Final Answer:
The final equilibrium temperature after mixing 4.4 kg of water at 19.8°C with 9 kg of alcohol at 35.5°C, neglecting energy processes associated with mixing, can be calculated using the principle of conservation of energy. The final temperature is approximately 32.35°C.
Step-by-step explanation:
To determine the final equilibrium temperature, we can use the principle that the total heat lost by one substance equals the total heat gained by the other substance when they reach thermal equilibrium, neglecting any energy changes during mixing.
The heat lost by water (Q_lost) is calculated using the formula:
\[ Q_{\text{lost}} = mc\Delta T \]
Where:
\(m\) = mass of water = 4.4 kg
\(c_{\text{water}}\) = specific heat capacity of water = 4190 J/(kg⋅K)
\(\Delta T_{\text{water}}\) = change in temperature of water = final temperature - initial temperature = \(T_{\text{f}} - 19.8°C\)
Similarly, the heat gained by alcohol (Q_gained) can be calculated using:
\[ Q_{\text{gained}} = mc\Delta T \]
Where:
\(m\) = mass of alcohol = 9 kg
\(c_{\text{alcohol}}\) = specific heat capacity of alcohol = 2460 J/(kg⋅K)
\(\Delta T_{\text{alcohol}}\) = change in temperature of alcohol = \(35.5°C - T_{\text{f}}\)
Setting \(Q_{\text{lost}} = Q_{\text{gained}}\):
\[ m_{\text{water}}c_{\text{water}}\Delta T_{\text{water}} = m_{\text{alcohol}}c_{\text{alcohol}}\Delta T_{\text{alcohol}} \]
Solving this equation yields the final equilibrium temperature, which is approximately 32.35°C.