Answer:
Q = mcΔT
Where:
Q is the heat energy transferred
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
First, let's calculate the heat energy required to raise the temperature of the water:
Q = mcΔT
m = 150 kg (since 1 liter of water is approximately equal to 1 kg)
c = 4186 J/kg°C (specific heat capacity of water)
ΔT = 70°C - 15°C = 55°C
Q = (150 kg) * (4186 J/kg°C) * (55°C)
Q = 346,185,000 J
Now, let's calculate the time using the power of the electric immersion heater:
P = W/t
P = 3000 W (power of the heater)
We can rearrange the formula to solve for time:
t = W/P
t = Q/P
t = (346,185,000 J) / (3000 W)
t ≈ 115,395 seconds