To find the mass of the iron, we can use the formula for heat transfer:
\[ Q = m \cdot c \cdot \Delta T \]
where:
- \( Q \) is the amount of heat added (in joules),
- \( m \) is the mass of the substance (in grams),
- \( c \) is the specific heat capacity (in J/g⋅K),
- \( \Delta T \) is the change in temperature (in °C or K).
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Calculate the change in temperature (\( \Delta T \)): \[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 31.4°C - 27.2°C = 4.2°C \]
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Substitute \( c \) and \( \Delta T \) into the heat transfer equation. We're looking to solve for the mass \( m \), so we rearrange the equation: \[ m = \frac{Q}{c \cdot \Delta T} \]
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Plug in the values: \[ m = \frac{Q}{0.450 , \text{J/g⋅K} \cdot 4.2 , \text{K}} \]
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We need to know the amount of energy \( Q \) added (in joules). Since that value is not provided in the question, we can't calculate the exact mass without knowing the amount of heat added.
If we assume the amount of energy added is \( Q = 0.0029 , \text{J} \): \[ m = \frac{0.0029 , \text{J}}{0.450 , \text{J/g⋅K} \cdot 4.2 , \text{K}} \approx \frac{0.0029}{1.89} \approx 0.00154 , \text{g} \]
Based on your provided responses, this calculation would yield a mass that does not match any of the given options.
Therefore, if we consider other appropriate values for \( Q \) (provided they reasonably fit into the equations), we could find different corresponding masses. If you provide the specific \( Q \), I can help compute the mass more accurately.
2 answers