Chapter 1

Energy –the driving force of change

Energy plays an important part

And it’s used in all this work;

Energy, yest energy with power so great,

A kind that cannot shirk.

If the farmer had not this energy,

He would be at a loss,

But it’s sad to think, this energy

Belongs to a little brown horse.

A school verse by Richard Feynman
a Nobel laureate for physics

Energy is the driving force for all changes: winds, rains, storms, thunders, forest fires, earthquakes, waves, plant growth, food decay, ocean tides, formation and melting of ice, combustion, and growing old to name just a few. Furthermore, nuclear changes such as radioactivity, nuclear fission, and nuclear fusion (reactions) are also driven by energy. Energy, unlike matter, has no weight, size, shape, color or appearance, and its recognition is difficult. There are still some aspects about energy we do not fully understand.

Energy is the heart of nuclear technology, because all nuclear phenomena are caused by energy. In fact, the amount of energy involved in nuclear technology is so large that it scares us. We, the human race, have the nuclear technology to destroy the civilization and perhaps the planet Earth, if we are not careful. Thus, we discuss some aspect of energy as an introduction to nuclear technology.

In this chapter, we are exploring the following questions.

  • What is energy?
    What are the forms of energy?
    How does energy convert from one form to another?
  • How can amounts of energy be measured or determined?
    How does energy cause changes?
    How does energy behave?
  • Why does it rain or snow?
    How is energy related to rain or snow?

Mechanical Work and Heat as Forms of Energy

Temperature scales were invented to compare hotness or coldness, and their invention enabled us to measure quantities of heat. During the same period when temperature scales were invented, Newtonian physics had defined mechanical work, but a long time elapsed before James P. Joule (1818-1889) recognized that heat and mechanical work were inter-convertible. Then inter-convertibility between mechanical work and heat led to the concept of energy, which was coined to represent all elusive driving forces of changes

Mechanical Work

Mechanical work, is defined in Newtonian physics, using distance, mass and force. Distance and mass are basic quantities, measured by comparing with the standard meter and kilogram. The force, however, is an elusive concept that is defined in terms of mass and distance (more precisely acceleration). Mechanical work is discussed fully in Newtonian mechanics, and only a brief review is given here.

Newtonian mechanics

Strictly speaking, Newtonian mechanics is valid only in a coordinate system with its origin at the center of the solar system.

The 1st law defines mass m as a measure of inertia. The 2nd law gives the acceleration a imparted to a body by a force F

a = F / m

Both F and a are vectors, having magnitudes and directions. (Newton = kgm/s2)

The 3rd law states that actions of two bodies upon each other are equal, but opposite.

  • What are mass and distance?
    How are masses and distances measured, and in what (SI or other) units?
  • What is force?
    How a force can be delivered?
    What units are used for force?
    How much force is 1 N?
  • What is mechanical work?
    What are the units for mechanical work?

The SI units for mass and distance are kilogram (kg) and meter (m) respectively. They are measured by comparing with the standard meter stick and kg mass. Please note the following quantities and units.

Force, F, is the ability to accelerate (or decelerate) a massm according to the law of motion,
F = m a,
where a is the acceleration. A force with the ability to accelerate a 1-kg mass by 1 m/s2 is 1 Newton (N), which is the SI unit for force. Its basic dimensions are kg-m/s2. A Newton is the gravitational pull on a 102-g mass.

Forces exist in various forms: gravitational, electromagnetic, strong interaction (between nucleons), and weak interaction are four basic types of forces matter exerts over matter, and force can be delivered by mechanical (springs), chemical (bonding) and physical (steam expansion) means. In chemistry, the inter-atomic forces within a molecule holding atoms together are chemical bonds. Weak intermolecular forces are generally called Van der Waal’s forces or London dispersion forces, but strong intermolecular forces include hydrogen bonding, ionic and dipole attractions.

Without the concept of force, there is no means of comparing masses and vice versa. Concepts of force and mass are mutually dependent. However, on Earth, we always associate mass with weight. A 70kg person weighing 686 N on Earth weighs 289 N on the moon while there is no change in mass. In a weightless region, everybody is equal (in weight)!

