Question

A ball of iron with a mass of 252 g was heated using 2263 J of energy. The initial temperature was 547 °C . What was the final temperature of the iron? (The specific heat capacity for iron is 0.449 Jg°C


Responses

567 °C

0.04 °C

− 527 °C

24.8 °C

Answer 1

To find the final temperature of the iron ball after it has been heated, we can use the formula for heat transfer:

\[
q = mc\Delta T
\]

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

The change in temperature \( \Delta T \) can be calculated as follows:

\[
\Delta T = \frac{q}{mc}
\]

Substituting the given values:

- \( q = 2263 \, \text{J} \)
- \( m = 252 \, \text{g} \)
- \( c = 0.449 \, \text{J/g°C} \)

Calculating \( \Delta T \):

\[
\Delta T = \frac{2263 \, \text{J}}{252 \, \text{g} \times 0.449 \, \text{J/g°C}}
\]

Calculating the denominator:

\[
252 \, \text{g} \times 0.449 \, \text{J/g°C} = 113.148 \, \text{J/°C}
\]

Now substituting this back into the equation for \( \Delta T \):

\[
\Delta T = \frac{2263 \, \text{J}}{113.148 \, \text{J/°C}} \approx 20.0 \, °C
\]

Now, since the initial temperature is 547 °C, we can find the final temperature \( T_f \):

\[
T_f = T_i + \Delta T
\]
\[
T_f = 547 \, °C + 20.0 \, °C = 567 \, °C
\]

Thus, the final temperature of the iron is:

\[
\boxed{567 \, °C}
\]