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Answer :
To find out how much heat energy in kilojoules is required to raise the temperature of 448 g of copper from 38.2 °C to 73.6 °C, you can follow these steps:
1. Understand the Formula: The formula to calculate heat energy is:
[tex]\[
Q = m \cdot c \cdot \Delta T
\][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy (in joules or kilojoules),
- [tex]\( m \)[/tex] is the mass of the substance (in grams),
- [tex]\( c \)[/tex] is the specific heat capacity (in joules per gram per degree Celsius, J/(g°C)),
- [tex]\( \Delta T \)[/tex] is the change in temperature (in degrees Celsius, °C).
2. Convert Specific Heat Capacity: The specific heat capacity of copper is 0.385 J/(g°C). To express this in kilojoules per gram per degree Celsius:
[tex]\[
c = 0.385 \text{ J/(g°C)} = \frac{0.385}{1000} \text{ kJ/(g°C)} = 0.000385 \text{ kJ/(g°C)}
\][/tex]
3. Calculate Temperature Change:
[tex]\[
\Delta T = \text{Final Temperature} - \text{Initial Temperature} = 73.6 \,^\circ\text{C} - 38.2 \,^\circ\text{C} = 35.4 \,^\circ\text{C}
\][/tex]
4. Calculate the Heat Energy: Substitute the values into the formula to find [tex]\( Q \)[/tex]:
[tex]\[
Q = 448 \, \text{g} \times 0.000385 \, \text{kJ/(g°C)} \times 35.4 \,^\circ\text{C}
\][/tex]
5. Calculate the Result:
The amount of heat energy is:
[tex]\[
Q \approx 6.1058 \text{ kJ}
\][/tex]
Therefore, approximately 6.106 kilojoules of heat energy are required to raise the temperature of 448 g of copper from 38.2 °C to 73.6 °C.
1. Understand the Formula: The formula to calculate heat energy is:
[tex]\[
Q = m \cdot c \cdot \Delta T
\][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy (in joules or kilojoules),
- [tex]\( m \)[/tex] is the mass of the substance (in grams),
- [tex]\( c \)[/tex] is the specific heat capacity (in joules per gram per degree Celsius, J/(g°C)),
- [tex]\( \Delta T \)[/tex] is the change in temperature (in degrees Celsius, °C).
2. Convert Specific Heat Capacity: The specific heat capacity of copper is 0.385 J/(g°C). To express this in kilojoules per gram per degree Celsius:
[tex]\[
c = 0.385 \text{ J/(g°C)} = \frac{0.385}{1000} \text{ kJ/(g°C)} = 0.000385 \text{ kJ/(g°C)}
\][/tex]
3. Calculate Temperature Change:
[tex]\[
\Delta T = \text{Final Temperature} - \text{Initial Temperature} = 73.6 \,^\circ\text{C} - 38.2 \,^\circ\text{C} = 35.4 \,^\circ\text{C}
\][/tex]
4. Calculate the Heat Energy: Substitute the values into the formula to find [tex]\( Q \)[/tex]:
[tex]\[
Q = 448 \, \text{g} \times 0.000385 \, \text{kJ/(g°C)} \times 35.4 \,^\circ\text{C}
\][/tex]
5. Calculate the Result:
The amount of heat energy is:
[tex]\[
Q \approx 6.1058 \text{ kJ}
\][/tex]
Therefore, approximately 6.106 kilojoules of heat energy are required to raise the temperature of 448 g of copper from 38.2 °C to 73.6 °C.
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