Final answer:
The specific heat of iron, given the energy used to increase its temperature, is calculated by dividing the energy by the product of the mass and the temperature change. For 1 mol of iron, this results in a specific heat closest to 0.62 J/g°C, which corresponds to option d.
Step-by-step explanation:
To find the specific heat of iron using the given data, we can apply the formula q = mcΔT, where 'q' is the heat energy in joules, 'm' is the mass in grams, 'ΔT' is the change in temperature in degrees Celsius, and 'c' is the specific heat capacity. The mass of iron in this case is 1 mol, which corresponds to its molar mass. Iron has a molar mass of approximately 55.845 g/mol.
The change in temperature (ΔT) is the final temperature minus the initial temperature, which is 1538°C - 1200°C = 338°C. We are given that the energy used (q) is 32,644.524 J. Therefore, we can solve for the specific heat (c) by rearranging the formula: c = q / (mΔT).
First, calculate the mass of 1 mol of iron:
m = 1 mol × 55.845 g/mol = 55.845 g
Then, use the values to compute the specific heat:
c = 32,644.524 J / (55.845 g × 338°C)
Carrying out the calculation:
c = 32,644.524 J / (18,875.43 g°C) = 0.61 J/g°C
The number we calculated (approximately 0.61 J/g°C) doesn’t exactly match any of the options given, but it is closest to option d. 0.62 J/g°C, which we can consider as the correct answer based on the data provided and assuming minimal rounding in the options.