3.1 Energy

Energy is the capacity to do work or transfer heat. All forms of energy are either kinetic or potential. Kinetic energy (E_k) is the energy of motion.

\[E_{\mathrm{k}} = \dfrac{1}{2}mv^2\] where m is the mass and v is the velocity.

One form of kinetic energy of interest to chemists is thermal energy, which is the energy associated with the random motion of atoms and molecules.

Potential energy is the energy possessed by an object by virtue of its position. There are two forms of potential energy of great interest to chemists:

Chemical energy is energy stored within the structural units of chemical substances
Electrostatic energy is potential energy that results from the interaction of charged particles

\[E_{\mathrm{el}} = \dfrac{Q_1Q_2}{d}\]

where Q₁ and Q₂ represent two charges separated by a distance, d.

Kinetic and potential energy are interchangeable – one can be converted to the other.

Although energy can assume many forms, the total energy of the universe is constant.

Energy can neither be created nor destroyed.
When energy of one form disappears, the same amount of energy reappears in another form or forms. This is known as the law of conservation of energy.

In the image below, a diver

has E_p due to macroscale position
converts E_p to macroscale E_k
converts E_k,macroscale to E_k,nanoscale (motion of water, heat)

Practice

Determine the type of energy (potential or kinetic) for each example.

A. Water in a damned-up lake
B. Water rushing through turbines
C. Moving baseball
D. Diver standing on a cliff
E. A gallon of gas

Solution

A: potential
B: kinetic
C: kinetic
D: potential
E: potential (chemical)

The SI unit of energy is the joule (J), named for the English physicist James Joule. A Joule is the amount of energy possessed by a 2 kg mass moving at a speed of 1 m s^–1.

\[E_{\mathrm{k}} = \dfrac{1}{2}mv^2 = \dfrac{1}{2}(2~\mathrm{kg})\left ( 1~\mathrm{m~s^{-1}}\right ) = 1~\mathrm{kg~m^2~s^{-2}} = 1~\mathrm{J} \]

The joule can also be defined as the amount of energy exerted when a force of 1 newton (N) is applied over 1 meter.

\[1~\mathrm{J} = 1~\mathrm{N~m}\]

Because the magnitude of a joule is so small, we often express large amounts of energy using the unit kilojoule (kJ).

\[1~\mathrm{kJ} = 10^3~\mathrm{J}\] Energy is also commonly represnted in the non-SI unit of the calorie (cal). This was due to the relationship that 1 g of water could be heated by 1 °C with exactly 1 cal of energy. The calorie is related to the joule via the following exact relationship:

\[1~\mathrm{cal} = 4.184~\mathrm{J}\]

Note that the “dietary calorie” (Cal) that is commonly used in nutrition is 1000 calories (1 kilocalorie or kcal).

\[1~\mathrm{``dietary~calorie''} = 1~\mathrm{Cal} = 1000~\mathrm{cal} = 1~\mathrm{kcal}\]