Final answer:
To find the mass of iron that would need 1380 cal of energy to raise its temperature by 17.4°C, we convert calories to joules and use the formula q = mcΔT. After converting to joules and rearranging the formula to solve for m, we find that 720 grams of iron are required.
Step-by-step explanation:
To calculate the mass of iron needed to absorb 1380 cal of energy to raise its temperature by 17.4°C, we need to use the formula q = mcΔT, where q is the heat in calories, m is the mass in grams, c is the specific heat capacity (0.45 J/g°C for iron, which is equivalent to 0.10752 cal/g°C), and ΔT is the change in temperature.
First, we convert 1380 cal to joules because the specific heat is given in J/g°C. One calorie is equal to 4.184 joules, so:
1380 cal * 4.184 J/cal = 5773.92 J
Now we use the formula, substituting the provided values:
5773.92 J = m * 0.45 J/g°C * 17.4°C
Solving for m gives:
m = 5773.92 J / (0.45 J/g°C * 17.4°C) = 720 g
Therefore, the mass of iron required to absorb this amount of energy is 720 grams.