Final answer:
Using the specific heat capacity formula, the heat required to increase the temperature of 4.11 kg of water from 18.96°C to 34.40°C is calculated as 266.436 kJ, which is 2.66436 × 10³ kJ in scientific notation.
Step-by-step explanation:
To calculate the amount of heat Q required to heat water from one temperature to another, we use the formula Q = m × c × ΔT, where m is the mass of the water in grams, c is the specific heat capacity of water, and ΔT is the change in temperature. Given the specific heat capacity of water as 4.184 J/g°C, the mass of the water as 4.11 kg, and the temperature change from 18.96°C to 34.40°C, we can calculate the required heat in joules and then convert to kilojoules.
First, we convert the mass from kilograms to grams: 4.11 kg × 1000 g/kg = 4110 g. Now, calculate the temperature change: 34.40°C - 18.96°C = 15.44°C. Then, we calculate the heat in joules: Q = 4110 g × 4.184 J/g°C × 15.44°C which equals 266435.584 J. Finally, we convert joules to kilojoules by dividing by 1000, resulting in Q = 266.436 kJ, which is 2.66436 × 10³ kJ in scientific notation.