Final answer:
To calculate the thermal energy needed to heat 4.0 kg of water from 50°C to 75°C, use the specific heat capacity formula with a value of 4186 J/kg°C for water, resulting in 418,600 J of energy required.
Step-by-step explanation:
To calculate the amount of thermal energy needed to raise the temperature of 4.0 kg of water from 50°C to 75°C, you would use the specific heat capacity formula Q = mCΔT, where 'Q' is the thermal energy, 'm' is the mass of the water, 'C' is the specific heat capacity of water, and 'ΔT' is the change in temperature. Given that the specific heat of water is 4186 J/kg°C, the mass of water is 4.0 kg, and the change in temperature (ΔT) is 75°C - 50°C = 25°C, the thermal energy needed can be calculated as follows:
Q = mCΔT = 4.0 kg × 4186 J/kg°C × 25°C = 418,600 J
The answer, 418,600 J, is the amount of thermal energy required to heat 4.0 kg of water from 50°C to 75°C.