Answer:
To find the heat of fusion (\(Q_f\)) of the alcohol, we can use the principle of conservation of energy. The heat gained by the water equals the heat lost by the alcohol during the phase change and temperature change.
Let's denote:
- \(m_{\text{water}}\) as the mass of water
- \(m_{\text{alcohol}}\) as the mass of alcohol
- \(T_{\text{initial}}\) as the initial temperature
- \(T_{\text{final}}\) as the final temperature after reaching thermal equilibrium
- \(C_{\text{water}}\) as the specific heat of water
- \(Q_f\) as the heat of fusion of the alcohol
For the first run:
\[Q_{\text{water}} = m_{\text{water}} \cdot C_{\text{water}} \cdot (T_{\text{final}} - T_{\text{initial}})\]
\[Q_{\text{alcohol}} = -Q_f\]
For the second run:
\[Q_{\text{water}} = m_{\text{water}} \cdot C_{\text{water}} \cdot (T_{\text{final}} - T_{\text{initial}})\]
\[Q_{\text{alcohol}} = -Q_f\]
Since the two runs involve the same cube of alcohol, we can set \(Q_{\text{alcohol}}\) for both runs equal to each other.
Solving the equations with the given values, you can find the heat of fusion (\(Q_f\)).
