To compare the energy required to bring 1 kg of each material to its melting point, we need to calculate the energy using the formula:
\[ Q = m \cdot c \cdot \Delta T \]
where:
- \( Q \) is the energy in joules,
- \( m \) is the mass (which is 1 kg for our comparison),
- \( c \) is the specific heat of the substance,
- \( \Delta T \) is the change in temperature (final temperature - initial temperature).
Given:
- Room temperature = 293 K
- Melting points:
- Aluminum = 933.5 K
- Copper = 1357.8 K
- Brass = 1173 K
- Silver = 1234.9 K
- Platinum = 2041 K
Let's calculate \( Q \) for each substance:
-
Aluminum: \[ \Delta T = 933.5 K - 293 K = 640.5 K \] \[ Q_{Al} = 1 , \text{kg} \cdot 900 , \text{J kg}^{-1} \text{K}^{-1} \cdot 640.5 K = 576450 , \text{J} \]
-
Copper: \[ \Delta T = 1357.8 K - 293 K = 1064.8 K \] \[ Q_{Cu} = 1 , \text{kg} \cdot 390 , \text{J kg}^{-1} \text{K}^{-1} \cdot 1064.8 K = 415872 , \text{J} \]
-
Brass: \[ \Delta T = 1173 K - 293 K = 880 K \] \[ Q_{Br} = 1 , \text{kg} \cdot 380 , \text{J kg}^{-1} \text{K}^{-1} \cdot 880 K = 334400 , \text{J} \]
-
Silver: \[ \Delta T = 1234.9 K - 293 K = 941.9 K \] \[ Q_{Ag} = 1 , \text{kg} \cdot 230 , \text{J kg}^{-1} \text{K}^{-1} \cdot 941.9 K = 216627 , \text{J} \]
-
Platinum: \[ \Delta T = 2041 K - 293 K = 1748 K \] \[ Q_{Pt} = 1 , \text{kg} \cdot 130 , \text{J kg}^{-1} \text{K}^{-1} \cdot 1748 K = 227264 , \text{J} \]
Now we can summarize the total energy required to reach the melting points:
- Aluminum: 576450 J
- Copper: 415872 J
- Brass: 334400 J
- Silver: 216627 J
- Platinum: 227264 J
Now, we will evaluate the statements based on energy required:
A) Silver requires more energy than copper. (False, Silver < Copper)
B) Brass requires more energy than silver. (True, Brass > Silver)
C) Platinum requires more energy than silver. (True, Platinum > Silver)
D) Platinum requires more energy than copper. (False, Platinum < Copper)
E) Aluminum requires more energy than copper. (True, Aluminum > Copper)
F) Aluminum requires more energy than brass. (True, Aluminum > Brass)
Therefore, the true statements are:
- B: Brass requires more energy than silver.
- C: Platinum requires more energy than silver.
- E: Aluminum requires more energy than copper.
So, the final selections are B, C, and E.
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