A more elegant definition of work

Mechanical work, W, is a scalar quantity or state quantity that is defined by a mathematical dot product of the two vectors: force, F, and the distance, s.
W (J) = F · s.(N  m)
This is useful if you have the background in vector geometry and understand the dot product of vectors.

Force that causes no change of state does no mechanical work. Gravity does no work on any stationary object. A force (F) acting on an object, causing it to move a distance (s) in the direction of the force, does mechanical work (W), and

W = F s (J = N m).

A force of 9.8 N pulling an object (1 kg) up by a distance of 10 m performs 98 Jules of work. The SI unit for work is Joule (J), which is a Newtonmeter (or 1 kgm2/s2).

Work is a state quantity; the same amount of work is required if the initial and final states are the same. The length of time or the methods used to raise the weight has nothing to do with the amount of work done. The unit used for work in the imperial system is footpound whereas erg (dynecm) is the unit used in the cgs (centimeter-gram-second) system.

Another definition of work is the distance times the component of the force in the direction of the distance. Both formulations give the same results.

What happens to the force components that are not in the direction of the displacement? If we push a strong wall with great strength but the wall does not budge (s=0), no useful work is produced; the effort (not work) is completely wasted. When a force is used to pull an object up a height, it gains potential energy, and when it accelerates an object, it gains kinetic energy.

Skill developing problems:

1. How much work is done to 1.0 L of water when it is pulled from the top of a water fall down by a distance of 100 m? Gravitational pull is 9.8 m/s2(Ans. 980 J)

2. A fish with 1-kg mass in water faces a total resistance of 1.0 N. It gains 10 m/s speed over a distance of 1 m of movement. What is the average force exerted by the fish in this movement? (F = 50 N)

3. A sled weighing 50 kg experiences a gravitational force of 490 N. When it is pulled across a frozen lake, the average force due to friction is 10 N. Calculate the amount of energy required to pull the sled across the lake for a distance of 10 km. (105 J).

Potential and Kinetic Energy

When a force acts upon an object for a distance, the state of the object has changed. The change in location results in a change in potential energy, and the change in velocity results in a change in kinetic energy. Although the concept of energy has yet to be defined, these terms are used loosely because most of you are already familiar with them.

  • What are potential and kinetic energy,
    and how they are evaluated?

Potential energy is the mechanical work stored in a particle or body or system due to location or height in a force field. In a gravitational force field, g, a mass m kg raised to a height ht, has a potential energy Ep
Ep = m g ht in Joules (J), (g = 9.8 m/s2 being gravitational acceleration).
For example, a person weighing 70 kg (154 lb) against a gravitational force of m g walking up a set of stairs for a total height of 10 m would acquire a potential energy of
Ep = 70 x 9.8 x 10 kgm2/s2 (or J)
= 6860 J
= 6.86 kJ

Kinetic energy is the mechanical work possessed by a particle or body by virtue of its motion. An object with mass m moving at a speed of v has the kinetic energy (Ek) of
Ek = (1/2) m v2
For example, a 70 kg mass moving at 14 m/s has a kinetic energy of
Ek = (1/2) 70 kg x 142 (m/s)2
= 6860 J

It can be shown that an object falling a distance of 10 m in a field of 9.8 m/s2 shall gain a speed of 14 m/s. In this process, all potential energy is converted to kinetic energy (Ep = Ek)

Skill developing problems:

1. A cat jumps down a 5-m cliff with no hesitation, but a dog doing the same may suffer serious injury, why?

2. How can the kinetic energy be stored and recovered during the braking process of a moving automobile?

3. During a marathon race, should a runner keep the same speed, run faster, or run slower on an up hill stretch of the track? What about the down hill stretch of the road?

4. A dog and a cat weighing 10.0 and 0.5 kg respectively had a free fall (no air resistance) from a cliff of 10 m in height. (1) Calculate the kinetic energies when they are just about to hit the ground. (2) Calculate the ratio of kinetic energy of the dog to that of the cat. (g = 9.8 m/s2) (Hint: K.E. = P.E. = mgh; Ans: Ek.(dog) = 990 J; ratio = 20).

