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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.

Amit Saxena , 10 Years ago
Grade upto college level
anser 1 Answers
Navjyot Kalra

Last Activity: 10 Years ago

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).

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