Answer :
Final answer:
We use the principle of conservation of energy and the formula for heat exchange to calculate how much water is necessary. The sum of the heat gained by the water and the heat lost by the coffee are equal, and through this, we can solve for the mass of the water.
Explanation:
The question requires us to find the mass of water that must be mixed with 181 g of coffee at 97.6 °C to achieve a temperature of 60.0 °C. We start by using the principle of conservation of energy. The sum of the heat gained by the water and the heat lost by the coffee is equal to zero, as they transfer heat to each other without any gain or loss to the environment. The equation for this is: m_c * c * (T_initial_c - T_final) = -m_w * c * (T_final - T_initial_w).
Here, m_c is the mass of the coffee (181g), c its specific heat (4.184 J/g °C - since we assume water and coffee have the same specific heat), T_initial_c is the initial temperature of the coffee (97.6°C), and T_final is the final temperature both substances reach (60.0°C).
The opposite side of the equation represents the heat exchange of the water, with m_w being the unknown mass of the water we are to find, T_initial_w its initial temperature (20.7°C), and the other variables being the same as for the coffee.
Solving this equation for m_w, we find that m_w = m_c * (T_initial_c - T_final) / (T_final - T_initial_w).
By substituting the given values into the equation, we will get the mass of the water needed.
Learn more about Conservation of Energy here:
https://brainly.com/question/35373077
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