Final answer:
The mass of the copper sample that requires 1000 J of energy to be heated from 15 °C to 40 °C, with a specific heat of 0.40 J/g °C, is calculated to be 100 grams using the formula q = mcΔT.
Step-by-step explanation:
The question requires the calculation of the mass of a copper sample based on the amount of energy needed to change its temperature. To find the mass, we use the formula q = mcΔT, where q is the energy in joules, m is the mass of the sample in grams, c is the specific heat capacity (0.40 J/g °C for copper), and ΔT is the temperature change in degrees Celsius (40 °C - 15 °C = 25 °C).
Rearranging the formula to solve for mass gives m = q / (cΔT). Plugging in the values results in m = 1000 J / (0.40 J/g °C × 25 °C) = 1000 J / 10 J/g = 100 grams. Therefore, the mass of the copper sample is 100 grams.