In the previous section, we completed a discussion on 'conservation of mechanical energy'. Next we will see the 'law of conservation' in other forms of energy such as heat energy, sound energy, nuclear energy etc.,
■ Total Mechanical energy possessed by a body is the sum of it’s kinetic energy and potential energy
• Kinetic energy is based on motion
• Potential energy is based on position or configuration
♦ Gravitational potential energy is based on the position (higher level or lower level)
♦ Spring potential energy is based on configuration (stretched or compressed configuration)
• Besides kinetic and potential energies, there are many other forms of energies
• Most of them obey the law of conservation. Let us see some of those energies:
• Let μk be the coefficient of kinetic friction between the block and the surface
2. We know that the kinetic energy will be used for overcoming friction
• We saw this:
The distance ‘x’ which the block is able to move is given by the equation: $\mathbf\small{\frac{mv^2}{2}=f_k x}$
$\mathbf\small{\Rightarrow \frac{mv^2}{2}=\mu_k mgx}$
$\mathbf\small{\Rightarrow \frac{v^2}{2}=\mu_k gx}$
$\mathbf\small{\Rightarrow x=\frac{v^2}{2 \mu_k g}}$
3. So when the block travels a distance ‘x’ given by the above equation, all the kinetic energy possessed by the block will be used up.
• We are inclined to say: ‘The kinetic energy possessed by the block is lost’
4. But that is not entirely true. Let us analyze:
(i) Just when the block comes to rest, if we touch the underside of the block and also the top of the horizontal surface, we will find that, the temperature of both the surfaces have increased.
(ii) That means, the kinetic energy was transformed into heat energy
5. Heat is generated when work is done against friction
• This phenomenon helps us to generate heat (even though in small quantities) by rubbing our hands together. We often do this during cold climates.
6. When two surfaces rub against each other, work is being done to overcome friction
• During the rubbing, the molecules on both the surfaces begins to move with greater velocities
• So the kinetic energies of those molecules increase
• This ‘increase in kinetic energy of molecules’ is the cause of ‘increased heat’.
• We say that the ‘internal energy of the objects increases’
• We will see more details in a later chapter
2. When two flint stones are rubbed against each other, we are doing mechanical work
• That is., we are 'spending' mechanical energy to rub the stones
3. This mechanical energy is used to overcome friction between the stones
• As a result, the stones get warmer and sparks are produced
4. The sparks are used to ignite a heap of dry leaves
• The fire is then transferred from the dry leaves to a heap of firewood. Thus early men got sustained heat
5. Now, what makes the dry leaves and firewood give us sustained heat?
• The answer is that, chemical energy is stored in dry leaves and firewood
• When ignited, this chemical energy is converted into heat energy
6. So what is chemical energy?
The answer can be written in the following 5 steps:
(i) Substances like dry leaves, firewood, kerosene etc., are known as fuels
(ii) They are made up of atoms
• Those atoms are bonded together by ‘bond-energy’
(iii) When ignited, reaction takes place between those atoms and oxygen
• As a result of this reaction, new substances such as carbon dioxide, ash, etc., are formed
• That means new bonds are formed
(iv) Now consider the two types of bonds:
(a) Bonds in the original fuel and bonds in oxygen (Reactants)
(b) Bonds in the carbon dioxide and bonds in ash (Products)
(v) Bonds in (b) have lesser bond-energy than the bonds in (a)
• That means, during the chemical reaction, some energy is released
• It is this ‘released energy’ that we receive as heat and light
• This 'released energy' is the chemical energy stored in the fuel
7. The reverse can also sometimes happen. That is.,
• Bonds in (iv.b) have a greater bond-energy than the bonds in (iv.a)
• In such cases, we will not receive any energy
• In fact, in such cases, we will have to supply energy for the reaction to occur
• The energy that we supply is absorbed by the reactants
8. If we receive energy, it is called an exothermic reaction
• If we have to supply energy, it is called an endothermic reaction
2. A flow of current takes place from a point of ‘high electric potential’ to a point of ‘low electric potential’
• Here ‘electric potential’ means ‘electrical energy’
• With out this energy, flow will not occur
3. In a bulb, electrical energy is converted into light and heat energies
• In a fan, electrical energy is converted into mechanical energy
• In an electrical iron, electric energy is converted into heat energy
• We will learn more about electrical energy in a later chapter
• Some examples:
(i) Consider the physical process of melting of ice:
