Final answer:
To calculate the mass of water left after evaporation, the energy provided by the kettle is used alongside the latent heat of vaporization. For 10 minutes, the kettle provides 900 kJ of energy, evaporating 400 g of water, leaving 1.6 kg. To fully evaporate 2.0 kg, 4,500 kJ is needed, which takes 50 minutes with the kettle's power output.
Step-by-step explanation:
This problem requires the application of thermodynamics and energy transfer concepts to calculate the mass of water evaporated and the time required for total evaporation. For water to evaporate, it needs to absorb energy, also known as heat of vaporization. The heat required to vaporize water can be calculated using the formula Q = m × Lv, where m is the mass of water and Lv is the latent heat of vaporization. The power of the kettle indicates the rate at which energy is provided to the water.
To calculate (i) the mass of water left after 10 minutes, one must first find the total energy provided by the kettle in that time: Energy = Power × Time = 1.5 kW × 10 min × 60 sec/min = 900 kJ. Then the mass of the water that can be evaporated with this energy can be calculated using Q = m × Lv. Thus, m = Q / Lv = 900,000 J / 2,250 J/g = 400g. Therefore, the mass of the water left after ten minutes is 2.0 kg - 0.4 kg = 1.6 kg.
(ii) To find out how long it would take to completely evaporate 2.0 kg of water, the calculation is similar. First, find the total energy needed to vaporize 2.0 kg of water: Q = m × Lv = 2,000 g × 2,250 J/g = 4,500,000 J. Then, using the power of the kettle, find out the time required: Time = Q / Power = 4,500,000 J / 1,500 J/s = 3,000 s, which is equivalent to 50 minutes.