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:
\[ \boxed{567 , °C} \]