Question

A 1-kW electric resistance heater in a room is turned on and kept on for $50 \mathrm{~min}$. The amount of energy transferred to the room by the heater is (a) \(1 \mathrm{~kJ}\) (b) \(50 \mathrm{~kJ}\) (c) \(3000 \mathrm{~kJ}\) (d) \(3600 \mathrm{~kJ}\) (e) \(6000 \mathrm{~kJ}\)

Short answer

Choose the correct answer. (a) 1 kJ (b) 50 kJ (c) 3000 kJ (d) 3600 kJ (e) 6000 kJ Answer: (c) 3000 kJ

Step-by-step solution

Convert the power rating into watts

The power rating of the heater is given in kilowatts (kW). Let's convert it to watts (W): 1 kW = 1000 W So, the power rating of the heater is 1000 W.

Convert the time into seconds

The time for which the heater is turned on is given in minutes. Let's convert it to seconds: 50 minutes = 50 × 60 = 3000 seconds So, the heater is turned on for 3000 seconds.

Calculate the energy transferred

Now, we will use the energy formula (Energy = Power × Time) to calculate the energy transferred to the room: Energy = 1000 W × 3000 s = 3000000 J The energy transferred to the room is 3000000 J (joules). Let's convert it to kJ (kilojoules): 3000000 J = 3000 kJ

Match the answer with the given options

We found that the energy transferred to the room by the heater is 3000 kJ. Now let's match this value with the given options: (a) 1 kJ (b) 50 kJ (c) 3000 kJ (d) 3600 kJ (e) 6000 kJ The correct answer is (c) 3000 kJ.