Definition of energy and units of its measurement (kcal
Answers
Energy is the ability to do work. Think about it: when you have a lot of energy, you can do a lot of work; but if you’re low on energy, you don’t want to do much work. Work (w) itself is defined as a force (F) operating over a distance (Δx):
w = F × Δx
In SI, force has units of newtons (N), while distance has units of meters. Therefore, work has units of N·m. This compound unit is redefined as a joule (J):
1 joule = 1 newton·meter
1 J = 1 N·m
Because energy is the ability to do work, energy is also measured in joules. This is the primary unit of energy we will use here.
How much is 1 J? It is enough to warm up about one-fourth of a gram of water by 1°C. It takes about 12,000 J to warm a cup of coffee from room temperature to 50°C. So a joule is not a lot of energy. It will not be uncommon to measure energies in thousands of joules, so the kilojoule (kJ) is a common unit of energy, with 1 kJ equal to 1,000 J.
An older—but still common—unit of energy is the calorie. The calorie (cal) was originally defined in terms of warming up a given quantity of water. The modern definition of calorie equates it to joules:
1 cal = 4.184 J
One area where the calorie is used is in nutrition. Energy contents of foods are often expressed in calories. However, the calorie unit used for foods is actually the kilocalorie (kcal). Most foods indicate this by spelling the word with a capital C—Calorie. Figure 7.1 "Calories on Food Labels" shows one example. So be careful counting calories when you eat!
EXAMPLE 1
The label in Figure 7.1 "Calories on Food Labels" states that the serving has 38 Cal. How many joules is this?
Solution
We recognize that with a capital C, the Calories unit is actually kilocalories. To determine the number of joules, we convert first from kilocalories to calories (using the definition of the kilo- prefix) and then from calories to joules (using the relationship between calories and joules). So
38 kcal × 1,000 cal1 kcal × 4.184 J1 cal=160,000 J