# Energy: A Derived Unit

Energy is another unit that is derived from the basic units. Energy is defined as the capacity to do work or to supply heat. Energy is classified as either potential energy (EP) or kinetic energy (EK). Kinetic energy is the energy of motion. The amount of kinetic energy in an object that is moving with mass (m) in kg and velocity (v)in m/s is given by the following equation:$$\mathbf{E_K\;=\;\frac{1}{2}\;m\textit{v}^2}$$From the equation, we see that the greater the velocity and mass, the larger the kinetic energy. A ball that is thrown from a greater height will have a larger kinetic energy than the same ball that is thrown from a shorter height. The mass in both cases is the same, but the ball that is thrown from the greater distance has a greater velocity, therefore, more kinetic energy. Potential energy is stored energy due the object’s relative position. When a ball is dropped from some height, it has potential energy. Once the ball is dropped, the potential energy decreases while the kinetic energy increases. We will talk more about energy in a later chapter.

There are many units for energy. From the above formula, the units would be $$kg\cdot{m^2}/s^2$$If a person’s body mass is 65.8 kg and she is running at a velocity of 5.6 m/s, her kinetic energy would be 1.03 x 103 (kg·m2)/s2$$E_K\;=\;\frac{1}{2}\;m\textit{v}^2\;=\;\frac{1}{2}\times65.8\;kg\times\left(5.6\;\frac{m}{s}\right)^2\;=\;\mathbf{1.03\times\;10^3\;kg\cdot{m^2}/s^2}$$

The joule (J) is the SI unit for energy. In chemistry, we frequently use kilojoules (kJ). Other units include the calorie (cal) which is equivalent to 4.184 joules (exact).

1 cal = 4.184 J and 1 kcal = 4.184 kJ

In nutrition, the food calorie is used, the Calorie (Cal) with a capital C. One food calorie is equivalent to 1000 calories, or 1 kcal.

1 Cal = 1000 cal = 1 kcal = 4.184 kJ

On a food label, the energy content of food is measured in Calories (Cal). So, that 325 Cal donut is actually 325 kcal or 325,000 calories.

## EXERCISES: Energy Units

1. A medium size glazed donut contains 255 Calories. How many kJ does this donut contain? How many hours could the energy in the donut light a 100 watt lightbulb? (1 watt = 1 J/s)
Check Answer and/or View Worked out Solution

2. Convert 686 J to calories. Convert 686 J to Calories.
Check Answer and/or View Worked out Solution for Exercise 2