Temperature Scales

1

You have used the Fahrenheit (F), Celsius (C ), and Kelvin (K) temperature scales, and know how to convert from one to another, but you might not be able to explain the principle of temperature measurement.

  • Why do we need temperature scales
    and how did these scales develop?
  • What is the principle used to measure temperature?
  • How have temperature scales affected the development of science and technology?
  • What is 0K in the Celsius and Fahrenheit scales?

Sensation for hot and cold is instinct for humans and other animals. However, sensation is subjective and circumstantial. For example, if you place one hand in cold and one hand in warm water for a while, and then put both hands in the same bucket of water, the two hands feel differently.

Peking man used fire about 500,000 years ago. Humans have recognized heat and fire at the dawn of civilization. The objective of fire at that time was to provide warmth and illumination, since cooking was not an art until much later. Despite the lack of thermometers, people in Egypt, Mesopotamia, India, and China used fire to produce metals, and to work copper, lead, tin and iron into tools. Fire played such an important role in early civilization that Plato (427-347 BC) thought it was one of four primal substances from which all other matter was derived.

During the 2nd century, the Greek physician Galen suggested a temperature scale based on boiling water and ice. Arab and Latin physicians developed a scale of 0-4 degrees for hot and cold depending on human senses. In 1688, the French physician Guillaume Amontons proposed to measure hotness and coldness by the variation in pressure of a fixed amount of gas contained in a constant volume. He defined absolute zero when the pressure is zero, and used a tube of mercury to measure the pressure. In 1701, Sir Isaac Newton (1643-1727) suggested 0 degrees for ice and 12 degrees for the human body as a temperature scale. G.D. Fahrenheit (1686-1736) proposed a temperature scale in 1714. The scale used a salt-water-ice mixture as a reference for 0, and the human body as 96 degrees. This scale had many more divisions than the one proposed by Newton, and the freezing point and boiling point of water was calibrated to be 32 and 212 degrees respectively. This finer scale greatly improved the precision of temperature measurements. The centigrade (Celsius) scale was proposed by the Anders Celsius (1701-1744) ten years after Fahrenheit’s proposal.

Using a temperature scale, Jacques-A.C. Charles (1746-1823) and Joseph L. Gay-Lussac (1778-1850) studied the expansion of gases. They found that hydrogen and most other gases expanded 1/273 of their volumes at 0oC per degree C increase. This is known as the Charles-Gay-Lussac law of gases. In general, when the pressure is held constant, the volume of a gas increases the same amount as the temperature increases each degree. William Thomson (1824-1907, known as Lord Kelvin of Glasgow) came up with the absolute temperature scale (K after Kelvin) in 1848 in conjunction with the Charles-Gay-Lussac law. Absolute zero corresponds to -273oC, and at this temperature, no heat can be extracted from the system any more.

Usually, thermometers use gases or liquids that expand upon heating. However, extreme low or high temperature measurements require instruments other than ordinary thermometers. For example, temperatures between -183 and 630oC can be determined from the electric conductance of platinum. In 1821, Thomas J. Seebeck (1770-1831) discovered that when the junctions of two dissimilar metals were placed in different temperatures, the circuit generated an electric potential (voltage). Such devices, called thermal couples, have been developed for temperature measurements. Spectra of light emitted by hot objects have also been used to determine their temperatures. Temperature measurements are an important part of scientific research and technological development.

Two bodies each equal in temperature to a third body are equal in temperature to each other.

Maxwell (19th century, now known as the 0th law of thermodynamics)

Skill developing problems:

1. On the Newton’s temperature scale of 0 for ice and water mixture and 12 for the human body temperature, what is the boiling point of water? What is the reading corresponding to absolute zero? (-88.5 N)

2. What is 0 K in the Celsius and Fahrenheit temperature scales? (-459.7 F)

3. What is the temperature at the surface of the Sun? (a few million degrees Kelvin).

Heat

Like work, heat is also an elusive quantity. Intuitively, we know that an object containing a lot of heat is hot, but the description is inadequate. After having invented and used temperature scales, humans wanted to better understand heat.

