You have 750 g of water at 10.0°C in a large insulated beaker. How much boiling water at 100.0°C must you add to this beaker so that the final temperature of the mixture will be 75°C?
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1
Identify the specific heat capacity of water, which is approximately 4.18 J/g°C. This value is crucial for calculating the amount of heat transferred.
Set up the heat transfer equation assuming no heat loss to the surroundings. The heat lost by the hot water should equal the heat gained by the cooler water. Use the formula: \(m_1 \cdot c \cdot (T_f - T_1) = m_2 \cdot c \cdot (T_2 - T_f)\), where \(m_1\) and \(m_2\) are the masses of the cooler and hotter water, \(T_1\) and \(T_2\) are their initial temperatures, and \(T_f\) is the final temperature.
Substitute the known values into the equation. Here, \(m_1 = 750\) g, \(T_1 = 10.0°C\), \(T_2 = 100.0°C\), and \(T_f = 75.0°C\).
Simplify the equation to solve for \(m_2\), the mass of boiling water needed. Rearrange the equation to isolate \(m_2\) on one side.
Calculate the value of \(m_2\) using the simplified equation. This will give you the mass of boiling water required to achieve the desired final temperature.