Final answer:
To heat a kilogram of water by 10 degrees Celsius, the amount of energy needed is calculated using the specific heat capacity formula, which yields 41,840 J.
Step-by-step explanation:
The amount of energy needed to increase the temperature of a kilogram of water by 10 degrees Celsius can be calculated using the specific heat capacity formula: energy (Q) = mass (m) × specific heat (c) × temperature change (ΔT). With water's specific heat capacity being 4.184 J/g°C, the mass being 1000 grams (since 1 kg = 1000 g), and the temperature change being 10°C, we can calculate the necessary energy as follows: Q = 1000 g × 4.184 J/g°C × 10°C.
Doing the math, Q = 1000 × 4.184 × 10, which equals 41840 J. Therefore, the correct answer is (b) 41,840 J.