# Energy

Skills to Develop

• Describe heat, mechanical work (including potential and kinetic energy), light, electric, and chemical energy as forms of energy.
• Use proper units for energy.
• Explain power as rate of energy conversion from one form to another.
• Use the concept of internal energy to explain how energy of a system changes.
• Calculate the change of internal energy of a system.

## Energy

Energy does not have a mass, nor a volume or shape. Thus, energy is very difficult to recognize. However, energy is everywhere. Absorption of energy causes temperature to rise, and its loss causes temperature to drop. Energy also causes the emission of electromagnetic radiations, melting, vaporization, crystallization, chemical reactions, fire, wind, and storms. Energy causes material to change and we see its effect. The changes may release heat, mechanical work (such as explosions), light (radiation energy), sound, and or electrical energy (batteries).

What is Energy?

Energy is an elusive driving force for all physical and chemical changes, and it exists in many forms such as heat, mechanical work (including potential and kinetic energy), light (radiation), sound, electric, and chemical energy. This is a simple description of energy, but not a complete one. A lot more needs to be said to do justice to explain what is energy. Please keep the question in mind and identify the effect of energy around you.

In the development of civilization, a long time passes before humans recognize what energy is. Its recognition is a relatively recent event in terms of the history. Heat was recognized very early, but its quantity was only defined after the invention of the temperature scale in 1714 by Fahrenheit (1686-1736), and in 1742 by Celsius. The quantity of potential and kinetic work was defined by Newton's theory of motion. The work of James Joule (1818-1889) led to the recognition of heat being equivalent to mechanical work.

Since energy is equivalent to mechanical work, it has the same units, J. The Joule (= 1 Newton-meter) is a very small unit, however it is equivalent to the amount of work of lifting a small apple (98 grams) vertically up one meter. In terms of heat,

$$\mathrm{1\: cal = 4.184\: J}$$

The rate of work done or energy transfer is called power, and its unit is watt.

$$\mathrm{1\: watt = 1\: J/s}$$

Your calculator may consume some milliwatt, and a computer consumes about 100 watt, as does a 100-W light bulb.

Rather recently, Albert Einstein (1879-1955) derived an equation which suggested that energy and matter are interconvertible. Energy can be converted into matter and matter can be converted into energy. Experiments have confirmed Einstein's theory to be true. Does this mean a fast-moving baseball has more mass than one that is resting? Well, this question is left for you to ponder.

Energy causes all the changes in the material world, but energy does not disappear (destroyed), nor is it ever created. This is known as the principle of conservation of energy.

### The Principle of Conservation of Energy

Energy is transmitted in the form of heat from one place to another or in the form of mechanical work (potential and kinetic energy). Both types of transmission need a medium. At the atomic and molecular level, transmission of heat is also a result of transferring of kinetic energy among atoms, molecules or ions in the medium.

Transmission of energy via no medium is a phenomena known as electromagnetic radiation, in which bundles of energy are emitted as photons of light according to Max Planck. We shall discuss this aspect of energy after we have introduced the quantum theory on the page of Electromagnetic Radiation.

Energy can be used to perform mechanical work. Energy is required to cause any change, physical or chemical. Energy is really the driving force for all changes. During the transformation from one form to another, amounts of energy remain the same. Energy cannot be destroyed or created. This is the principle of conservation of energy.

There are demonstrations to illustrate the principle of conservation of energy, but there is no proof for this theory. However, so far, those who claimed to have invented a machine that will perform work without the input of energy have been shown to be wrong.

To understand the principle of conservation of energy in the energy transfer processes, we have to isolate a system from its surroundings.

### The System and its Surrounding or Environment

A system is some thing we isolate either by imagination or by physical means. For example, a closed container with gas or liquid in it is a system; so is a machine. Anything that comes into contact with the system is called the surrounding or environment. After the isolation, we can identify material or energy to be transferred from the system into the surrounding or from the surrounding into the system. A system is isolated for the convenience of discussion, and it can be as small as a subatomic particle or as big as the entire universe.

With a defined system, we can identify energy transferred from the system to the surrounding and vice versa.

Since energy is conserved, the amount of energy contained in a system will not change, unless energy is transferred into or out of the system. To measure the energy contained in a system is very difficult, and usually a net change of energy content is more meaningful. For the purpose of evaluating the net change of energy in a system, the concept of internal energy is devised.

### Internal Energy

Internal energy, represented by $$U$$, is essentially the thermal energy contained in a system (or particles making up the system). Unless change takes place, we usually have no way of evaluating it. A change in internal energy dE is due to the transfer of energy into or out of a system, but the volume stays constant. For example, energy transferred into the system, usually heat (q) and work (w), represents an increase of internal energy, $$\Delta{U}$$, of the system. Thus,

$$\Delta{U} = q + w$$.

In the case when heat or work is transferred from the system to its surroundings, the heat and work will be treated as negative quantities, resulting in a decrease in internal energy $$U$$.