If we take ‘m’ kg of ice, we will get the exact ‘m’ kg of water when the ice melts
(ii) Consider a normal chemical reaction:
The ‘sum of the masses of the reactants’ will be exactly equal to the ‘sum of the masses of the products’
(ii) So we are inclined to think that, mass is always conserved
■ But Albert Einstein showed that mass and energy are equivalent and are related by the equation:
$\mathbf\small{E=mc^2}$
• Where c is the speed of light in vacuum which is approximately 3 × 108 ms-1
(iv) According to this equation, even a small quantity of mass can give a large amount of energy
• But the conversion of mass into energy involves expensive processes
• Let us see the details:
2. Four hydrogen nuclei fuse together to form one helium nucleus
• This is a fusion reaction
3. On the reactant side we have four hydrogen nuclei
• On the product side, we have one helium nucleus
4. But the mass of the product is less than the 'sum of the masses of the reactants'
• We can say that when the reaction takes place, there will be a deficiency of mass on the product side
• This deficiency is indicated as Δm
5. This Δm is converted into energy
The amount of energy released = $\mathbf\small{E=(\Delta m)c^2}$
6. Nuclear energy can be obtained by fission reaction also
• In this reaction, a heavy nucleus of an 'isotope of uranium' is split into lighter nuclei
7. On the reactant side, we have one uranium nucleus
• On the product side, we have more than one nuclei
8. But 'sum of the masses of the products' is less than the mass of the reactant
• Here also, we can say that, there is a deficiency in the mass of the products
• This deficiency is indicated as Δm
9. This Δm is converted into energy
• The amount of energy released = $\mathbf\small{E=(\Delta m)c^2}$
10. If a fission reaction takes place in a controlled manner, the energy can be supplied to work a power plant. Thus electricity can be produced
• Such power plants are called Nuclear power plants
11. If the fission reaction takes place in an uncontrolled manner, huge amounts of energy will be produced in a very short interval of time
• This property of nuclear fission is used for making nuclear weapons
Solved example 6.27
A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated. (a) How much work does she do against the gravitational force? (b) Fat supplies 3.8 × 107 J of energy per kilogram which is converted into mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?
Solution:
• Lifting prescribed weights is an effective way for reducing fat
• When the weight is lifted upwards, the dieter is doing work against gravity
• The energy required for doing that work is obtained from the fat
♦ Thus the fat gets used up
• When the dieter lifts up the weight, potential energy get stored in that weight
• When the weight is brought down, no work is needed from the dieter
■ But what happens to the stored energy?
• When the weight comes down, the potential energy gets converted into kinetic energy
• That is why the dieter is able to bring down the weight easily
• But this kinetic energy is dissipated as heat, sound etc.,
• So the dieter has to find ‘new energy’ each time the weight is lifted upwards
• This ‘new energy’ required each time is supplied by the fat
Now we can write the steps:
1. Work done for lifting once = mgh = 10 × 9.8 × 0.5 = 49 J
• So work done for lifting 1000 times = 1000 × 49 = 49000 J
2. Given that, energy supplied by 1 kg of fat = 3.8 × 107 J
• But only 20% of this is available for the ‘mechanical work of weight lifting’
• So energy available from 1 kg = 3.8 × 0.2 × 107 = 0.76 × 107
3. So total fat required = $\mathbf\small{\frac{49000}{0.76 \times 10^{-7}}=0.006447 \,\, \text{kg}}$ = 6.447 grams
■ Total Mechanical energy possessed by a body is the sum of it’s kinetic energy and potential energy
• Kinetic energy is based on motion
• Potential energy is based on position or configuration
♦ Gravitational potential energy is based on the position (higher level or lower level)
♦ Spring potential energy is based on configuration (stretched or compressed configuration)
• Besides kinetic and potential energies, there are many other forms of energies
• Most of them obey the law of conservation. Let us see some of those energies:
Heat energy
1. Consider a block of mass ‘m’ moving on a horizontal surface with a velocity of ‘v’• Let μk be the coefficient of kinetic friction between the block and the surface
2. We know that the kinetic energy will be used for overcoming friction
• We saw this:
The distance ‘x’ which the block is able to move is given by the equation: $\mathbf\small{\frac{mv^2}{2}=f_k x}$
$\mathbf\small{\Rightarrow \frac{mv^2}{2}=\mu_k mgx}$
$\mathbf\small{\Rightarrow \frac{v^2}{2}=\mu_k gx}$
$\mathbf\small{\Rightarrow x=\frac{v^2}{2 \mu_k g}}$
3. So when the block travels a distance ‘x’ given by the above equation, all the kinetic energy possessed by the block will be used up.
