Answered

Discover a world of knowledge and get your questions answered at IDNLearn.com. Whether it's a simple query or a complex problem, our community has the answers you need.

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

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

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

A. [tex]$\text{Al, Fe, Zn, Ag}$[/tex]
B. [tex]$\text{Ag, Zn, Fe, Al}$[/tex]
C. [tex]$\text{Al, Fe, Ag, Zn}$[/tex]
D. [tex]$\text{Ag, Al, Zn, Fe}$[/tex]

Sagot :

GinnyAnsweridn
To determine the order in which the samples reach [tex]\( 90.0^{\circ} \text{C} \)[/tex], we need to calculate the amount of heat required for each sample to go from room temperature (assumed to be [tex]\( 25.0^{\circ} \text{C} \)[/tex]) to [tex]\( 90.0^{\circ} \text{C} \)[/tex]. The heat required ([tex]\( q \)[/tex]) can be found using the formula:

[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]

where:
- [tex]\( m \)[/tex] is the mass of the sample.
- [tex]\( C_p \)[/tex] is the specific heat capacity.
- [tex]\( \Delta T \)[/tex] is the change in temperature.

Let's calculate [tex]\( \Delta T \)[/tex] first:
[tex]\[ \Delta T = 90.0^{\circ} \text{C} - 25.0^{\circ} \text{C} = 65.0^{\circ} \text{C} \][/tex]

Given data:
- Mass of each sample, [tex]\( m = 10 \, \text{g} \)[/tex]
- Specific heat capacities ([tex]\( C_p \)[/tex]):
- Aluminum (Al): [tex]\( 0.897 \, \text{J/(g°C)} \)[/tex]
- Silver (Ag): [tex]\( 0.234 \, \text{J/(g°C)} \)[/tex]
- Iron (Fe): [tex]\( 0.450 \, \text{J/(g°C)} \)[/tex]
- Zinc (Zn): [tex]\( 0.387 \, \text{J/(g°C)} \)[/tex]

Now we will calculate the heat required for each sample:

1. For Aluminum (Al):
[tex]\[ q_{\text{Al}} = 10 \, \text{g} \times 0.897 \, \text{J/(g°C)} \times 65.0^{\circ} \text{C} = 583.05 \, \text{J} \][/tex]

2. For Silver (Ag):
[tex]\[ q_{\text{Ag}} = 10 \, \text{g} \times 0.234 \, \text{J/(g°C)} \times 65.0^{\circ} \text{C} = 152.10 \, \text{J} \][/tex]

3. For Iron (Fe):
[tex]\[ q_{\text{Fe}} = 10 \, \text{g} \times 0.450 \, \text{J/(g°C)} \times 65.0^{\circ} \text{C} = 292.50 \, \text{J} \][/tex]

4. For Zinc (Zn):
[tex]\[ q_{\text{Zn}} = 10 \, \text{g} \times 0.387 \, \text{J/(g°C)} \times 65.0^{\circ} \text{C} = 251.55 \, \text{J} \][/tex]

Now we have the following heat requirements:
- [tex]\( q_{\text{Al}} = 583.05 \, \text{J} \)[/tex]
- [tex]\( q_{\text{Ag}} = 152.10 \, \text{J} \)[/tex]
- [tex]\( q_{\text{Fe}} = 292.50 \, \text{J} \)[/tex]
- [tex]\( q_{\text{Zn}} = 251.55 \, \text{J} \)[/tex]

To determine the order in which the samples will reach [tex]\( 90.0^{\circ} \text{C} \)[/tex], we order the samples by increasing heat required:
1. Silver (Ag): [tex]\( 152.10 \, \text{J} \)[/tex]
2. Zinc (Zn): [tex]\( 251.55 \, \text{J} \)[/tex]
3. Iron (Fe): [tex]\( 292.50 \, \text{J} \)[/tex]
4. Aluminum (Al): [tex]\( 583.05 \, \text{J} \)[/tex]

Thus, the order in which these samples will reach [tex]\( 90.0^{\circ} \text{C} \)[/tex] from first to last is:

[tex]\[ \boxed{\text{Ag , Zn , Fe , Al}} \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.