Question

A sample of iron weighing 111.6 g was subjected to heating, experiencing a temperature increase from 0°C to 20°C. The sample absorbed a total of 1004 J of energy during this process. What is the specific heat capacity of iron?
A. 0.00578 J/g°C
B. 4.18 J/g°C
C. 0.45 J/g°C
D. 2.20 J/g°C

Answer 1

To calculate the specific heat capacity (\(c\)) of iron, we can use the formula:

\[
q = mc\Delta T
\]

where:
- \(q\) is the heat absorbed (in joules),
- \(m\) is the mass of the substance (in grams),
- \(c\) is the specific heat capacity (in J/g°C),
- \(\Delta T\) is the change in temperature (in °C).

From the problem:
- \(q = 1004 \, \text{J}\)
- \(m = 111.6 \, \text{g}\)
- \(\Delta T = 20°C - 0°C = 20°C\)

Now we can rearrange the formula to solve for \(c\):

\[
c = \frac{q}{m \Delta T}
\]

Substituting the values into the formula:

\[
c = \frac{1004 \, \text{J}}{111.6 \, \text{g} \times 20 \, \text{°C}}
\]
\[
c = \frac{1004 \, \text{J}}{2232 \, \text{g°C}}
\]
\[
c \approx 0.450 \, \text{J/g°C}
\]

Therefore, the specific heat capacity of iron is approximately \(0.45 \, \text{J/g°C}\), which corresponds to option **C**.