_f = \frac{m_1 \times c_1 \times T_1 + m_2 \times c_2 \times T_2}{m_1 \times c_1 + m_2 \times c_2} \]

Where:

\( T_f \) — Final temperature (°C)
\( m_1 \) — Mass of substance 1 (kg)
\( c_1 \) — Specific heat capacity of substance 1 (J/kg°C)
\( T_1 \) — Initial temperature of substance 1 (°C)
\( m_2 \) — Mass of substance 2 (kg)
\( c_2 \) — Specific heat capacity of substance 2 (J/kg°C)
\( T_2 \) — Initial temperature of substance 2 (°C)

Explanation: The equation balances the thermal energy of both substances to find their equilibrium temperature when mixed.

3. Importance of Final Temperature Calculation

Details: Calculating the final mixture temperature is essential in thermodynamics, chemical engineering, cooking, and various industrial processes where temperature control is critical.

4. Using the Calculator

Tips: Enter all values in the specified units. Mass and specific heat must be positive values. The calculator assumes no heat loss to the surroundings.

5. Frequently Asked Questions (FAQ)

Q1: What if the substances have different phases?
A: This calculator assumes both substances remain in the same phase. For phase changes, latent heat calculations would be needed.

Q2: How accurate is this calculation?
A: It's accurate for ideal mixing with no heat loss to the environment. Real-world applications may need to account for container heat capacity.

Q3: Can I use this for more than two substances?
A: The calculator is designed for two substances. For more substances, you would need to extend the formula.

Q4: What if one substance is much hotter than the other?
A: The equation works for any temperature difference, as long as no phase change occurs.

Q5: Why is specific heat capacity important?
A: Substances with higher specific heat require more energy to change temperature, significantly affecting the final mixture temperature.