Equilibrium Temperature Calculator

Formula

The formula to calculate Equilibrium Temperature (T_eq) is:

\[ T_{eq} = \frac{E_1 \times m_1 \times c_1 + E_2 \times m_2 \times c_2}{m_1 \times c_1 + m_2 \times c_2} \]

Where:

\( T_{eq} \) is the Equilibrium Temperature
\( E_1 \) is the Thermal Energy of Object 1 (Joules)
\( m_1 \) is the Mass of Object 1 (kg)
\( c_1 \) is the Specific Heat of Object 1 (J/kg·K)
\( E_2 \) is the Thermal Energy of Object 2 (Joules)
\( m_2 \) is the Mass of Object 2 (kg)
\( c_2 \) is the Specific Heat of Object 2 (J/kg·K)

What is Equilibrium Temperature?

Equilibrium temperature is the temperature at which two objects in thermal contact no longer exchange heat energy. At this point, the objects have reached a state of thermal equilibrium, meaning their temperatures are equal and stable. This concept is crucial in thermodynamics and helps in understanding heat transfer processes. The equilibrium temperature depends on the thermal energy, mass, and specific heat capacities of the objects involved.

Example Calculation

Let's consider an example:

Thermal Energy of Object 1 (E_1): 500 J
Mass of Object 1 (m_1): 2 kg
Specific Heat of Object 1 (c_1): 1000 J/kg·K
Thermal Energy of Object 2 (E_2): 300 J
Mass of Object 2 (m_2): 1 kg
Specific Heat of Object 2 (c_2): 900 J/kg·K

Using the formula to calculate Equilibrium Temperature:

\[ T_{eq} = \frac{500 \times 2 \times 1000 + 300 \times 1 \times 900}{2 \times 1000 + 1 \times 900} = \frac{1000000 + 270000}{2900} \approx 439.66 \, \text{K} \]

This means that the equilibrium temperature is approximately 439.66 K.