Answer :
To determine how much heat is needed to raise the temperature of the copper rod, we use the formula for calculating heat:
[tex]\[ Q = m \times c \times \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy (in joules),
- [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),
- [tex]\( \Delta T \)[/tex] is the change in temperature (in degrees Celsius).
Let's go step-by-step through this problem:
1. Identify the Given Values:
- Mass, [tex]\( m = 5.05 \)[/tex] grams
- Initial Temperature, [tex]\( T_{\text{initial}} = 27.6^\circ C \)[/tex]
- Final Temperature, [tex]\( T_{\text{final}} = 46.6^\circ C \)[/tex]
- Specific Heat of Iron, [tex]\( c = 0.385 \, \text{J/g°C} \)[/tex]
2. Calculate the Change in Temperature, [tex]\(\Delta T\)[/tex]:
- [tex]\(\Delta T = T_{\text{final}} - T_{\text{initial}}\)[/tex]
- [tex]\(\Delta T = 46.6^\circ C - 27.6^\circ C = 19.0^\circ C\)[/tex]
3. Calculate the Amount of Heat Needed, [tex]\( Q \)[/tex]:
- Use the formula [tex]\( Q = m \times c \times \Delta T \)[/tex]
- [tex]\( Q = 5.05 \, \text{g} \times 0.385 \, \text{J/g°C} \times 19.0^\circ C \)[/tex]
- [tex]\( Q = 36.94075 \, \text{J} \)[/tex]
4. Convert Joules to Kilojoules:
- Since 1 kilojoule (kJ) = 1000 joules (J), divide the result by 1000 to convert to kilojoules.
- [tex]\( Q = 36.94075 \, \text{J} \div 1000 = 0.03694075 \, \text{kJ} \)[/tex]
So, the amount of heat needed is approximately [tex]\( 0.0369 \, \text{kJ} \)[/tex].
This corresponds to option c. 0.0369 kJ.
[tex]\[ Q = m \times c \times \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy (in joules),
- [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),
- [tex]\( \Delta T \)[/tex] is the change in temperature (in degrees Celsius).
Let's go step-by-step through this problem:
1. Identify the Given Values:
- Mass, [tex]\( m = 5.05 \)[/tex] grams
- Initial Temperature, [tex]\( T_{\text{initial}} = 27.6^\circ C \)[/tex]
- Final Temperature, [tex]\( T_{\text{final}} = 46.6^\circ C \)[/tex]
- Specific Heat of Iron, [tex]\( c = 0.385 \, \text{J/g°C} \)[/tex]
2. Calculate the Change in Temperature, [tex]\(\Delta T\)[/tex]:
- [tex]\(\Delta T = T_{\text{final}} - T_{\text{initial}}\)[/tex]
- [tex]\(\Delta T = 46.6^\circ C - 27.6^\circ C = 19.0^\circ C\)[/tex]
3. Calculate the Amount of Heat Needed, [tex]\( Q \)[/tex]:
- Use the formula [tex]\( Q = m \times c \times \Delta T \)[/tex]
- [tex]\( Q = 5.05 \, \text{g} \times 0.385 \, \text{J/g°C} \times 19.0^\circ C \)[/tex]
- [tex]\( Q = 36.94075 \, \text{J} \)[/tex]
4. Convert Joules to Kilojoules:
- Since 1 kilojoule (kJ) = 1000 joules (J), divide the result by 1000 to convert to kilojoules.
- [tex]\( Q = 36.94075 \, \text{J} \div 1000 = 0.03694075 \, \text{kJ} \)[/tex]
So, the amount of heat needed is approximately [tex]\( 0.0369 \, \text{kJ} \)[/tex].
This corresponds to option c. 0.0369 kJ.