Question

If a 4.0 gram sample of iron metal absorbs 127.8 J of heat, causing its temperature to rise from 25°C to 97°C, what is the specific heat of iron?

(1 point)
Responses

0.0044 J/g°C
0.0044 J/g°C

0.044 J/g°C
0.044 J/g°C

0.444 J/g°C
0.444 J/g°C

4.4 J/g°C

Answer 1

To calculate the specific heat of iron, we can use the formula for heat absorbed or released:

\[ q = m \cdot c \cdot \Delta T \]

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)

Given:
- \( q = 127.8 \, \text{J} \)
- \( m = 4.0 \, \text{g} \)
- Initial temperature \( T_i = 25 \, \text{°C} \)
- Final temperature \( T_f = 97 \, \text{°C} \)

First, calculate the change in temperature (\( \Delta T \)):

\[
\Delta T = T_f - T_i = 97 \, \text{°C} - 25 \, \text{°C} = 72 \, \text{°C}
\]

Now, we can rearrange the formula to solve for the specific heat capacity \( c \):

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

Substituting the known values:

\[
c = \frac{127.8 \, \text{J}}{4.0 \, \text{g} \cdot 72 \, \text{°C}} = \frac{127.8}{288} \approx 0.444 \, \text{J/g°C}
\]

Thus, the specific heat of iron is approximately:

**0.444 J/g°C**

So the correct response is:

**0.444 J/g°C**