work, heat and energy -...

Unit 5: Work, heat & energy

© Patricio Gómez Lesarri

Work, heat and energy

1. Definition of work 2. Power 3. Energy. Energy-work theorem 4. Principle of conservation of mechanical energy 5. Heat 6. Heat capacity. Latent heat 7. Methods of heat transfer.

1. Definition of work In the XVIIth century, Newton stated his three laws of Mechanics and studied the motion

of an object by means of forces and accelerations. In the XIXth century, an alternative approach for Mechanics and Physics was developed. This new conceptual frame led to an unification of all phenomena related to motion and heat.

First of all, we need to define the dot product (or scalar product) of two vectors. Given two vectors,

a and b , their dot

product a.b is defined as:

a.b = a . b .cosθ

@ http://mathinsight.org Dot product is an operation which determines the product of two vectors which are

pointing to different directions. It refers to a quantity which depends on two vector quantities and its direction. For instance, try to imagine you want to collect rain water in a rain gauge. The amount of water stored in the rain gauge depends on the intensity of rain, the area of the collector and, finally, the angle between both vectors. Particularly, when the rain flows through the same direction of the collector, the amount of water is maximal, but when the rain falls perpendicular to the rain gauge, the amount of water collected must be equal to zero.

@ http://pveducation.org Dot product has the same properties: as it depends on cosine of an angle, it has a

minimum when the angle is 90º (π/2 radians) and has a maximum when both vectors have a common direction (0 or π radians).

When a force acts upon an object, it can change its state of motion. Hence we´ll define

a new physical quantity, work, which refers to the effect of a force upon the motion of an object. Work is the dot product of force and the displacement of the body, which means the product of the component of a force in the direction of motion times its displacement. It is measured in Newtons.m, which is usually called as Joule, whose symbol is J.

W =

F.Δs = F . Δs .cosθ

Work is a scalar which can be positive or negative. When work is positive, the force is pointing to the same direction of the motion, so the effect of the force is speeding up the particle. On the other hand, when work is negative, the effect of the force is slowing down the body. Finally, when work equals to zero, the motion keeps at the same speed.

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© http://hyperphysics.phy-astr.gsu.edu

• Activity 1: A body slides along an inclined ramp which makes 30º to the baseline. Determine the work done by all the forces acting upon it

2. Power It is also important to know the time required to do a work. Power is a physical quantity

which refers to the rate at which a work is done or energy is produced. It is defined as work per unit of time.

P =WΔt

=

F.ΔsΔt

=F.v

Power is measured in Joule per second, which is called Watt, W, in the International System. Its magnitude is very tiny, so we usually use multiples as kilowatt, kW, or Megawatt, MW. There are others units which are still used by engineers, such as Horsepower, which was defined by James Watt to measure power of steam engines. One horsepower equals to 746 W, which has the same order than kilowatts.

1 HP = 746 W

Watts let us define new units for work, such as kilowatt.hour, which is the amount of work transferred by a 1 kW engine for an hour. It is usually used to express electric energy conssumption.

1 kW.h = 1000 W.3600 s = 3.6 106 J = 3.6 MJ

• Activity 2: Make a list of all your electric appliances at home and write their powers. Find out your power supply at home. How many electric appliances can work simultaneosly?

3. Energy. Work-energy theorem In the XIXth century, new experimental evidence showed there was a connection

between different branches of Physics: team engines produce motion from heat and electricity can be used for generating heat or motion.

Particularly, there is a strong relationship between work and motion, because

positive work means that a particle speeds up and negative work is equivalent to slowing down motion. For the simplest system, a particle which has a linear uniform accelerated motion:



F =m.a s = vo.t + 12.at

2 v2 = vo2 + 2a.s

W =F.Δs = m.a( ).Δ

s = 12.mv2 − 12.mvo

2

We have shown that work is transformed into a new physical quantity which is called

kinetic energy. This statement is known as work-energy theorem: “The net work done by all the forces which are applied to a body is equal to its

change of kinetic energy”

Wnet = ΔKE = KE −KEo = 12mv2 − 12.mvo

2

Energy is a new physical quantity which refers to the ability of a system to produce an action. A system which has energy can produce an action or do a work. On the other hand, we can do a work on a system and it will store this amount of work and release the energy later on. In other words, work is type of energy exchange by means of the action of forces. Kinetic energy is a type of energy related to motion: every object which is moving has this kind of energy. It is proportional to its mass and to the speed squared.

