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Answer :
To determine the specific heat capacity of the metal, we can use the formula for specific heat capacity:
[tex]\[ c = \frac{Q}{m \cdot \Delta T} \][/tex]
Where:
- [tex]\( c \)[/tex] is the specific heat capacity in joules per kilogram per degree Celsius (J/kg°C).
- [tex]\( Q \)[/tex] is the heat energy absorbed, in joules (J).
- [tex]\( m \)[/tex] is the mass of the metal, in kilograms (kg).
- [tex]\( \Delta T \)[/tex] is the change in temperature in degrees Celsius (°C).
Given:
- The mass of the metal, [tex]\( m \)[/tex], is 99 kg.
- The heat energy absorbed, [tex]\( Q \)[/tex], is 108 J.
- Initial temperature is [tex]\( 109^\circ C \)[/tex], and the final temperature is [tex]\( 110^\circ C \)[/tex].
Steps:
1. Calculate the Change in Temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{Final Temperature} - \text{Initial Temperature} = 110^\circ C - 109^\circ C = 1^\circ C
\][/tex]
2. Use the Formula to Solve for Specific Heat Capacity ([tex]\( c \)[/tex]):
Substitute the given values into the formula:
[tex]\[
c = \frac{108 \, \text{J}}{99 \, \text{kg} \times 1^\circ C}
\][/tex]
3. Calculate the Result:
[tex]\[
c = \frac{108}{99}
\][/tex]
[tex]\[
c \approx 1.0909 \, \text{J/kg°C}
\][/tex]
Thus, the specific heat capacity of the metal is approximately [tex]\( 1.0909 \, \text{J/kg°C} \)[/tex].
[tex]\[ c = \frac{Q}{m \cdot \Delta T} \][/tex]
Where:
- [tex]\( c \)[/tex] is the specific heat capacity in joules per kilogram per degree Celsius (J/kg°C).
- [tex]\( Q \)[/tex] is the heat energy absorbed, in joules (J).
- [tex]\( m \)[/tex] is the mass of the metal, in kilograms (kg).
- [tex]\( \Delta T \)[/tex] is the change in temperature in degrees Celsius (°C).
Given:
- The mass of the metal, [tex]\( m \)[/tex], is 99 kg.
- The heat energy absorbed, [tex]\( Q \)[/tex], is 108 J.
- Initial temperature is [tex]\( 109^\circ C \)[/tex], and the final temperature is [tex]\( 110^\circ C \)[/tex].
Steps:
1. Calculate the Change in Temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{Final Temperature} - \text{Initial Temperature} = 110^\circ C - 109^\circ C = 1^\circ C
\][/tex]
2. Use the Formula to Solve for Specific Heat Capacity ([tex]\( c \)[/tex]):
Substitute the given values into the formula:
[tex]\[
c = \frac{108 \, \text{J}}{99 \, \text{kg} \times 1^\circ C}
\][/tex]
3. Calculate the Result:
[tex]\[
c = \frac{108}{99}
\][/tex]
[tex]\[
c \approx 1.0909 \, \text{J/kg°C}
\][/tex]
Thus, the specific heat capacity of the metal is approximately [tex]\( 1.0909 \, \text{J/kg°C} \)[/tex].
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