To calculate the amount of heat absorbed by the sample, you can use the formula for heat transfer, which is given by:
\[ q = m \cdot c \cdot \Delta T \]
where:
- \( q \) is the heat absorbed (in joules),
- \( m \) is the mass of the substance (in grams),
- \( c \) is the specific heat capacity (in J/g-K), and
- \( \Delta T \) is the change in temperature (in °C or K).
Given:
- Mass of gold \( m = 24.4 , \text{g} \)
- Specific heat capacity of gold \( c = 0.129 , \text{J/g-K} \)
- Initial temperature \( T_{\text{initial}} = 23.7 , \text{°C} \)
- Final temperature \( T_{\text{final}} = 30.8 , \text{°C} \)
First, we need to calculate the change in temperature:
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 30.8 , \text{°C} - 23.7 , \text{°C} = 7.1 , \text{°C} \]
Now, we can plug the values into the heat transfer formula:
\[ q = (24.4 , \text{g}) \cdot (0.129 , \text{J/g-K}) \cdot (7.1 , \text{K}) \]
Calculating this step by step:
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Calculate \( (24.4 , \text{g}) \cdot (0.129 , \text{J/g-K}) \): \[ 24.4 \times 0.129 = 3.1506 , \text{J/K} \]
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Now multiply by the change in temperature \( (7.1 , \text{K}) \): \[ q = 3.1506 , \text{J/K} \cdot 7.1 , \text{K} = 22.38926 , \text{J} \]
Rounding this to three significant figures (based on the precision of the given values), we find:
\[ q \approx 22.4 , \text{J} \]
Thus, the amount of heat absorbed by the gold is approximately 22.4 joules.