Atticus30idn
Answered

Find accurate and reliable answers to your questions on IDNLearn.com. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.

Loren has samples of the elements listed below at room temperature. He exposes the samples to the same heat source until each sample reaches a temperature of [tex][tex]$90.0^{\circ} C$[/tex][/tex].

[tex]\[
\begin{array}{l}
10 \text{ g of } Al (s) \left( C_{p} = 0.897 \text{ J} / \left( \text{g} \cdot {}^{\circ} \text{C} \right) \right) \\
10 \text{ g of } Ag (s) \left( C_{p} = 0.234 \text{ J} / \left( \text{g} \cdot {}^{\circ} \text{C} \right) \right) \\
10 \text{ g of } Fe (s) \left( C_{p} = 0.450 \text{ J} / \left( \text{g} \cdot {}^{\circ} \text{C} \right) \right) \\
10 \text{ g of } Zn (s) \left( C_{p} = 0.387 \text{ J} / \left( \text{g} \cdot {}^{\circ} \text{C} \right) \right)
\end{array}
\][/tex]

From first to last, which lists the order in which these samples will reach [tex]$90.0^{\circ} C$[/tex]?

A. Ag, Zn, Fe, Al
B. Al, Fe, Zn, Ag
C. Al, Fe, Ag, Zn
D. Ag, Al, Zn, Fe

Sagot :

GinnyAnsweridn
To determine the order in which the elements will reach [tex]\(90.0^\circ \text{C}\)[/tex], we need to calculate the amount of heat required for each sample to reach this temperature from room temperature ([tex]\(25.0^\circ \text{C}\)[/tex]).

Given:
- Mass of each sample: [tex]\(10 \text{g}\)[/tex]
- Initial temperature: [tex]\(25.0^\circ \text{C}\)[/tex]
- Final temperature: [tex]\(90.0^\circ \text{C}\)[/tex]

The specific heats ([tex]\(C_p\)[/tex]) for the elements are:
- Aluminum (Al): [tex]\(0.897 \ \frac{J}{(g \cdot {}^\circ C)}\)[/tex]
- Silver (Ag): [tex]\(0.234 \ \frac{J}{(g \cdot {}^\circ C)}\)[/tex]
- Iron (Fe): [tex]\(0.450 \ \frac{J}{(g \cdot {}^\circ C)}\)[/tex]
- Zinc (Zn): [tex]\(0.387 \ \frac{J}{(g \cdot {}^\circ C)}\)[/tex]

The formula to calculate the heat required ([tex]\(q\)[/tex]) for each sample is:
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
where
- [tex]\(m\)[/tex] is the mass,
- [tex]\(C_p\)[/tex] is the specific heat,
- [tex]\(\Delta T\)[/tex] is the change in temperature ([tex]\(90.0^\circ \text{C} - 25.0^\circ \text{C} = 65.0^\circ \text{C}\)[/tex]).

Let's compute the heat required for each element:

1. For Aluminum:
[tex]\[ q_{\text{Al}} = 10 \text{g} \times 0.897 \ \frac{J}{(g \cdot {}^\circ C)} \times 65.0^\circ \text{C} = 583.050 \ \text{J} \][/tex]

2. For Silver:
[tex]\[ q_{\text{Ag}} = 10 \text{g} \times 0.234 \ \frac{J}{(g \cdot {}^\circ C)} \times 65.0^\circ \text{C} = 152.100 \ \text{J} \][/tex]

3. For Iron:
[tex]\[ q_{\text{Fe}} = 10 \text{g} \times 0.450 \ \frac{J}{(g \cdot {}^\circ C)} \times 65.0^\circ \text{C} = 292.500 \ \text{J} \][/tex]

4. For Zinc:
[tex]\[ q_{\text{Zn}} = 10 \text{g} \times 0.387 \ \frac{J}{(g \cdot {}^\circ C)} \times 65.0^\circ \text{C} = 251.550 \ \text{J} \][/tex]

Now, sort the elements by the amount of heat required in ascending order:
1. [tex]\(152.100 \ \text{J}\)[/tex] (Ag)
2. [tex]\(251.550 \ \text{J}\)[/tex] (Zn)
3. [tex]\(292.500 \ \text{J}\)[/tex] (Fe)
4. [tex]\(583.050 \ \text{J}\)[/tex] (Al)

So, the order in which the elements will reach [tex]\(90.0^\circ \text{C}\)[/tex] from first to last is:
[tex]\[ \text{Ag}, \text{Zn}, \text{Fe}, \text{Al} \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{\text{Ag , Zn , Fe , Al}} \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.