To determine which material experiences the largest increase in temperature when the same amount of energy is added, we can use the concept of specific heat capacity. The formula to calculate the temperature increase ([tex]\(\Delta T\)[/tex]) is:
[tex]\[
\Delta T = \frac{Q}{m \cdot c}
\][/tex]
where:
- [tex]\(Q\)[/tex] is the energy added (100 J),
- [tex]\(m\)[/tex] is the mass of the material (10.0 g),
- [tex]\(c\)[/tex] is the specific heat capacity of the material.
Given the specific heats and the mass of the materials, we can calculate the temperature increase for each metal.
Cadmium (Cd):
[tex]\[
\Delta T_{Cd} = \frac{100 \, J}{10 \, g \times 0.231 \, \frac{J}{g \cdot ^\circ C}} = 43.290 \, ^\circ C
\][/tex]
Copper (Cu):
[tex]\[
\Delta T_{Cu} = \frac{100 \, J}{10 \, g \times 0.385 \, \frac{J}{g \cdot ^\circ C}} = 25.974 \, ^\circ C
\][/tex]
Iron (Fe):
[tex]\[
\Delta T_{Fe} = \frac{100 \, J}{10 \, g \times 0.412 \, \frac{J}{g \cdot ^\circ C}} = 24.272 \, ^\circ C
\][/tex]
Silver (Ag):
[tex]\[
\Delta T_{Ag} = \frac{100 \, J}{10 \, g \times 0.233 \, \frac{J}{g \cdot ^\circ C}} = 42.918 \, ^\circ C
\][/tex]
Now that we have the calculated temperature increases:
- Cadmium (Cd): 43.290 [tex]\( ^\circ C \)[/tex]
- Copper (Cu): 25.974 [tex]\( ^\circ C \)[/tex]
- Iron (Fe): 24.272 [tex]\( ^\circ C \)[/tex]
- Silver (Ag): 42.918 [tex]\( ^\circ C \)[/tex]
The material with the largest increase in temperature is cadmium (Cd) with a temperature increase of 43.290 [tex]\( ^\circ C \)[/tex].
Therefore, the correct answer is:
B. cadmium
