Answer :
To determine the specific heat capacity of the substance, we need to use the formula:
[tex]\[ q = m \cdot C \cdot \Delta T \][/tex]
Where:
- [tex]\( q \)[/tex] is the heat added (in joules, [tex]\( J \)[/tex])
- [tex]\( m \)[/tex] is the mass of the substance (in grams, [tex]\( g \)[/tex])
- [tex]\( C \)[/tex] is the specific heat capacity (in [tex]\( J / (g \cdot ^\circ C) \)[/tex])
- [tex]\( \Delta T \)[/tex] is the change in temperature (in [tex]\( ^\circ C \)[/tex])
### Step-by-Step Solution:
1. Convert the mass from kilograms to grams:
[tex]\[ \text{mass\_kg} = 0.465 \, \text{kg} \][/tex]
[tex]\[ \text{mass\_g} = 0.465 \, \text{kg} \times 1000 \, \text{g/kg} = 465 \, \text{g} \][/tex]
2. Identify the heat added [tex]\( q \)[/tex]:
[tex]\[ q = 3000.0 \, J \][/tex]
3. Determine the change in temperature [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = 100.0^\circ C - 50.0^\circ C = 50.0^\circ C \][/tex]
4. Use the formula to solve for the specific heat capacity [tex]\( C \)[/tex]:
[tex]\[ q = m \cdot C \cdot \Delta T \][/tex]
[tex]\[ 3000.0 \, J = 465 \, g \cdot C \cdot 50.0^\circ C \][/tex]
5. Rearrange the equation to solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{q}{m \cdot \Delta T} \][/tex]
[tex]\[ C = \frac{3000.0 \, J}{465 \, g \cdot 50.0^\circ C} \][/tex]
6. Calculate the specific heat capacity [tex]\( C \)[/tex]:
[tex]\[ C \approx \frac{3000.0 \, J}{23250 \, g \cdot ^\circ C} \][/tex]
[tex]\[ C \approx 0.129 \, J/(g \cdot ^\circ C) \][/tex]
### Conclusion:
The specific heat of the substance is approximately [tex]\( 0.129 \, J/(g \cdot ^\circ C) \)[/tex].
Thus, the correct answer from the given options is:
[tex]\[ 0.129 \, J/ (g \cdot ^\circ C) \][/tex]
[tex]\[ q = m \cdot C \cdot \Delta T \][/tex]
Where:
- [tex]\( q \)[/tex] is the heat added (in joules, [tex]\( J \)[/tex])
- [tex]\( m \)[/tex] is the mass of the substance (in grams, [tex]\( g \)[/tex])
- [tex]\( C \)[/tex] is the specific heat capacity (in [tex]\( J / (g \cdot ^\circ C) \)[/tex])
- [tex]\( \Delta T \)[/tex] is the change in temperature (in [tex]\( ^\circ C \)[/tex])
### Step-by-Step Solution:
1. Convert the mass from kilograms to grams:
[tex]\[ \text{mass\_kg} = 0.465 \, \text{kg} \][/tex]
[tex]\[ \text{mass\_g} = 0.465 \, \text{kg} \times 1000 \, \text{g/kg} = 465 \, \text{g} \][/tex]
2. Identify the heat added [tex]\( q \)[/tex]:
[tex]\[ q = 3000.0 \, J \][/tex]
3. Determine the change in temperature [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = 100.0^\circ C - 50.0^\circ C = 50.0^\circ C \][/tex]
4. Use the formula to solve for the specific heat capacity [tex]\( C \)[/tex]:
[tex]\[ q = m \cdot C \cdot \Delta T \][/tex]
[tex]\[ 3000.0 \, J = 465 \, g \cdot C \cdot 50.0^\circ C \][/tex]
5. Rearrange the equation to solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{q}{m \cdot \Delta T} \][/tex]
[tex]\[ C = \frac{3000.0 \, J}{465 \, g \cdot 50.0^\circ C} \][/tex]
6. Calculate the specific heat capacity [tex]\( C \)[/tex]:
[tex]\[ C \approx \frac{3000.0 \, J}{23250 \, g \cdot ^\circ C} \][/tex]
[tex]\[ C \approx 0.129 \, J/(g \cdot ^\circ C) \][/tex]
### Conclusion:
The specific heat of the substance is approximately [tex]\( 0.129 \, J/(g \cdot ^\circ C) \)[/tex].
Thus, the correct answer from the given options is:
[tex]\[ 0.129 \, J/ (g \cdot ^\circ C) \][/tex]
