To determine the final temperature of the mixed water, we use the principle of heat exchange, which states that the heat lost by the hot water will be equal to the heat gained by the cold water in an isolated system.
The formula for heat exchange in this context is:

\(m_1 \cdot c \cdot (T_1 - T_f) = m_2 \cdot c \cdot (T_f - T_2)\)

Where:

• \(m_1\): mass of hot water
• \(T_1\): initial temperature of hot water
• \(m_2\): mass of cold water
• \(T_2\): initial temperature of cold water
• \(c\): specific heat capacity of water (can be ignored in ratio form as it is the same)
• \(T_f\): final temperature after mixing

Given, \(m_1=2\,l\), \(T_1=100^\circ C\), \(m_2=18\,l\), \(T_2=32^\circ C\). Since mass is proportional to volume and c is constant, the equation becomes:
\(2 \cdot (100 - T_f) = 18 \cdot (T_f - 32)\)

Now, solve for \(T_f\):

\(200 - 2T_f = 18T_f - 576\)

Combine like terms:

\(200 + 576 = 18T_f + 2T_f\)

\(776 = 20T_f\)

Divide both sides by 20:

\(T_f = 38.8\)

Thus, the final temperature of the water after mixing will be \(38.8^\circ C\).