The internal energy, $$U$$, does not depend on how energy is transferred and at what rate. It is purely an accounting of energy content of the system, and as such, the internal energy, $$U$$, is called a state function. The difference of a state function depends on the final and initial states, and we represent the change by

$$\Delta{U} = E_{\textrm{final}} - E_{\textrm{initial}}$$

As an illustration, let's put some air into a tire. All the air that will be put into the tire is the system. As we pump, the volume is reduced by the pumping (compression), and work is done on the system, w. The change of $$U$$ is equal to the amount of work done to the system, $$w$$.

$$\Delta{U} = w\: (q = \textrm{0 in this case})$$

If the tire is heated, and the amount of heat transferred into it is q, additional increase E results in

$$\Delta{U} = q + w$$

On the other hand, if the tire leaks, and the air is expanded, then work is done by the system (- w) resulting in a decrease in $$U$$.

$$\Delta{U} = - w\: (q = \textrm{0 in this case})$$

If q amount of heat is transferred to the tire, and the tire does -w amount of work, then

$$\Delta{U} = q - w\: (q = \textrm{0 in this case})$$

Today, you all know that heat and work are interconvertible. In fact, we can use the same units (J) for both heat and work. In short, heat or work transferred into the system raises the internal energy, and they are treated as positive quantities. Heat transferred out of the system and work done by the system lower the internal energy, and they are treated as negative quantities.

Example 1

A radiator loses 99 J per minute. What is the internal energy loss in an hour?

Solution
The loss of internal energy is

$$\Delta{U} = \mathrm{99\: (J/min) \times 60\: (min/hr) = 5940\: J / hr}$$

Discussion
The radiator receives the same amount of energy from the engine per hour, and in reality the radiator is at a steady state. Thus the temperature is constant.

Example 2

A cup of water (250 mL) is heated from 10 to 90oC. What is the change in internal energy for the cup of water?

Solution
It is well known that 4.2 J is required to raise the temperature of 1.0 gram of water by 1oC. The density of water is 1.0 g per mL. Thus, the internal energy increase is

\begin{align} \Delta{U} &= \mathrm{4.184\: J/(g\, ^\circ C) \times 250\: g \times 80 ^\circ C} \\ &= \mathrm{83680\: J\: or\: 84\: kJ} \end{align}

Discussion
The increase in internal energy causes the temperature to increase.

The heat can be provided by electric work. In the heating process, not all energy is absorbed by the cup of water. The wasted energy does not contribute to the increase in internal energy of the cup of water.

## Confidence Building Questions

1. Brian heated a cup of milk in a microwave oven, so that its temperature raised from 4 to 50oC for his daughter. What is absorbed by the milk to raise the temperature?

Hint: energy

Skill -
Recognize what energy is. Microwaves cause water molecules to vibrate more vigorously, raising the temperature.

2. Peter drives his sports car at 110 km/hr and Mary drives her truck at 50 km/hr. Who will need a longer distance to stop? Why?

Hint: Peter. Why? See Discussion.

Discussion
Braking transforms kinetic energy into other forms of energy. More time is required to transform the larger quantity of kinetic energy of Peter's sports car, assuming the brakes are compensated for the design of the car and truck. However, the weights should also be taken into account.

3. Under what condition will a particle move at constant speed in a straight line?

Hint: When energy of the system (particle) remains constant.

Skill -
Explain the principle of conservation of energy.

4. Joule's experiments show that 4.184 J is equivalent to 1.0 cal. It is well known that 80 cal is required to melt 1.0 g of ice. How many J of energy are required to melt 18.0 g of ice (1.0 mole)?

Hint: 6025 J or 6 kJ

Skill -
Explain energy conversion and perform conversion calculations.

5. Joule's experiments show that 4.184 J is equivalent to 1.0 cal. Estimate the increase in internal energy for 18.0 g of ice after it is melted.

Hint: 6025 J or 6 kJ

Skill -
Explain energy conversion and perform conversion calculations.

6. A liter of water is heated from 10 to 90oC for coffee. What is the change in internal energy for the cup of water?

Hint: 336 kJ

Skill -
Calculate internal energy changes.

7. At a constant temperature of 273 K, if you compress 1.0 mole of gas from a pressure of 101.3 kPa to a pressure of 202.6 kPa, the work required is 1573 kJ. What is the internal energy change?

Hint: 1573 kJ

Discussion
The required work is calculated with the assumption of constant temperature. If you want to know how the work is calculated, here is the formulation:

$$w = \textrm{Ij}\, V dP = \textrm{Ij} \dfrac{R T}{P} dP = R T \ln 2$$

Here Ij stands for a definite integral from 101.3 to 202.6 kPa.

8. The temperature of a balloon containing 1 mole of $$\ce{He}$$ increased 2 K, and it expanded to maintain a constant pressure. Does internal energy for the balloon increase or decrease?

Hint: increase

Skill -
Qualitatively describe the change in internal energy.

9. A balloon is heated very slowly, and absorbs 500 kJ of heat. It expanded against a constant pressure of the atmosphere (101.3 kPa) and did 350 kJ of work. Calculate the change in internal energy, dE.

Hint: 150 kJ

Skill -
Apply $$dE = q + w$$ to solve problems.