Final answer:
It takes 319 kcal to heat 4.0 kg of water from 20°C to its boiling point at 100°C, using the specific heat capacity of water which is 4.184 J/g°C.
Step-by-step explanation:
The energy necessary to heat 4.0 kg of water from room temperature (20°C) to its boiling point is determined by the specific heat capacity of water and the temperature change required. The specific heat of water is 4.184 J/g°C. To calculate the energy in kilocalories (kcal), we first convert the mass of water from kilograms to grams (4.0 kg = 4000 g), then multiply by the temperature change (100°C - 20°C = 80°C), and finally by the specific heat capacity. So the energy required in Joules (J) is 4000 g × 80°C × 4.184 J/g°C = 1,334,400 J. To convert to kcal, using the conversion 1 kcal = 4,184 J, we get 1,334,400 J / 4,184 J/kcal = 319 kcal.