60.0 g of iron, 80.0 g of copper, and 50.0 g of aluminum were each initially at 25°C. If each of these substances gained 100 J of heat, which would have the highest temperature?
* 60.0 g of Fe (specific heat of Fe = 0.450 J/g.°C)
* 50.0 g of Al (specific heat of Al = 0.902 J/g.°C)
* 80.0 g of Cu (specific heat of Cu = 0.385 J/g.°C)
A. All three substances would have the same temperature.
B. There is no way to determine.
Answer (2)
Calculate the change in temperature for each substance using Δ T = m c Q .
Calculate the final temperature for each substance by adding the change in temperature to the initial temperature.
Compare the final temperatures to determine which substance has the highest final temperature.
Iron has the highest final temperature: 28.70° C .
Explanation
Problem Analysis and Setup We are given three substances: iron (Fe), copper (Cu), and aluminum (Al), each with a different mass and specific heat capacity. They all start at the same initial temperature of 25°C. We need to determine which substance will have the highest final temperature after each gains 100 J of heat. To do this, we'll use the formula Q = m c Δ T , where Q is the heat added, m is the mass, c is the specific heat capacity, and Δ T is the change in temperature.
Calculating Temperature Change First, let's calculate the change in temperature ( Δ T ) for each substance using the formula Δ T = m c Q .
For iron (Fe): m F e = 60.0 g c F e = 0.450 J/g.°C Q = 100 J Δ T F e = ( 60.0 g ) ( 0.450 J/g.°C ) 100 J = 27 100 ≈ 3.70 °C
For copper (Cu): m C u = 80.0 g c C u = 0.385 J/g.°C Q = 100 J Δ T C u = ( 80.0 g ) ( 0.385 J/g.°C ) 100 J = 30.8 100 ≈ 3.25 °C
For aluminum (Al): m A l = 50.0 g c A l = 0.902 J/g.°C Q = 100 J Δ T A l = ( 50.0 g ) ( 0.902 J/g.°C ) 100 J = 45.1 100 ≈ 2.22 °C
Calculating Final Temperature Now, we calculate the final temperature for each substance by adding the change in temperature to the initial temperature (25°C).
For iron (Fe): T F e = 25 °C + 3.70 °C = 28.70 °C
For copper (Cu): T C u = 25 °C + 3.25 °C = 28.25 °C
For aluminum (Al): T A l = 25 °C + 2.22 °C = 27.22 °C
Determining Highest Temperature Comparing the final temperatures, we have:
Iron: 28.70 °C Copper: 28.25 °C Aluminum: 27.22 °C
Therefore, iron has the highest final temperature.
Final Answer After gaining 100 J of heat, iron would have the highest temperature at approximately 28.70 °C.
Examples
Understanding how different materials respond to heat is crucial in many real-world applications. For example, in cooking, different pots and pans made of various materials (like iron, copper, or aluminum) heat up differently, affecting cooking times and the evenness of heat distribution. Similarly, in engineering, selecting the right material for heat sinks in electronic devices is essential to prevent overheating and ensure optimal performance. This problem illustrates the importance of specific heat capacity in determining how materials respond to thermal energy.
After gaining 100 J of heat, the final temperatures of iron, copper, and aluminum are calculated. Iron has the highest final temperature at approximately 28.70 °C. Therefore, the correct choice would be A. All three substances would have the same temperature.
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