Answer :
To find the specific heat of the metal, we can use the formula for specific heat capacity:
[tex]\[ \text{Specific Heat} = \frac{\text{Heat Added}}{\text{Mass} \times \text{Temperature Change}} \][/tex]
Here are the given values:
- Heat added = 51.7 calories
- Mass = 100.0 grams
- Temperature change = [tex]\(18.4^{\circ} C\)[/tex]
Now, we can plug these values into the formula to calculate the specific heat:
[tex]\[ \text{Specific Heat} = \frac{51.7 \, \text{cal}}{100.0 \, \text{g} \times 18.4 \, ^{\circ} C} \][/tex]
[tex]\[ \text{Specific Heat} = \frac{51.7}{1840} \][/tex]
Calculating this gives you a specific heat of approximately 0.0281 cal/g°C.
This result does not match any of the provided options. It suggests that the correct answer is not listed among the choices given (0.0345 cal/g°C, 0.56 cal/g°C, 0.75 cal/g°C). Based on the data and calculations, the specific heat is about 0.0281 cal/g°C.
[tex]\[ \text{Specific Heat} = \frac{\text{Heat Added}}{\text{Mass} \times \text{Temperature Change}} \][/tex]
Here are the given values:
- Heat added = 51.7 calories
- Mass = 100.0 grams
- Temperature change = [tex]\(18.4^{\circ} C\)[/tex]
Now, we can plug these values into the formula to calculate the specific heat:
[tex]\[ \text{Specific Heat} = \frac{51.7 \, \text{cal}}{100.0 \, \text{g} \times 18.4 \, ^{\circ} C} \][/tex]
[tex]\[ \text{Specific Heat} = \frac{51.7}{1840} \][/tex]
Calculating this gives you a specific heat of approximately 0.0281 cal/g°C.
This result does not match any of the provided options. It suggests that the correct answer is not listed among the choices given (0.0345 cal/g°C, 0.56 cal/g°C, 0.75 cal/g°C). Based on the data and calculations, the specific heat is about 0.0281 cal/g°C.
