Question

A 2-kW electric resistance heater in a room is turned on and kept on for 50 minutes. The amount of energy transferred to the room by the heater is (a) \(2 \mathrm{~kJ}\) (b) \(100 \mathrm{~kJ}\) (c) \(6000 \mathrm{~kJ}\) (d) \(7200 \mathrm{~kJ}\) (e) \(12,000 \mathrm{~kJ}\)

Short answer

a) 1000 kJ b) 5000 kJ c) 6000 kJ d) 7000 kJ Answer: c) 6000 kJ

Step-by-step solution

Convert the time to seconds

To convert the time from minutes to seconds, we should multiply the time in minutes (50) by 60 seconds, as there are 60 seconds in 1 minute: Time (seconds) = 50 minutes x 60 seconds/minute = 3000 seconds

Convert the power to Watts

The power of the heater is given in kilowatts (kW), and we need to convert it to watts (W). To do this, we should multiply the power in kilowatts (2) by 1000 watts, as there are 1000 watts in 1 kilowatt: Power (Watts) = 2 kW x 1000 watts/kW = 2000 watts

Calculate the energy transferred to the room

Now, we can use the formula for calculating the energy transferred to the room: Energy (Joules) = Power (Watts) x Time (Seconds) Energy (Joules) = 2000 watts x 3000 seconds = 6,000,000 J As the energy is given in kJ (kilojoules) in the exercise options, we should convert the energy from Joules (6,000,000 J) to kilojoules by dividing it by 1000: Energy (kJ) = 6,000,000 J ÷ 1000 = 6000 kJ

Match the result with given options

The calculated energy transferred to the room is 6000 kJ. Comparing it to the given options, we find that it corresponds to the option (c) 6000 kJ. So, the correct answer is (c) 6000 kJ.

Key concepts

Electric Resistance Heater

An electric resistance heater is a device that converts electrical energy into heat energy. This is achieved through a process known as resistive heating. The heater contains a resistive element, typically made of materials such as nichrome. When electric current passes through this element, it encounters resistance which converts electrical energy into heat.
The generated heat is then transferred to the surrounding area, such as a room, to raise its temperature.

• Electric resistance heaters are simple and reliable, often used as space heaters in homes and offices.
• They are easy to control, allowing for quick adjustment of temperature output.
• However, they can be less efficient overall compared to other heating methods because they consume substantial electrical energy.

Understanding how electric resistance heaters work is fundamental to grasp the concept of energy conversion and power calculation.

Energy Conversion

Energy conversion in an electric resistance heater involves transforming electrical energy into thermal energy. This transformation follows the law of conservation of energy, which states that energy cannot be created nor destroyed, only changed from one form to another.
When we turn on an electric resistance heater, the electrical energy flowing through the resistive wire is converted to thermal energy due to the resistance. This thermal energy is then used to heat the room.

• The energy conversion efficiency in an electric resistance heater is determined primarily by the resistance of the wire and the power of the electrical source.
• The higher the power and resistance, the greater the amount of thermal energy produced.

Such heaters are effective for direct heating applications because nearly all the electrical energy is converted directly into heat. Hence, understanding energy conversion helps explain how heaters warm up spaces effectively and calculate the amount of energy delivered to a room.

Power Calculation

The power calculation is crucial for determining how much energy is transferred in a given time by a device like an electric resistance heater. Power is the rate at which energy is used or transferred. It is typically measured in watts (W) or kilowatts (kW).
In this exercise, the power of the heater is 2 kW, which means it uses 2000 Joules of energy per second. To find the total energy transferred over a period, you must multiply the power by the time the heater runs.
A step-by-step power calculation is as follows:

• First, convert time from minutes to seconds because power is typically given in watts, meaning Joules per second.
• Multiply power (in watts) by time (in seconds) to get total energy in Joules.
• Convert Joules to kilojoules by dividing by 1000, as energy is often expressed in kilojoules for convenience.

For the given problem, the calculation shows that during 50 minutes, or 3000 seconds, the 2 kW heater transfers 6000 kJ of energy to the room. Power calculations are vital in assessing and optimizing energy usage in heating applications.