Final answer:
To find the final temperature when two bodies of water are mixed, we can use the principle of conservation of energy. The heat lost by the hot water is equal to the heat gained by the cold water. By substituting the known values into the equations and solving for T`f, we can find the final temperature to be 58.3 °C.
Step-by-step explanation:
To find the final temperature when two bodies of water are mixed, we can use the principle of conservation of energy. The heat lost by the hot water is equal to the heat gained by the cold water.
We can use the equation:
Q_hot = -Q_cold
where Q_hot is the heat lost by the hot water, and Q_cold is the heat gained by the cold water.
We can calculate the heat lost by the hot water using the formula:
Q_hot = m_hot * c * (T_hot - T`f)
where m_hot is the mass of the hot water, c is the specific heat capacity of water, T_hot is the initial temperature of the hot water, and T`f is the final temperature.
Similarly, we can calculate the heat gained by the cold water using the formula:
Q_cold = m_cold * c * (T`f - T_cold)
where m_cold is the mass of the cold water, T_cold is the initial temperature of the cold water.
By substituting the known values into the equations and solving for T`f, we can find the final temperature:
T`f = (m_hot * T_hot + m_cold * T_cold) / (m_hot + m_cold)
Substituting the given values:
T`f = (42.3 g * 0 °C + 255.8 g * 76.78 °C) / (42.3 g + 255.8 g) = 58.3 °C