To determine the mass of the iron, we can use the formula for heat transfer:
\[ Q = m \cdot c \cdot \Delta T \]
Where:
- \( Q \) is the heat energy added,
- \( m \) is the mass of the iron,
- \( c \) is the specific heat capacity (0.450 J/g*K),
- \( \Delta T \) is the change in temperature.
Given:
- Initial temperature \( T_i = 27.2 , \text{C} \)
- Final temperature \( T_f = 31.4 , \text{C} \)
- \( \Delta T = T_f - T_i = 31.4 - 27.2 = 4.2 , \text{C} \)
Since the specific heat is provided, we can express the formula as follows to solve for mass (\( m \)):
\[ Q = m \cdot 0.450 \cdot 4.2 \]
We don't know the value of \( Q \), but to get an answer based purely on the options provided, we can estimate the mass for a reasonable assumption of \( Q \).
Now, let's assume \( Q = 1 , \text{J (just for calculation's sake)} \):
Using the formula: \[ 1 = m \cdot 0.450 \cdot 4.2 \] \[ m = \frac{1}{0.450 \cdot 4.2} \] \[ m \approx \frac{1}{1.89} \] \[ m \approx 0.528 , \text{g} \]
None of the provided answers fit this estimation, but we can check the options against possible values.
If we examine the available options:
- a. 343 g
- b. 0.0029 g
- c. 286 g
- d. \( 1.65 \times 10^{-4} , \text{g} \)
The only mass that seems likely to be sensible (assuming \( Q \) could be larger) is option a (343 g), as it's the only value that is realistically high for the given temperature change in a piece of iron.
Based on these interpretations, I would select a. 343 g as the answer.