An electric immersion heater rated at 1.5\,\text{kW} is operated on a 240\,\text{V} mains … — JAMB UTME

An electric immersion heater rated at $1.5\,\text{kW}$ is operated on a $240\,\text{V}$ mains supply for $14\,\text{minutes}$ . Calculate the total electrical energy consumed by the heater during this period, in megajoules ( $\text{MJ}$ ).

Answer: 1.26 MJ

Answer

The total electrical energy consumed by the heater is

1.26\,\text{MJ}

Electrical energy consumed is obtained by multiplying electrical power by time (

E = P \times t

). Converting power to watts (

1.5\,\text{kW} = 1500\,\text{W}

) and time to seconds (

14\,\text{min} = 840\,\text{s}

) yields

E = 1500 \times 840 = 1,260,000\,\text{J} = 1.26\,\text{MJ}

Step-by-Step Solution

Convert power rating from kilowatts to watts

P = 1.5\,\text{kW} = 1500\,\text{W}

The standard SI unit of power for energy calculation in Joules is Watts.

Convert time duration from minutes to seconds

t = 14\,\text{minutes} \times 60\,\text{seconds/minute} = 840\,\text{seconds}

The standard SI unit of time in Joule calculations is seconds.

Calculate energy consumed in Joules using

E = P \times t

E = 1500\,\text{W} \times 840\,\text{s} = 1,260,000\,\text{J}

Electrical energy is the product of power in watts and time in seconds.

Convert energy from Joules to Megajoules

E = \frac{1,260,000}{10^6} = 1.26\,\text{MJ}

One Megajoule (

1\,\text{MJ}

) is equivalent to

10^6\,\text{Joules}

Key Concept

Electrical Energy Consumption

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