JOULE EFFECT: EXPLANATION, EXAMPLES, EXERCISES, APPLICATIONS - PHYSICAL - 2025

The Joule effect or Joule's law is the result of the transformation of electrical energy into heat, which takes place when an electrical current passes through a conductor. This effect is present whenever any appliance or device that needs electricity to function is turned on.

Other times it is undesirable and it is sought to minimize it, that is why fans are added to the desktop PC to dissipate heat, since it can cause failure of the internal components.

The devices that use the Joule effect to produce heat, have inside a resistance that heats up when a current is passed through it, called a heating element.

Explanation

The Joule effect has its origin on a microscopic scale in particles, both those that make up a material and those that carry electrical charge.

Atoms and molecules in a substance are in their most stable position within the substance. For its part, the electric current consists of an ordered movement of electric charges, which come from the positive pole of the battery. When they get out of there they have a lot of potential energy.

As they pass, the charged particles impact those of the material and cause them to vibrate. These will try to regain the balance they previously had, delivering excess energy to their surroundings in the form of perceptible heat.

The amount of heat Q released depends on the intensity of the current I, the time for which it circulates inside the conductor Δt and the resistive element R:

The above equation is called the Joule-Lenz law.

Examples

Two physicists, the British James Joule (1818-1889) and the Russian Heinrich Lenz (1804-1865) independently observed that a current-carrying wire not only became hot, but that its current decreased during the process.

Then it was established that the amount of heat dissipated by the resistance is proportional to:

- The square of the intensity of the circulating current.

- The time that said current remained flowing through the conductor.

- The resistance of said conductor.

The units of heat are the same units of energy: joules, abbreviated as J. The joule is a fairly small unit of energy, so others are often used, such as calories, for example.

To transform joules to calories, simply multiply by the factor 0.24, so that the equation given at the beginning is directly expressed in calories:

Joule effect and electric energy transport

The Joule effect is welcome to produce localized heat, like burners and hair dryers. But in other cases, it has unwanted effects, such as:

- A very great heating in the conductors can be dangerous, causing fires and burns.

- Electronic devices with transistors decrease their performance and can fail even if they get too hot.

- The wires that carry electrical energy always experience heating, even slightly, which leads to notable energy losses.

This is because the cables that carry current from power plants run for hundreds of kilometers. So much of the energy they carry does not reach its destination, because it is wasted on the way.

To avoid this, it is sought that the conductors have the least possible resistance. This is influenced by three important factors: the length of the wire, the cross-sectional area, and the material from which it is made.

The best conductors are metals, with gold, silver, platinum or copper being some of the most efficient. The wires of the cables are made of copper filaments, a metal that, although it does not conduct as well as gold, it is much cheaper.

The longer a wire is, the more resistance it will have, but by making them thicker, the resistance decreases, because this facilitates the movement of the charge carriers.

Another thing that can be done is to decrease the intensity of the current, so that the heating is minimized. Transformers are responsible for controlling the intensity properly, that is why they are so important in the transmission of electrical energy.

Exercises

Exercise 1

A radiator indicates that it has a power of 2000W and is connected to the 220 V socket. Calculate the following:

a) Intensity of the current flowing through the radiator

b) Amount of electrical energy that has been transformed after half an hour

c) If all this energy is invested in heating 20 liters of water that are initially at 4 ºC, what will be the maximum temperature to which the water can be heated?

Solution to

Power is defined as energy per unit time. If in the equation given at the beginning we pass the factor Δt to the right, we will have precisely energy per unit of time:

The resistance of the heating element can be known through Ohm's law: V = IR, from which it follows that I = V / R. Thus:

Thus the current results:

Solution b

In this case Δt = 30 minutes = = 30 x 60 seconds = 1800 seconds. The value of the resistance is also required, which is cleared from Ohm's law:

The values ​​are substituted in Joule's law:

Solution c

The amount of heat Q necessary to raise a quantity of water to a certain temperature depends on the specific heat and the variation in temperature that needs to be obtained. It is calculated by:

Here m is the mass of water, C _e is the specific heat, which is already taken as data for the problem, and ΔT is the temperature variation.

The mass of water is that in 20 L. It is calculated with the help of density. The density of water ρ _water is the ratio of mass to volume. In addition, you have to convert liters to cubic meters:

Since m = density x volume = ρV, the mass is.

Note that we have to go from degrees centigrade to kelvin, adding 273.15 K. Substituting the above in the heat equation:

Exercise 2

a) Find expressions for power and the average power for a resistance connected to an alternating voltage.

b) Suppose you have a hair dryer with 1000W power connected to the 120 V socket, find the resistance of the heating element and the peak current - maximum current - through it.

c) What happens to the dryer when it is connected to a 240 V socket?

Solution to

The tap voltage is alternating, in the form V = V _o. sen ωt. Because it is variable in time, it is very important to define the effective values ​​of both voltage and current, which are denoted by the subscript “rms”, which stands for root mean square.

