Expand your horizons with the diverse and informative answers found on IDNLearn.com. Get comprehensive answers to all your questions from our network of experienced experts.
Sagot :
To compute the specific heat values for Copper (Cu), Iron (Fe), and Lead (Pb), we need to use the following given equation for each metal:
[tex]\[ c_{\text{metal}} = \frac{-c_{\text{water}} m_{\text{water}} \Delta T_{\text{water}}}{m_{\text{metal}} \Delta T_{\text{metal}}} \][/tex]
Given:
- The specific heat of water, [tex]\( c_{\text{water}} = 4.184 \text{ J/g} ^{\circ} \text{C} \)[/tex]
Let's calculate the specific heat values for each metal step-by-step.
### Copper (Cu):
1. Mass of water ([tex]\(m_{\text{water}}\)[/tex]): 40.13 g
2. Mass of metal ([tex]\(m_{\text{metal}}\)[/tex]): 12.14 g
3. Change in temperature of water ([tex]\(\Delta T_{\text{water}}\)[/tex]): 1.9 [tex]\(^{\circ}\)[/tex]C
4. Change in temperature of metal ([tex]\(\Delta T_{\text{metal}}\)[/tex]): -75.4 [tex]\(^{\circ}\)[/tex]C
Substitute these values into the equation:
[tex]\[ c_{\text{Cu}} = \frac{-4.184 \times 40.13 \times 1.9}{12.14 \times -75.4} \][/tex]
#### Simplification (performed by calculator):
[tex]\[ c_{\text{Cu}} \approx 0.35 \text{ J/g} ^{\circ} \text{C} \][/tex]
### Iron (Fe):
1. Mass of water ([tex]\(m_{\text{water}}\)[/tex]): 40.24 g
2. Mass of metal ([tex]\(m_{\text{metal}}\)[/tex]): 12.31 g
3. Change in temperature of water ([tex]\(\Delta T_{\text{water}}\)[/tex]): 2.4 [tex]\(^{\circ}\)[/tex]C
4. Change in temperature of metal ([tex]\(\Delta T_{\text{metal}}\)[/tex]): -75.1 [tex]\(^{\circ}\)[/tex]C
Substitute these values into the equation:
[tex]\[ c_{\text{Fe}} = \frac{-4.184 \times 40.24 \times 2.4}{12.31 \times -75.1} \][/tex]
#### Simplification (performed by calculator):
[tex]\[ c_{\text{Fe}} \approx 0.44 \text{ J/g} ^{\circ} \text{C} \][/tex]
### Lead (Pb):
1. Mass of water ([tex]\(m_{\text{water}}\)[/tex]): 39.65 g
2. Mass of metal ([tex]\(m_{\text{metal}}\)[/tex]): 12.46 g
3. Change in temperature of water ([tex]\(\Delta T_{\text{water}}\)[/tex]): 0.7 [tex]\(^{\circ}\)[/tex]C
4. Change in temperature of metal ([tex]\(\Delta T_{\text{metal}}\)[/tex]): -76.7 [tex]\(^{\circ}\)[/tex]C
Substitute these values into the equation:
[tex]\[ c_{\text{Pb}} = \frac{-4.184 \times 39.65 \times 0.7}{12.46 \times -76.7} \][/tex]
#### Simplification (performed by calculator):
[tex]\[ c_{\text{Pb}} \approx 0.12 \text{ J/g} ^{\circ} \text{C} \][/tex]
Therefore, the specific heat values are:
- Copper ([tex]\(Cu\)[/tex]): [tex]\( 0.35 \text{ J/g} ^{\circ} \text{C} \)[/tex]
- Iron ([tex]\(Fe\)[/tex]): [tex]\( 0.44 \text{ J/g} ^{\circ} \text{C} \)[/tex]
- Lead ([tex]\(Pb\)[/tex]): [tex]\( 0.12 \text{ J/g} ^{\circ} \text{C} \)[/tex]
[tex]\[ c_{\text{metal}} = \frac{-c_{\text{water}} m_{\text{water}} \Delta T_{\text{water}}}{m_{\text{metal}} \Delta T_{\text{metal}}} \][/tex]
Given:
- The specific heat of water, [tex]\( c_{\text{water}} = 4.184 \text{ J/g} ^{\circ} \text{C} \)[/tex]
Let's calculate the specific heat values for each metal step-by-step.
### Copper (Cu):
1. Mass of water ([tex]\(m_{\text{water}}\)[/tex]): 40.13 g
2. Mass of metal ([tex]\(m_{\text{metal}}\)[/tex]): 12.14 g
3. Change in temperature of water ([tex]\(\Delta T_{\text{water}}\)[/tex]): 1.9 [tex]\(^{\circ}\)[/tex]C
4. Change in temperature of metal ([tex]\(\Delta T_{\text{metal}}\)[/tex]): -75.4 [tex]\(^{\circ}\)[/tex]C
Substitute these values into the equation:
[tex]\[ c_{\text{Cu}} = \frac{-4.184 \times 40.13 \times 1.9}{12.14 \times -75.4} \][/tex]
#### Simplification (performed by calculator):
[tex]\[ c_{\text{Cu}} \approx 0.35 \text{ J/g} ^{\circ} \text{C} \][/tex]
### Iron (Fe):
1. Mass of water ([tex]\(m_{\text{water}}\)[/tex]): 40.24 g
2. Mass of metal ([tex]\(m_{\text{metal}}\)[/tex]): 12.31 g
3. Change in temperature of water ([tex]\(\Delta T_{\text{water}}\)[/tex]): 2.4 [tex]\(^{\circ}\)[/tex]C
4. Change in temperature of metal ([tex]\(\Delta T_{\text{metal}}\)[/tex]): -75.1 [tex]\(^{\circ}\)[/tex]C
Substitute these values into the equation:
[tex]\[ c_{\text{Fe}} = \frac{-4.184 \times 40.24 \times 2.4}{12.31 \times -75.1} \][/tex]
#### Simplification (performed by calculator):
[tex]\[ c_{\text{Fe}} \approx 0.44 \text{ J/g} ^{\circ} \text{C} \][/tex]
### Lead (Pb):
1. Mass of water ([tex]\(m_{\text{water}}\)[/tex]): 39.65 g
2. Mass of metal ([tex]\(m_{\text{metal}}\)[/tex]): 12.46 g
3. Change in temperature of water ([tex]\(\Delta T_{\text{water}}\)[/tex]): 0.7 [tex]\(^{\circ}\)[/tex]C
4. Change in temperature of metal ([tex]\(\Delta T_{\text{metal}}\)[/tex]): -76.7 [tex]\(^{\circ}\)[/tex]C
Substitute these values into the equation:
[tex]\[ c_{\text{Pb}} = \frac{-4.184 \times 39.65 \times 0.7}{12.46 \times -76.7} \][/tex]
#### Simplification (performed by calculator):
[tex]\[ c_{\text{Pb}} \approx 0.12 \text{ J/g} ^{\circ} \text{C} \][/tex]
Therefore, the specific heat values are:
- Copper ([tex]\(Cu\)[/tex]): [tex]\( 0.35 \text{ J/g} ^{\circ} \text{C} \)[/tex]
- Iron ([tex]\(Fe\)[/tex]): [tex]\( 0.44 \text{ J/g} ^{\circ} \text{C} \)[/tex]
- Lead ([tex]\(Pb\)[/tex]): [tex]\( 0.12 \text{ J/g} ^{\circ} \text{C} \)[/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.
