To calculate the specific heat capacity (\(c\)) of the aluminum sample, you can use the formula:
\[ q = mc\Delta T \]
Where:
- \(q\) is the heat absorbed (10.3 J)
- \(m\) is the mass of the sample (unknown)
- \(c\) is the specific heat capacity (unknown)
- \(\Delta T\) is the change in temperature
First, calculate \(\Delta T\):
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 30.5 , °C - 23.2 , °C = 7.3 , °C \]
Now, substituting into the formula gives:
\[ 10.3 , \text{J} = m \cdot c \cdot 7.3 , °C \]
To solve for \(c\), we need to know the mass \(m\) of the aluminum sample. If you do not have the mass provided, you cannot find the specific heat capacity directly without that information.
However, if you know the mass of the aluminum sample, you can rearrange the formula to solve for \(c\):
\[ c = \frac{q}{m \Delta T} \]
If you provide the mass \(m\) of the aluminum, I can help you calculate the specific heat capacity \(c\).
In general, the specific heat capacity of aluminum is approximately \(0.897 , \text{J/g°C} \). If you compare your calculated value to this, you can check the accuracy of your measurement.
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