How do you find the equilibrium temperature of a mixture?

To find the equilibrium temperature of a mixture, you can use the principle of conservation of energy, which states that the heat lost by the hotter substance must equal the heat gained by the cooler substance. Start by setting up the equation ( m_1c_1(T_f - T_1) = -m_2c_2(T_f - T_2) ), where ( m ) is mass, ( c ) is specific heat capacity, ( T_f ) is the final equilibrium temperature, and ( T_1 ) and ( T_2 ) are the initial temperatures of the two substances. Solve for ( T_f ) using the known values of mass, specific heat, and initial temperatures. Ensure that the units are consistent throughout the calculation.