Answer :
Alright, let's dive into the solution step by step to understand how the specific heat capacities of different substances compare with that of water.
### 1. Understanding Specific Heat
Specific heat capacity ([tex]\(C_p\)[/tex]) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C. A higher specific heat means that the substance can absorb or release more heat without changing temperature significantly.
Given:
- Specific heat of Iron ([tex]\(C_p\)[/tex]): [tex]\(0.461 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Sodium ([tex]\(C_p\)[/tex]): [tex]\(1.21 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Lithium ([tex]\(C_p\)[/tex]): [tex]\(3.56 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Copper ([tex]\(C_p\)[/tex]): [tex]\(0.377 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Water ([tex]\(C_p\)[/tex]): [tex]\(4.18 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
### 2. Comparisons with Water
To understand how water's specific heat compares to these metals, we will calculate the ratio of the specific heat of water to each metal:
- Iron:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(iron)}} = \frac{4.18}{0.461} \approx 9.067 \][/tex]
Water can absorb approximately 9.067 times more heat per gram per degree Celsius than iron.
- Sodium:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(sodium)}} = \frac{4.18}{1.21} \approx 3.455 \][/tex]
Water can absorb approximately 3.455 times more heat per gram per degree Celsius than sodium.
- Lithium:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(lithium)}} = \frac{4.18}{3.56} \approx 1.174 \][/tex]
Water can absorb approximately 1.174 times more heat per gram per degree Celsius than lithium.
- Copper:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(copper)}} = \frac{4.18}{0.377} \approx 11.088 \][/tex]
Water can absorb approximately 11.088 times more heat per gram per degree Celsius than copper.
### 3. Explanation of Holding Copper Wire
Now, let's explain why we were able to hold copper wire that had just been taken out of boiling water:
Water has a specific heat capacity ([tex]\(C_p = 4.18 \, \text{J/g} \, ^\circ \text{C}\)[/tex]) that is much higher than that of copper ([tex]\(C_p = 0.377 \, \text{J/g} \, ^\circ \text{C}\)[/tex]). This means that water can absorb or release more heat per gram per degree Celsius compared to copper. When copper is heated and then cooled, it releases less heat energy compared to water for the same temperature change. Therefore, when you hold a piece of copper wire that has just been taken out of boiling water, it feels hot, but not as severely hot as it would feel if it had the same specific heat as water.
### 4. Which Metal Causes a More Severe Burn?
If equal masses of two metals are heated to 100°C, the metal with the lower specific heat capacity will cause a more severe burn. This is because a lower specific heat means the metal retains more energy for a given decrease in temperature.
- For example, copper ([tex]\(C_p = 0.377 \, \text{J/g} \, ^\circ \text{C}\)[/tex]) will cause a more severe burn than any other metal mentioned (Iron, Sodium, Lithium) for the same mass and temperature change.
This is due to the fact that the lower the specific heat, the less heat energy is required to raise the temperature of the metal, and hence, it can reach a higher temperature quicker, transferring more heat to your skin and causing a more severe burn.
In summary, copper is more dangerous in this context because it transfers heat more effectively due to its low specific heat capacity.
### 1. Understanding Specific Heat
Specific heat capacity ([tex]\(C_p\)[/tex]) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C. A higher specific heat means that the substance can absorb or release more heat without changing temperature significantly.
Given:
- Specific heat of Iron ([tex]\(C_p\)[/tex]): [tex]\(0.461 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Sodium ([tex]\(C_p\)[/tex]): [tex]\(1.21 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Lithium ([tex]\(C_p\)[/tex]): [tex]\(3.56 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Copper ([tex]\(C_p\)[/tex]): [tex]\(0.377 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
- Specific heat of Water ([tex]\(C_p\)[/tex]): [tex]\(4.18 \, \text{J/g} \, ^\circ \text{C}\)[/tex]
### 2. Comparisons with Water
To understand how water's specific heat compares to these metals, we will calculate the ratio of the specific heat of water to each metal:
- Iron:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(iron)}} = \frac{4.18}{0.461} \approx 9.067 \][/tex]
Water can absorb approximately 9.067 times more heat per gram per degree Celsius than iron.
- Sodium:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(sodium)}} = \frac{4.18}{1.21} \approx 3.455 \][/tex]
Water can absorb approximately 3.455 times more heat per gram per degree Celsius than sodium.
- Lithium:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(lithium)}} = \frac{4.18}{3.56} \approx 1.174 \][/tex]
Water can absorb approximately 1.174 times more heat per gram per degree Celsius than lithium.
- Copper:
[tex]\[ \frac{C_p \text{(water)}}{C_p \text{(copper)}} = \frac{4.18}{0.377} \approx 11.088 \][/tex]
Water can absorb approximately 11.088 times more heat per gram per degree Celsius than copper.
### 3. Explanation of Holding Copper Wire
Now, let's explain why we were able to hold copper wire that had just been taken out of boiling water:
Water has a specific heat capacity ([tex]\(C_p = 4.18 \, \text{J/g} \, ^\circ \text{C}\)[/tex]) that is much higher than that of copper ([tex]\(C_p = 0.377 \, \text{J/g} \, ^\circ \text{C}\)[/tex]). This means that water can absorb or release more heat per gram per degree Celsius compared to copper. When copper is heated and then cooled, it releases less heat energy compared to water for the same temperature change. Therefore, when you hold a piece of copper wire that has just been taken out of boiling water, it feels hot, but not as severely hot as it would feel if it had the same specific heat as water.
### 4. Which Metal Causes a More Severe Burn?
If equal masses of two metals are heated to 100°C, the metal with the lower specific heat capacity will cause a more severe burn. This is because a lower specific heat means the metal retains more energy for a given decrease in temperature.
- For example, copper ([tex]\(C_p = 0.377 \, \text{J/g} \, ^\circ \text{C}\)[/tex]) will cause a more severe burn than any other metal mentioned (Iron, Sodium, Lithium) for the same mass and temperature change.
This is due to the fact that the lower the specific heat, the less heat energy is required to raise the temperature of the metal, and hence, it can reach a higher temperature quicker, transferring more heat to your skin and causing a more severe burn.
In summary, copper is more dangerous in this context because it transfers heat more effectively due to its low specific heat capacity.
