To solve this problem, we need to use the formula for heat transfer:
Q = mcΔT
Where:
Q is the heat transfer (in Joules)
m is the mass of water (in kilograms)
c is the specific heat capacity of water (in J/kg·°C)
ΔT is the change in temperature (in °C)
We can rearrange the formula to solve for time:
t = Q / P
Where:
t is the time (in seconds)
Q is the heat transfer (in Joules)
P is the power of the kettle (in Watts)
Given:
P = 2000 W
m = 2.0 kg
ΔT = (100 - 20) °C = 80 °C (200°C - 20°C)
First, let's calculate the heat transfer:
Q = mcΔT
Q = 2.0 kg * 4186 J/kg·°C * 80 °C
Q = 669,760 J
Now, let's calculate the time:
t = Q / P
t = 669,760 J / 2000 W
t ≈ 334.88 seconds
Therefore, it will take approximately 334.88 seconds for the temperature of the water to rise from 20°C to 100°C.