To calculate the time required to raise the temperature of water using an electric heater, we can utilize the formula:
Q = mcΔT
where: Q is the heat energy absorbed by the water, m is the mass of the water (200g), c is the specific heat capacity of water (4.18 J/g°C), ΔT is the change in temperature (90°C - 20°C = 70°C).
First, let's calculate the amount of heat energy needed to raise the temperature of the water:
Q = (200g) * (4.18 J/g°C) * (70°C) Q = 586,800 Joules
Now, we can calculate the time required using the formula:
t = Q / P
where: t is the time required, Q is the heat energy needed (586,800 J), P is the power of the electric heater (1000 J/s).
t = (586,800 J) / (1000 J/s) t = 586.8 seconds
Therefore, it would take approximately 586.8 seconds, or 9 minutes and 46.8 seconds, to raise the temperature of 200g of water from 20°C to 90°C using an electric heater with a power output of 1000 joules per second.