A small electric immersion heater is used to boil 136 g o water for a cup of instant coffee. The heater is labelled 220 watts. Calculate the time required to bring this water from 23.5ºC to the boiling point, ignoring any heat losses.

To solve this problem, we will use the formula for heat energy:

Q = mcΔT

where:
Q = heat energy (Joules)
m = mass of water (grams)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = temperature change (final temperature - initial temperature)

Given:
m = 136 g
c = 4.18 J/g°C
Initial temperature = 23.5°C
Final temperature = 100°C (boiling point of water)
Power of heater = 220 W (1 W = 1 J/s)

Step 1: Calculate the required heat energy (Q)
ΔT = 100 - 23.5 = 76.5°C

Q = (136 g) × (4.18 J/g°C) × (76.5°C)
Q = 43491.72 J

Step 2: Calculate time required using power equation

Power = Energy / Time
Time = Energy / Power

Time = 43491.72 J / 220 J/s
Time ≈ 197.7 seconds

Final Answer: The time required to bring the water to a boil is approximately 198 seconds (or about 3 minutes and 18 seconds).