To determine the heat transfer that occurs when the aluminum block is placed into water, we can apply the principle of conservation of energy, which states that the heat lost by the aluminum block will equal the heat gained by the water until thermal equilibrium is reached.
Let:
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\( m_{Al} \) = mass of aluminum (in grams)
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\( c_{Al} \) = specific heat capacity of aluminum (approximately 0.897 J/g°C)
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\( T_{i,Al} \) = initial temperature of aluminum (300°C)
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\( T_f \) = final equilibrium temperature (unknown)
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\( m_{H2O} \) = mass of water (in grams)
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\( c_{H2O} \) = specific heat capacity of water (approximately 4.186 J/g°C)
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\( T_{i,H2O} \) = initial temperature of water (20°C)
First, we calculate the mass of water. The density of water is about 1 g/mL, so:
\[ m_{H2O} = 200 , \text{mL} \times 1 , \text{g/mL} = 200 , \text{g} \]
Next, we set up the heat transfer equations. The heat lost by the aluminum block can be expressed as:
\[ Q_{Al} = m_{Al} \cdot c_{Al} \cdot (T_f - T_{i,Al}) \]
The heat gained by the water is expressed as:
\[ Q_{H2O} = m_{H2O} \cdot c_{H2O} \cdot (T_f - T_{i,H2O}) \]
According to conservation of energy, the heat lost by aluminum equals the heat gained by water:
\[ m_{Al} \cdot c_{Al} \cdot (T_f - 300) + m_{H2O} \cdot c_{H2O} \cdot (T_f - 20) = 0 \]
To find specific values for \(m_{Al}\), we would need to know the dimensions or volume of the aluminum block, which are not provided in your question. However, under this relationship, we can solve for \(T_f\) if \(m_{Al}\) is known.
But theoretically, typically for a heat transfer problem, we expect \(T_f\) to lie between 20°C and 300°C, and depending on the mass of aluminum, \(T_f\) will vary.
If we had values for \(m_{Al}\) and could solve for \(T_f\), we could then calculate the total heat transfer \(Q\):
- For the aluminum block, you would calculate \(Q_{Al}\).
- For the water, you would calculate \(Q_{H2O}\).
In conclusion, without the mass of the aluminum block, we cannot compute the actual values, but this is the method you would follow to find the heat transfer that occurs. The total heat transfer will be the absolute values of \(Q_{Al}\) or \(Q_{H2O}\) depending on final equilibrium conditions.
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