  • What is heat and how does it flow?
    How did our interpretation of heat evolve?
    What is the relationship or difference between heat and temperature?
  • How is heat stored in an object or a system?
    What is the meaning of heat capacity?
    How does heat differ from chemical energy?

In 1760, Joseph Black (1728-1799) recognized that "heat is evidently not passive; it is an expansive fluid, which dilates in consequence of the repulsion subsisting among its own particles”. He considered this caloric fluid to be indestructible and to be accumulated when matter was heated. Comparing heat with a fluid was a good step in our effort to understand heat. Black differentiates heat from hotness. Like mass and volume that describe amounts, heat is a typical additive quantity. Thus, heat, volume, and mass are extensive properties. In contrast, temperature is not a quantity measured in amount; it is a measure of the type called intensive property, as are pressure, density, heat capacity, latent heat of melting, latent heat of evaporation, etc.

With the help of a temperature scale and his caloric (weightless fluid) theory, Black defined heat capacity as the amount of calorie required for raising or lowering the temperature of a body by 1o. Furthermore, he realized latent heat of melting of a solid such as ice. He demonstrated that a fixed amount of ice always requires the same quantity of heat to melt. Now, we know that a fixed quantity of liquid also requires a certain amount of heat to evaporate. Heat capacity, latent heat of melting and heat of evaporation are also intensive properties. The caloric theory was believed for more than 100 years, until the middle of the 19th century, when the concept that heat was a fluid-like quantity could not explain phenomena related to mechanical work, radiation, and chemical reactions.

As an extensive property, the amount of heat must be precisely described. An amount of heat required to raise the temperature of 1.00 g of water from 288.5 to 289.5 K is defined as 1.00 calorie. This strict definition hints that the heat capacity for water changes with temperature, even between freezing point and boiling point. On average, the heat capacity for water is 1.00 cal g-1 K-1, whereas the heat capacity for ice is only 0.50 cal g-1 K-1.

Skill developing problems:

1. The caloric fluid concept explains what aspect of heat, but cannot explain what properties of heat?

2. On average, 1 cal. is required to raise the temperature of 1 mL water by 1 K. How many calories are required to warm up a cup (250 mL) of water (for tea) from 288 K to 363 K? (18.8 kcal.)

3. The heat of fusion for ice is 80 cal per gram (or 6.02 kJ/mole) and the heat of vaporization for water is 540 cal per gram (or 40.67 kJ/mol). The heat capacities for water and ice are 1.00 and 0.50 cal g–1 K–1 respectively. How much heat in kcal and kJ is required to convert one mole (18 g) of ice from 263 to 373 K. (Ans. 13.1 kcal or 54.6 kJ).

Figure 3

Inter-conversion of heat and mechanical work

That mechanical work can be converted to heat was discovered unexpectedly.

  • Why is heat not a fluid?
  • What is energy?
    Why is the concept of energy useful?
    How is energy stored in a body of material?
  • When energy is transferred from one place to another, what phenomena do you observe?

Sir Benjamin Thompson (1753-1814) used horse-turned machines for boring brass into cannons in the military arsenal at Munich. He observed the brass getting hot in this process, and concluded that heat is hardly a substance or fluid, but is generated by mechanical work done to the system. He recognized that heat is furnished as long as parts in it persisted moving. He calculated the equivalence between the heat generated and the mechanical work done to the system, and James P. Joule (1818-1889) who studied under J. Dalton, refined the experiments by measuring the temperature rise in water churned by a paddle driven by a descending weight. These experiments showed that heat, and mechanical work, are inter-convertible.

In 1852, Joule and Thomson discovered that temperatures of gases decrease when they are expanded. During expansions, heat is converted to mechanical work.

Since heat and mechanical work are inter-convertible, they should be treated as a single entity. This entity was called effort, living force, and travail, before the term energy was accepted. This term was coined by Thomas Young (1773-1829) in 1807, from the Greek words energia; en meaning in, and ergon, work. Since then, the term energy is used to mean mechanical work (or simply work), heat, and other forms of energy.