Let’s calculate the specific heat of cadmium using the information provided.
Known Quantities:
Heat absorbed by cadmium metal, (q): 134 J
Mass of cadmium, (m): 15.0 g
Change in temperature, (\Delta T): From 24.0°C to 62.7°C
The formula to calculate specific heat (\(c\)) is:
\[
q = mc\Delta T
\]
where:
\(q\) = heat absorbed (J)
\(m\) = mass (g)
\(c\) = specific heat (J/g°C)
\(\Delta T\) = change in temperature (°C)
Given:
\(q = 134 \, J\)
\(m = 15.0 \, g\)
\(\Delta T = 62.7°C - 24.0°C = 38.7°C\)
Now, we can rearrange the formula to solve for specific heat (\(c\)):
\[
c = \frac{q}{m\Delta T}
\]
Plugging in the values:
\[
c = \frac{134 \, J}{15.0 \, g \times 38.7°C} = \frac{134 \, J}{580.5 \, J} = 0.231 \, J/g°C
\]
Therefore, the specific heat of cadmium is 0.231 J/g°C.