Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of 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]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
