Final answer:
To heat 500 kg of water from 20.0°C to 50.0°C, approximately 1,736 grams of coke are needed, calculated using the specific heat capacity of water and the heat of combustion of coke.
Step-by-step explanation:
To calculate the amount of coke (C) needed to heat 500 kg of water from 20.0°C to 50.0°C, we first need to use the specific heat capacity of water and the given temperature change to find the required energy. The specific heat capacity of water is approximately 4,184 J/kg/°C. We apply the formula Q = mcΔT, where Q is heat energy, m is mass, c is specific heat capacity, and ΔT is the temperature change.
Q = (500,000 g) * (4,184 J/kg/°C) * (50.0°C - 20.0°C)
Q = (500,000 g) * (4,184 J/kg/°C) * (30.0°C)
Q = 62,760,000 J or 62,760 kJ
After finding the heat required in kJ, we convert it to grams of coke using the heat of combustion of coke, which is 36.15 kJ/g.
Amount of coke = Q / Heat of combustion
Amount of coke = 62,760 kJ / 36.15 kJ/g
Amount of coke ≈ 1,736 g
Thus, approximately 1,736 grams of coke are required to heat 500 kg of water from 20.0°C to 50.0°C.