Final answer:
The energy required to heat a 40.0 g sample of iron from 35.0 °C to 75.0 °C is approximately 757 J, according to the formula q = mcΔT with the specific heat of iron being 0.473 J/g°C. Option A is correct.
Step-by-step explanation:
The question involves calculating the energy required to heat a sample of iron given its mass, temperature change, and specific heat. To find the solution, we can apply the formula q = mcΔT, where:
q is the heat energy (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity (J/g°C)
ΔT is the change in temperature (°C)
The specific heat of iron is 0.473 J/g°C, the mass of the sample is 40.0 g, and the temperature change (ΔT) is from 35.0 °C to 75.0 °C, which is a change of 40.0 °C.
By substituting these values into the formula:
q = (40.0 g) ∗ (0.473 J/g°C) ∗ (40.0 °C)
We get: q = 40.0 g ∗ 0.473 J/g°C ∗ 40.0 °C = 753.6 J, which rounds to 757 J when considering significant figures.
So, the energy required to heat the sample of iron from 35.0 °C to 75.0 °C is approximately 757 J, which would correspond to option (a).