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What is heat generation in a solid? Give examples.

Short Answer

Expert verified
Answer: Heat generation in a solid refers to the process where energy is produced within the material, resulting in a rise in its temperature. Some examples of situations where heat is generated within a solid are electrical resistance heating, chemical reactions like combustion, nuclear decay, and friction heating between two solid surfaces.

Step by step solution

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Definition of Heat Generation in a Solid

Heat generation in a solid refers to the process where energy is produced within the material, resulting in a rise in its temperature. This can be due to various physical, chemical, or even biological processes taking place in the solid.
02

Example 1: Electrical Resistance Heating

When an electrical current passes through a conductive solid (like a metal wire or a heating element), the electrons in the material collide with the atom, causing the material to heat up. This results in the generation of heat within the solid. This principle is applied in everyday devices like toasters, electric stoves, and space heaters.
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Example 2: Chemical Reactions

Some chemical reactions, known as exothermic reactions, generate heat as a byproduct. For example, the combustion of wood, coal, or any fuel releases heat as the chemical bonds are broken and new bonds are formed. This heat generation occurs within the solid fuel as the reaction proceeds.
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Example 3: Nuclear Decay

Certain solid materials contain radioactive isotopes, which release heat as they undergo nuclear decay. This process is called radioactive decay heating. The heat generation in this case can result in a substantial temperature increase within the solid material, especially in cases of concentrated radioactive substances. For example, this principle is used in radioisotope thermoelectric generators (RTGs) for producing electricity and heat in remote locations and space missions.
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Example 4: Friction Heating

When two solid surfaces are rubbed against each other, the friction between them generates heat. This heat generation within the solids can cause their temperatures to rise significantly, depending on the applied force and materials involved. Examples of this phenomenon include heat generated by car brakes, machinery, and even earthquakes, as tectonic plates move against each other.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrical Resistance Heating
One of the ways heat is generated within solids is through a process known as electrical resistance heating. This occurs when an electric current flows through a conducting material, such as a metal wire. Inside this material, free-flowing electrons constantly collide with metal ions, causing energy to be released in the form of heat. This resistance to the flow of electric current is a property inherent to the material and varies based on its composition.

Electrical resistance heating is a principle integral to numerous household appliances and industrial machinery. It heats our homes via baseboard heaters, cooks our food in toasters and ovens, and even provides the warmth in electric blankets. An understanding of this process is crucial for designing efficient electrical heating systems and for troubleshooting when a device isn't working as it should. To ensure safety and efficiency, materials are chosen for their specific resistance characteristics to match the desired heat output for the intended application.
Exothermic Chemical Reactions
Heat production in solids can also be a result of exothermic chemical reactions. These reactions release energy by forming chemical bonds that are stronger than the ones broken at the start of the reaction. Many everyday materials, like wood and fossil fuels, when ignited, undergo exothermic reactions—combustion being a classic example.

When these materials burn, they react with oxygen in the air to form water, carbon dioxide, and other compounds, releasing a substantial amount of heat energy. This heat is intrinsic to processes like power generation in power plants, where coal is burned to create steam, which in turn drives turbines to produce electricity. A firm grasp of exothermic reactions is essential for fields ranging from environmental science to engineering, impacting how we harness energy and minimize pollution.
Radioactive Decay Heating
Radioactive decay heating is another intriguing method by which heat is generated within solids. This process stems from the decay of unstable isotopes, which shed energy to reach a more stable form. This emitted energy comes in the form of kinetic energy, radiation, and heat. Materials such as uranium and plutonium used in nuclear reactors are classic examples of this, where the controlled decay process heats water to produce steam and generate electricity.

Radioisotope thermoelectric generators (RTGs), mentioned in the textbook exercise, are unique applications of this principle. They supply heat and electricity to space probes or facilities cut off from conventional power sources. RTGs are essential for long-term missions to space where sunlight may not be available to power solar panels. Knowledge about radioactive decay heating is vital for developing safe and effective nuclear technologies.
Friction Heating
Friction heating is generated when two surfaces come into contact and move relative to one another. The microscopic asperities—or peaks and valleys—of the surfaces interfere, causing mechanical resistance. As a result, kinetic energy is converted into thermal energy, thus heating the solids involved.

We witness friction heating all around us; when we rub our hands together to warm up, in the brakes of a vehicle slowing down, or during the catastrophic event of an earthquake caused by shifting tectonic plates. The understanding of friction-induced heat is vital for designers of mechanical systems to ensure the integrity of components over time and for the safe operation of a wide array of machinery.

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Most popular questions from this chapter

A large plane wall has a thickness \(L=50 \mathrm{~cm}\) and thermal conductivity \(k=25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). On the left surface \((x=0)\), it is subjected to a uniform heat flux \(\dot{q}_{0}\) while the surface temperature \(T_{0}\) is constant. On the right surface, it experiences convection and radiation heat transfer while the surface temperature is \(T_{L}=225^{\circ} \mathrm{C}\) and the surrounding temperature is \(25^{\circ} \mathrm{C}\). The emissivity and the convection heat transfer coefficient on the right surface are \(0.7\) and \(15 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. Show that the variation of temperature in the wall can be expressed as \(T(x)=\left(\dot{q}_{0} / k\right)(L-x)+T_{L}\), where \(\dot{q}_{0}=5130 \mathrm{~W} / \mathrm{m}^{2}\), and determine the temperature of the left surface of the wall at \(x=0\).

The conduction equation boundary condition for an adiabatic surface with direction \(n\) being normal to the surface is (a) \(T=0\) (b) \(d T / d n=0\) (c) \(d^{2} T / d n^{2}=0\) (d) \(d^{3} T / d n^{3}=0\) (e) \(-k d T / d n=1\)

Exhaust gases from a manufacturing plant are being discharged through a 10 - \(\mathrm{m}\) tall exhaust stack with outer diameter of \(1 \mathrm{~m}\), wall thickness of \(10 \mathrm{~cm}\), and thermal conductivity of \(40 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The exhaust gases are discharged at a rate of \(1.2 \mathrm{~kg} / \mathrm{s}\), while temperature drop between inlet and exit of the exhaust stack is \(30^{\circ} \mathrm{C}\), and the constant pressure specific heat of the exhaust gasses is \(1600 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\). On a particular day, the outer surface of the exhaust stack experiences radiation with the surrounding at \(27^{\circ} \mathrm{C}\), and convection with the ambient air at \(27^{\circ} \mathrm{C}\) also, with an average convection heat transfer coefficient of \(8 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Solar radiation is incident on the exhaust stack outer surface at a rate of \(150 \mathrm{~W} / \mathrm{m}^{2}\), and both the emissivity and solar absorptivity of the outer surface are 0.9. Assuming steady one-dimensional heat transfer, (a) obtain the variation of temperature in the exhaust stack wall and (b) determine the inner surface temperature of the exhaust stack.

A spherical metal ball of radius \(r_{o}\) is heated in an oven to a temperature of \(T_{i}\) throughout and is then taken out of the oven and dropped into a large body of water at \(T_{\infty}\) where it is cooled by convection with an average convection heat transfer coefficient of \(h\). Assuming constant thermal conductivity and transient one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem. Do not solve.

The heat conduction equation in a medium is given in its simplest form as $$ \frac{1}{r} \frac{d}{d r}\left(r k \frac{d T}{d r}\right)+\dot{e}_{\text {gen }}=0 $$ Select the wrong statement below. (a) The medium is of cylindrical shape. (b) The thermal conductivity of the medium is constant. (c) Heat transfer through the medium is steady. (d) There is heat generation within the medium. (e) Heat conduction through the medium is one-dimensional.

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