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Answer :
To find the specific heat of the metal, we'll use the formula for specific heat capacity:
[tex]\[ \text{specific heat (c)} = \frac{\text{energy}}{\text{mass} \times \Delta T} \][/tex]
where:
- Energy is the amount of heat added (in calories).
- Mass is the mass of the sample (in grams).
- [tex]\( \Delta T \)[/tex] is the change in temperature (in Fahrenheit).
Let's break it down step-by-step:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 36.3 grams
- Energy ([tex]\( q \)[/tex]) = 60.4 calories
- Initial temperature ([tex]\( T_i \)[/tex]) = 7.7°F
- Final temperature ([tex]\( T_f \)[/tex]) = 21.3°F
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[ \Delta T = T_f - T_i = 21.3^\circ \text{F} - 7.7^\circ \text{F} = 13.6^\circ \text{F} \][/tex]
3. Use the specific heat formula:
[tex]\[ c = \frac{q}{m \times \Delta T} \][/tex]
[tex]\[ c = \frac{60.4 \text{ cal}}{36.3 \text{ g} \times 13.6^\circ \text{F}} \][/tex]
[tex]\[ c = \frac{60.4}{493.68} \][/tex]
4. Calculate the specific heat:
[tex]\[ c \approx 0.122 \, \text{cal/g°F} \][/tex]
So, the specific heat of the metal is approximately 0.122 cal/g°F, calculated to three decimal places.
[tex]\[ \text{specific heat (c)} = \frac{\text{energy}}{\text{mass} \times \Delta T} \][/tex]
where:
- Energy is the amount of heat added (in calories).
- Mass is the mass of the sample (in grams).
- [tex]\( \Delta T \)[/tex] is the change in temperature (in Fahrenheit).
Let's break it down step-by-step:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 36.3 grams
- Energy ([tex]\( q \)[/tex]) = 60.4 calories
- Initial temperature ([tex]\( T_i \)[/tex]) = 7.7°F
- Final temperature ([tex]\( T_f \)[/tex]) = 21.3°F
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[ \Delta T = T_f - T_i = 21.3^\circ \text{F} - 7.7^\circ \text{F} = 13.6^\circ \text{F} \][/tex]
3. Use the specific heat formula:
[tex]\[ c = \frac{q}{m \times \Delta T} \][/tex]
[tex]\[ c = \frac{60.4 \text{ cal}}{36.3 \text{ g} \times 13.6^\circ \text{F}} \][/tex]
[tex]\[ c = \frac{60.4}{493.68} \][/tex]
4. Calculate the specific heat:
[tex]\[ c \approx 0.122 \, \text{cal/g°F} \][/tex]
So, the specific heat of the metal is approximately 0.122 cal/g°F, calculated to three decimal places.
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