These values ​​for current and voltage are:

When applying Ohm's law, the current as a function of time is as:

In this case, the power in a resistor crossed by an alternating current is:

It is seen that the power also varies with time, and that it is a positive quantity, since everything is squared and R is always> 0. The mean value of this function is calculated by integration in a cycle and results:

In terms of effective voltage and current, the power looks like this:

Solution b

Applying the last equation with the supplied data:

_Mean P = 1000 W and V _rms = 120 V

Therefore the maximum current through the heating element is:

Resistance can be solved from the equation of mean power:

P _mean = V _rms. I _rms = 240 V x 16.7 A ≈ 4000 W

This is approximately 4 times the wattage the heating element is designed for, which will burn out shortly after being plugged into this outlet.

Applications

Incandescent bulbs

An incandescent light bulb produces light and also heat, which we can notice immediately when we connect it. The element that produces both effects is a very thin conductor filament, which therefore has a high resistance.

Thanks to this increase in resistance, although the current has decreased in the filament, the Joule effect is concentrated to such an extent that incandescence occurs. The filament, made of tungsten due to its high melting point of 3400 ºC, emits light and also heat.

The device should be enclosed in a transparent glass container, which is filled with an inert gas, such as argon or nitrogen at low pressure, to avoid deterioration of the filament. If not done this way, the oxygen in the air consumes the filament and the bulb stops working instantly.

Magneto-thermal switches

The magnetic effects of magnets disappear at high temperatures. This can be used to create a device that interrupts the flow of current, when it is excessive. This is a magnetothermic switch.

A part of the circuit through which the current flows is closed by a magnet attached to a spring. The magnet sticks to the circuit thanks to the magnetic attraction and remains so, as long as it is not weakened by heating.

When the current exceeds a certain value, the magnetism weakens and the spring detaches the magnet, causing the circuit to open. And since the current needs the circuit to be closed in order to flow, it opens and the flow of current is interrupted. This prevents the cables from heating up, which could cause accidents such as fires.

Fuses

Another way to protect a circuit and interrupt the flow of current in a timely manner is by means of a fuse, a metal strip that, when heated by the Joule effect, melts, leaving the circuit open and interrupting the current.

Figure 2. A fuse is a circuit protector element. Metal melts when it is passed through by excessive current. Source: Pixabay.

Ohmic heating pasteurization

It consists of passing an electric current through food, which naturally has electrical resistance. For this, electrodes made of anticorrosive material are used. The temperature of the food rises and the heat destroys the bacteria, helping to preserve it for longer.

The advantage of this method is that heating occurs in much less time than that required by conventional techniques. Prolonged heating destroys bacteria but also neutralizes essential vitamins and minerals.

Ohmic heating, which lasts just a few seconds, helps preserve the nutritional content of food.

Experiments

The next experiment consists of measuring the amount of electrical energy converted into thermal energy by measuring the amount of heat absorbed by a known mass of water. To do this, a heating coil is immersed in water, through which a current is passed.

materials

- 1 polystyrene cup

- Multimeter

- Celsius thermometer

- 1 adjustable power source, range 0-12 V

- Balance

- Connection cables

- Stopwatch

Process

The coil heats up by the joule effect and therefore the water too. We must measure the mass of water and its initial temperature, and determine to what temperature we are going to heat it.

Figure 3. Experiment to determine how much electrical energy is transformed into heat. Source: F. Zapata.

Successive readings are taken every minute, recording the current and voltage values. Once the record is available, the electrical energy supplied is calculated using the equations:

Q = I ².R. Δt (Joule's Law)

V = IR (Ohm's Law)

And compare with the amount of heat absorbed by the body of water:

Q = m. C _e. ΔT (see solved exercise 1)

Since energy is conserved, both quantities should be equal. However, although polystyrene has low specific heat and absorbs almost no thermal energy, there will still be some losses to the atmosphere. The experimental error must also be taken into account.

Losses to the atmosphere are minimized if the water is heated the same number of degrees above room temperature as it was below before starting the experiment.

In other words, if the water was at 10ºC and the ambient temperature was 22ºC, then you have to bring the water up to 32ºC.

References

1. Kramer, C. 1994. Physics Practices. McGraw Hill. 197.
2. The sieve. Joule effect. Recovered from: eltamiz.com.
3. Figueroa, D. (2005). Series: Physics for Science and Engineering. Volume 5. Electrostatics. Edited by Douglas Figueroa (USB).
4. Giancoli, D. 2006. Physics: Principles with Applications. 6 ^th. Ed Prentice Hall.
5. Hypertextual. What is the Joule effect and why it has become something transcendental in our lives. Recovered from: hypertextual.com
6. Wikipedia. Joule effect. Recovered from: es.wikipedia.org.
7. Wikipedia. Joule heating. Recovered from: en. wikipedia.org.