4. Principle of conservation of mechanical energy • Activity 3: Levers or hydraulic systems can mutiply forces by thousands of times. Do

you think they can be used to produce energy? • Activity 4: Why does the motion of a pendulum seem not to stop for a long time?

A lever transforms a little force at one side into a greater force at the other. However, the distance covered by one side is proportional to the length of its arm and, therefore, inversely proportional to its force. Hence, there is a quantity which is conserved in a lever, the work done by both forces are the same.

An object which is tied to the end of a pendulum or a spring can keep its motion for a

long time. On the other hand, some others , such as friction forces, try to stop the motion. Consequently, forces are divided into two types:

• Nonconservative: work done by nonconservative forces is converted into heat and

causes objects to stop • Conservative: work done by conservative forces is converted into a special kind of

energy, which is called potential energy. Wcon = −ΔPE

• Activity 5: Move a wood block on a table and leave it in a dfferent place . Do you think it

can go back to tis initial position?. Now lift the wood block to a point which is one metre higher Does it come back to its original position?

Potential energy just depends on position of the object and is defined as the energy of

an object according to its position with respect of forces acting upon it. For instance, a stone which is placed at a higher position can move along a greater distance, so it can do a greater work and gain more energy.

Non conservative forces cause the bodies to stop. On the other hand, work applied by a

conservative force is transformed into two different kinds of energy: potential and kinetic. As changes of both energies are opposite, total energy is conserved. In other words, when



conservative forces are applied to a body, every increase of kinetic energy is counterbalanced by the same decrease of potential energy. On the other hand, when the body loses kinetic energy, it also gains the same amount of potential energy.

The sum of kinetic and potential energies is called mechanical energy. Principle of

conservation of mechanical energy states: “The mechanical energy of a system remains constant in the absence of

nonconservative forces”

5. Heat

Review Kinetic theory is a physical theory about the microscopic constitution of matter. It could be summed up according to the following statements:

1. Matter is composed by tiny particles, called atoms or molecules 2. Particles which form matter has a continuous and random motion which depends on its

thermal energy. Furthermore, its average kinetic energy is proportional to its temperature. Temperature is measured in Kelvin in the International System of Units

3. Interactions between particles are inversely proportional to a power of the distance between them. This statement means that as the particles are closer, they will be more attracted, and as the distance increases, the interaction will decrease.

• Activity 6: Consider a liquid which has a great temperature placed in a container and

another one which has a lower temperature. What happends when we mix both liquids in the same container?. Can you explain this process?

As we explained last year, molecules of liquid

are in constant and random motion with a kinetic energy which is proportional to temperature. When we mix both systems, one molecule of the hot liquid is free to collide with another molecule of the other liquid. As a result of their collision, their kinetic energies tend to be averaged, so after a short interval of time all the molecules of both systems will get the same kinetic energy or, in other words, the same temperature.

Hence we define heat as a process of

transferring energy by means of a change of temperature or a change of state. Consequently, a system can exchange energy with its surrounding by 2

© http://aprendiendomasfisica2.blogspot.com.es/ different ways: work or heat. Work is a way of transferring by means of a force. On the other hand, heat is a way of

transferring energy from a hot system - at a greater temperature- to a cooler system – at a lower temperature-. This process finishes when both system achieve a thermal equilibrium or, in other words, they have the same temperature

6. Heat capacity. Latent heat Generally speaking the amount of heat absorbed or released by a system depends on

three different factors:

• Mass: heat is proportional to mass, because a greater amount of energy is required to heat a system which has a greater mass



• Change of temperature: as we have explained before, a greater amount of energy is required to heat a system at a greater temperature

• Specific heat capacity,: it is a quantity which refers to how easy or difficult is to heat a system. In other words, the greater the heat capacity, the more difficult is to heat a body and lower difference of temperature. It is defined as the amount of heat per unit of mass required to increase 1 K of temperature. It is measured in J.kg-1.K-1.

