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Answer :
To determine the specific heat capacity of the metal, we can follow these simple steps:
1. Understand the Given Data:
- Mass of the metal, [tex]\( m = 99 \, \text{kg} \)[/tex]
- Initial temperature, [tex]\( T_{\text{initial}} = 10^\circ \text{C} \)[/tex]
- Final temperature, [tex]\( T_{\text{final}} = 110^\circ \text{C} \)[/tex]
- Heat energy absorbed, [tex]\( Q = 108 \, \text{J} \)[/tex]
2. Calculate the Change in Temperature:
- The change in temperature, [tex]\(\Delta T\)[/tex], is calculated using the formula:
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 110^\circ C - 10^\circ C = 100^\circ C
\][/tex]
3. Use the Formula for Specific Heat Capacity:
- The specific heat capacity ([tex]\( c \)[/tex]) of a substance can be found using the formula:
[tex]\[
Q = mc\Delta T
\][/tex]
- Rearranging this formula to solve for the specific heat capacity gives:
[tex]\[
c = \frac{Q}{m \cdot \Delta T}
\][/tex]
- Substitute in the known values:
[tex]\[
c = \frac{108 \, \text{J}}{99 \, \text{kg} \times 100 \, \text{K}}
\][/tex]
4. Calculate the Specific Heat Capacity:
- Perform the division to find the specific heat capacity:
[tex]\[
c \approx 0.0109 \, \text{J/kg/K}
\][/tex]
Therefore, the specific heat capacity of the metal is approximately [tex]\( 0.0109 \, \text{J/kg/K} \)[/tex].
1. Understand the Given Data:
- Mass of the metal, [tex]\( m = 99 \, \text{kg} \)[/tex]
- Initial temperature, [tex]\( T_{\text{initial}} = 10^\circ \text{C} \)[/tex]
- Final temperature, [tex]\( T_{\text{final}} = 110^\circ \text{C} \)[/tex]
- Heat energy absorbed, [tex]\( Q = 108 \, \text{J} \)[/tex]
2. Calculate the Change in Temperature:
- The change in temperature, [tex]\(\Delta T\)[/tex], is calculated using the formula:
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 110^\circ C - 10^\circ C = 100^\circ C
\][/tex]
3. Use the Formula for Specific Heat Capacity:
- The specific heat capacity ([tex]\( c \)[/tex]) of a substance can be found using the formula:
[tex]\[
Q = mc\Delta T
\][/tex]
- Rearranging this formula to solve for the specific heat capacity gives:
[tex]\[
c = \frac{Q}{m \cdot \Delta T}
\][/tex]
- Substitute in the known values:
[tex]\[
c = \frac{108 \, \text{J}}{99 \, \text{kg} \times 100 \, \text{K}}
\][/tex]
4. Calculate the Specific Heat Capacity:
- Perform the division to find the specific heat capacity:
[tex]\[
c \approx 0.0109 \, \text{J/kg/K}
\][/tex]
Therefore, the specific heat capacity of the metal is approximately [tex]\( 0.0109 \, \text{J/kg/K} \)[/tex].
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