• We are inclined to say: ‘The kinetic energy possessed by the block is lost’
4. But that is not entirely true. Let us analyze:
(i) Just when the block comes to rest, if we touch the underside of the block and also the top of the horizontal surface, we will find that, the temperature of both the surfaces have increased.
(ii) That means, the kinetic energy was transformed into heat energy
5. Heat is generated when work is done against friction
• This phenomenon helps us to generate heat (even though in small quantities) by rubbing our hands together. We often do this during cold climates.
6. When two surfaces rub against each other, work is being done to overcome friction
• During the rubbing, the molecules on both the surfaces begins to move with greater velocities
• So the kinetic energies of those molecules increase
• This ‘increase in kinetic energy of molecules’ is the cause of ‘increased heat’.
• We say that the ‘internal energy of the objects increases’
• We will see more details in a later chapter
Chemical energy
1. Consider the process of making fire using flint stones2. When two flint stones are rubbed against each other, we are doing mechanical work
• That is., we are 'spending' mechanical energy to rub the stones
3. This mechanical energy is used to overcome friction between the stones
• As a result, the stones get warmer and sparks are produced
4. The sparks are used to ignite a heap of dry leaves
• The fire is then transferred from the dry leaves to a heap of firewood. Thus early men got sustained heat
5. Now, what makes the dry leaves and firewood give us sustained heat?
• The answer is that, chemical energy is stored in dry leaves and firewood
• When ignited, this chemical energy is converted into heat energy
6. So what is chemical energy?
The answer can be written in the following 5 steps:
(i) Substances like dry leaves, firewood, kerosene etc., are known as fuels
(ii) They are made up of atoms
• Those atoms are bonded together by ‘bond-energy’
(iii) When ignited, reaction takes place between those atoms and oxygen
• As a result of this reaction, new substances such as carbon dioxide, ash, etc., are formed
• That means new bonds are formed
(iv) Now consider the two types of bonds:
(a) Bonds in the original fuel and bonds in oxygen (Reactants)
(b) Bonds in the carbon dioxide and bonds in ash (Products)
(v) Bonds in (b) have lesser bond-energy than the bonds in (a)
• That means, during the chemical reaction, some energy is released
• It is this ‘released energy’ that we receive as heat and light
• This 'released energy' is the chemical energy stored in the fuel
7. The reverse can also sometimes happen. That is.,
• Bonds in (iv.b) have a greater bond-energy than the bonds in (iv.a)
• In such cases, we will not receive any energy
• In fact, in such cases, we will have to supply energy for the reaction to occur
• The energy that we supply is absorbed by the reactants
8. If we receive energy, it is called an exothermic reaction
• If we have to supply energy, it is called an endothermic reaction
Electrical energy
1. We know that 'flow of electric current' is required for operating electrical appliances like fans, bulbs, heater etc.,2. A flow of current takes place from a point of ‘high electric potential’ to a point of ‘low electric potential’
• Here ‘electric potential’ means ‘electrical energy’
• With out this energy, flow will not occur
3. In a bulb, electrical energy is converted into light and heat energies
• In a fan, electrical energy is converted into mechanical energy
• In an electrical iron, electric energy is converted into heat energy
• We will learn more about electrical energy in a later chapter
The equivalence of mass and energy
1. During physical and chemical processes, we generally do not observe a change in mass.• Some examples:
(i) Consider the physical process of melting of ice:
