Answer:
To calculate the final temperature of the water when equilibrium is reached, you can use the principle of conservation of energy, specifically the principle of heat exchange. This principle states that the heat lost by the hot object equals the heat gained by the cold object in an isolated system.
The equation for heat exchange can be expressed as:
\[ Q_{\text{lost}} = -Q_{\text{gain}} \]
Where \( Q_{\text{lost}} \) is the heat lost by the hot object, and \( Q_{\text{gain}} \) is the heat gained by the cold object.
The heat gained or lost by an object can be calculated using the equation:
\[ Q = mc\Delta T \]
Where:
- \( Q \) is the heat gained or lost
- \( m \) is the mass of the object
- \( c \) is the specific heat capacity of the material
- \( \Delta T \) is the change in temperature
First, we can calculate the heat lost by the copper cube and the heat gained by the water:
\[ Q_{\text{lost, copper}} = mc\Delta T \]
Next, we can calculate the heat gained by the water:
\[ Q_{\text{gain, water}} = mc\Delta T \]
We then set the two equations equal to each other and solve for the final temperature, \( T_f \):
\[ mc_{\text{copper}}(T_f - 59.1^\circ C) = mc_{\text{water}}(T_f - 22.0^\circ C) \]
Where:
- \( m \) is the mass of the copper cube (assumed to be the same for both the copper and aluminum cubes)
- \( c_{\text{copper}} \) is the specific heat capacity of copper
- \( c_{\text{water}} \) is the specific heat capacity of water
Solving this equation for \( T_f \) will give you the final temperature of the water when equilibrium is reached. Note that the specific heat capacities of copper and water are different, so they need to be taken into account when solving for the final temperature.