The heat of Joule's Law "Applications - Exercises"
Joule studied the effect produced when an electric current circulates through a conductor and so established by the well-known Joule law. As the electric charge moves through a conductor, the electrons collide with each other generating heat.
Making use of the Joule effect, multiple household appliances and industrial equipment have been designed, where electrical energy is converted into heat by this principle, such as electric cookers and irons.
Joule's Law is used in equipment design to reduce energy losses through heat.
Getting to know James Joule a little:
James Prescott Joule (1818-1889)
He was a British physicist who conducted research in thermodynamics, energy, electricity, and magnetism.
Together with William Thomson they discovered the so-called Joule - Thomson effect by which they demonstrated that it was possible to cool a gas when expanding without doing external work, a basic principle of the development of current refrigerators and air conditioners. He worked with Lord Kelvin to develop the absolute scale of temperature, helped explain the kinetic theory of gases.
The international unit of energy, heat and work, the joule, was named in his honor. [1]
Joule's law
What does Joule's Law propose?
When an electrical current flows through an element, some of the energy is dissipated as heat. Joule's law allows us to determine the amount of heat that is dissipated in an element, as a result of the electric current that circulates through it. See figure 1.
Joule's Law states that the heat (Q) that is generated in a conductor is proportional to its electrical resistance R, to the square of the current that passes through it, and to the time interval. See figure 2.
Mathematical expression of Joule's Law
The heat that is dissipated in an element, when a current circulates through it, is given by the mathematical expression in figure 3. It is required to know the value of the electric current that circulates through the element, its electrical resistance and the interval of time. [two].
When studying the heat loss in an element, it is usually expressed as the heat dissipated in the unit "calorie" instead of in Joule. Figure 4 shows the formula for determining the amount of heat in calories.
How does the warming happen?
When an electric current flows through a conductor, the electric charge collides with the atoms of the conductor as they move through it. Due to these shocks, a part of the energy is converted into heat, increasing the temperature of the conductive material. See figure 5.
The more current flows, the greater the increase in temperature, and the more heat is dissipated. The heat produced by the electric current flowing through a conductor is a measure of the work done by the current in overcoming the resistance of the conductor.
Moving the electric charge requires a voltage source. The voltage source must supply more power the more heat dissipates. By determining how much heat is produced, you can determine how much energy the voltage source must supply.
Joule's law applications
Joule effect in incandescent bulbs
Incandescent bulbs are made by placing a high melting tungsten filament in a glass bulb. At a temperature of 500 ºC, bodies emit a reddish light, which evolves to white if the temperature increases. The filament of the bulb, upon reaching 3.000 ºC, emits white light. Inside the ampoule a high vacuum is made and an inert gas is placed so that the filament does not burn.
The heat given off by the current (Joule effect) as it passes through said filament allows it to reach the temperature necessary for incandescence to occur, an effect of materials to emit light when subjected to high temperatures. See figure 6.
It is important to choose the right bulb for greater Energy Efficiency . In incandescent bulbs only a maximum 15% of the energy is used, the rest of the electrical energy is dissipated in heat. In led bulbs 80 to 90% is transformed into light energy, only 10% is wasted when dissipating in the form of heat. Led bulbs are the best option, having greater energy efficiency and lower electricity consumption. See figure 7. [3]
1 Exercise
For a 100 W, 110 V incandescent bulb, determine:
a) The intensity of the current flowing through the bulb.
b) The energy it consumes per hour.
Solution:
a) Electric current:
The expression of electrical power is used:
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By Ohm's Law the value of the electrical resistance of the bulb is obtained:
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b) Energy consumed per hour
Joule's Law determines the amount of heat that is dissipated in the bulb
If 1 Kilowatt-hour = 3.600.000 Joule, the energy consumed per hour is:
Q = 0,002 kWh
Result:
i = 0,91 A; Q = 0,002 kWh
Joule effect - Transmission and distribution of electrical energy
The electrical energy, which is generated in a plant, is transported by conductive cables to be used later in homes, businesses and industries. [4]
As the current circulates, heat is dissipated by the Joule effect, losing part of the energy to the environment. The greater the current, the greater the heat that is dissipated. To avoid energy loss, currents are transported at low currents and high voltages of 380 kV. This improves the efficiency in the transport of electrical energy. In substations and transformers they are reduced to the voltage levels at 110 V and 220 V for their final use25 or 220 volts). See figure 8.
In many appliances the Joule effect is used, where electrical energy is transformed into heat, such as in electric irons, water heaters, fuses, toasters, electric stoves, among others. See figure 9.
2 Exercise
A 400W electric iron is used for 10 minutes. Knowing that the iron is connected to a 110 V electrical outlet, determine:
a) The intensity of the current flowing through the iron.
b) The amount of heat dissipated by the iron.
Solution:
Electric current
The expression of electrical power is used:
p = vi
By Ohm's Law the value of the electrical resistance of the bulb is obtained:
Heat
Joule's Law determines the amount of heat that is dissipated in the plate. If a minute contains 60 seconds, then 10 minutes = 600 s.
If 1 Kilowatt-hour = 3.600.000 Joule, the heat released is:
Q = 0,07 kWh
Conclusions
Joule's Law states that the heat produced by an electric current when it circulates through a conductor is directly proportional to the square of the intensity of the current, times the resistance and the time it takes for the current to circulate. In homage to Joule the unit of energy in the international system is now called “Joule”.
Many devices use the “joule effect”, By generating heat by passing current through a conductor, such as ovens, stoves, toasters, plates, among others.
We invite you to leave your comments and questions on this interesting topic.