If we take ‘m’ kg of ice, we will get the exact ‘m’ kg of water when the ice melts
(ii) Consider a normal chemical reaction:
The ‘sum of the masses of the reactants’ will be exactly equal to the ‘sum of the masses of the products’
(ii) So we are inclined to think that, mass is always conserved
■ But Albert Einstein showed that mass and energy are equivalent and are related by the equation:
$\mathbf\small{E=mc^2}$
• Where c is the speed of light in vacuum which is approximately 3 × 108 ms-1
(iv) According to this equation, even a small quantity of mass can give a large amount of energy
• But the conversion of mass into energy involves expensive processes
Nuclear energy
1. The huge amounts of energy produced in the sun can be explained using the equation: $\mathbf\small{E=mc^2}$• Let us see the details:
2. Four hydrogen nuclei fuse together to form one helium nucleus
• This is a fusion reaction
3. On the reactant side we have four hydrogen nuclei
• On the product side, we have one helium nucleus
4. But the mass of the product is less than the 'sum of the masses of the reactants'
• We can say that when the reaction takes place, there will be a deficiency of mass on the product side
• This deficiency is indicated as Δm
5. This Δm is converted into energy
The amount of energy released = $\mathbf\small{E=(\Delta m)c^2}$
6. Nuclear energy can be obtained by fission reaction also
• In this reaction, a heavy nucleus of an 'isotope of uranium' is split into lighter nuclei
7. On the reactant side, we have one uranium nucleus
• On the product side, we have more than one nuclei
8. But 'sum of the masses of the products' is less than the mass of the reactant
• Here also, we can say that, there is a deficiency in the mass of the products
• This deficiency is indicated as Δm
9. This Δm is converted into energy
• The amount of energy released = $\mathbf\small{E=(\Delta m)c^2}$
10. If a fission reaction takes place in a controlled manner, the energy can be supplied to work a power plant. Thus electricity can be produced
• Such power plants are called Nuclear power plants
11. If the fission reaction takes place in an uncontrolled manner, huge amounts of energy will be produced in a very short interval of time
• This property of nuclear fission is used for making nuclear weapons
Solved example 6.27
A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated. (a) How much work does she do against the gravitational force? (b) Fat supplies 3.8 × 107 J of energy per kilogram which is converted into mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?
Solution:
• Lifting prescribed weights is an effective way for reducing fat
• When the weight is lifted upwards, the dieter is doing work against gravity
• The energy required for doing that work is obtained from the fat
♦ Thus the fat gets used up
• When the dieter lifts up the weight, potential energy get stored in that weight
• When the weight is brought down, no work is needed from the dieter
■ But what happens to the stored energy?
• When the weight comes down, the potential energy gets converted into kinetic energy
• That is why the dieter is able to bring down the weight easily
• But this kinetic energy is dissipated as heat, sound etc.,
• So the dieter has to find ‘new energy’ each time the weight is lifted upwards
• This ‘new energy’ required each time is supplied by the fat
Now we can write the steps:
1. Work done for lifting once = mgh = 10 × 9.8 × 0.5 = 49 J
• So work done for lifting 1000 times = 1000 × 49 = 49000 J
2. Given that, energy supplied by 1 kg of fat = 3.8 × 107 J
• But only 20% of this is available for the ‘mechanical work of weight lifting’
• So energy available from 1 kg = 3.8 × 0.2 × 107 = 0.76 × 107
3. So total fat required = $\mathbf\small{\frac{49000}{0.76 \times 10^{-7}}=0.006447 \,\, \text{kg}}$ = 6.447 grams
In the next section we will see power
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