• Activity 7: We can notice that sand becomes quite hot in summer on the beach, but water is cooler. How can you explain the difference?

• Activity 8: Consider you have parked your car at the street in a hot summer day. How would you manage to open the door when you come back after a while?

Hence we can determine the heat absorbed or lost by means of a change of temperature as follows:

Q =m.c.ΔT Sometimes we can find a non SI unit for measuring heat or food energy: calorie, which is the amount of heat required to raise the temperature of one gram of water by one Celsius degree. According to this definition, specific heat capacity of water equals to 1 cal/g.ºC . As one calorie equals exactly to 4,184 J, specific heat capacity of water equals to 4184 J/kg.K.

Last year we explained that a heating curve is a graph which shows the variation of temperature as we heat a system. In these graphs, temperature increases uniformly until a phase change occurs, where we find a “plateau” phase. Therefore, every phase change has a characteristic temperature, at which it occurs. This temperature doesn´t change until this phase change finishes. As heat is still absorbed by a system, despite of having the same temperature, we can notice that heat depends on two factors: © https://gcps.desire2learn.com

• Mass, as we esplained before heat depends on the amount of matter • Latent heat, It is a specifi property of a substance, which measures the amount of heat

required to carry out the phase change per unit of mass of substace

Q =m.L

To sum up, heat is an amount of energy transferred directly to the molecules of a system. It can be used for two different phenomena:

• a change the temperature of the body, by means of a change of the average kinetic

energy of its own molecules • a phase change, by means of a weakening or breaking of the interactions applied

among its molecules

7. Methods of heat transfer

We can find three different ways of transferring energy between systems: conduction, convection and radiation. Conduction occurs in solids. When we heat the end of a metal rod, molecules which have already absorbed the energy start vibrating greater and greater, bump into the



neighbouring molecules transferring an amount of their energy to. By this way, energy is transferred from the hot end to the cooler one without matter motion.

Conduction depends on two different quantities: type of material and its thickness. Materials which allow transferring energy very easily are called heat conductors, such as metals. On the other hand, materials which not allow energy to travel through them are called insulators, such as wool, cork or plastics. The physical quantity which measures this property is called thermal conductivity.

© http://www.vtaide.com/png/heat2.htm Apart from thermal conductivity, conduction depends on the length or thicknes of the material. In other words, the thicker the material, the greater number of atoms layers and greater reduction of temperature.

• Activity 9: Bioclimatic houses are buidings which are designed to save fuel, energy or water, taking advantage of the local materials and solar radiation. Bioclimatic houses require the best thermal insulation, which is achieved by means of thicker walls with a thermal insulator layer between two layers of brick or stone. Find out information about thermal insulators used in bioclimatic houses

• Activity 10: Design a research project about the thermal insulation at your home,

which find out answers to these questions: is it designed for energy saving (walls, windows, orientation)? What is its energy cost per year? Which energy measures (thermal insulation, heating system, etc) can you apply at home? How much do they cost? What is the expected saving per year? How many years do you need to recover the investment?

Convection is a way of heat transfer which occurs in fluids and involves any kind of matter motion. On a general basis, density of a fluid is inversely proportional to temperature, so when an amount of fluid is hot, its density is lower than density of its surrounding. As Archimedes law states, materials whose density Is lower tend to float because their buoyant force is greater than their weight. Consequently, the hot fluid tend to rise up and it is replaced by a cooler portion of the same fluid, producing matter currents which are called convection currents. By this way, as molecules of fluid travel, the energy is transferred from the hotter points of a fluid to the cooler ones. © http://www.free-online-private-pilot-ground-school.com/ • Activity 11: Have you heard about continental drift, a theory which explains the Earth

Dynamics? Do you know how continents can move on the mantle?



Radiation is the last method of heat transfer. Energy travels through vacuum or a material medium by means of electromagnetic radiation. Energy which comes from the Sun is an example of this way of transferring energy

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