Final answer:
To find the total heat transfer required, calculate the heat needed to raise both water and the aluminum pot to the boiling point, and then the heat to vaporize 0.750 kg of water. Add all these amounts to get the total energy. Divide this total by the heat transfer rate to determine the time required.
Step-by-step explanation:
To calculate the total heat transfer required to raise the temperature of a 0.750-kg aluminum pot and 2.50 kg of water from 30.0°C to the boiling point, and then to boil away 0.750 kg of water, we take the following steps:
- Calculate the heat needed to raise the temperature of the water to the boiling point using the formula Qw = mw * cw * ΔTw, where Qw is the heat for the water, mw is the mass of the water (2.50 kg), cw is the specific heat capacity of water (4186 J/kg°C), and ΔTw is the temperature change.
- Calculate the heat needed to raise the temperature of the aluminum pot to the boiling point using the formula QAl = mAl * cAl * ΔTAl, where QAl is the heat for the aluminum, mAl is the mass of the aluminum (0.750 kg), cAl is the specific heat capacity of aluminum (900 J/kg°C), and ΔTAl is the temperature change.
- Calculate the heat required to boil away 0.750 kg of water using the formula Qv = mv * Lv, where Qv is the latent heat for vaporization, mv is the mass of the water being boiled away, and Lv is the latent heat of vaporization of water (2257000 J/kg).
- Add the heats from steps 1, 2, and 3 to find the total heat transfer required.
- To determine how long it takes if the rate of heat transfer is 500 W, divide the total heat transfer by 500 W, since 1 W = 1 J/s.
The exact calculations and numbers will yield the total amount of energy needed and the time required, based on the above formulas and the specific heat and latent heat values.