13.3. Heat http://www.ck12.org
The Calorie
The amount of energy required to raise the temperature of one gram of water by one degree Celsius is defined as
onecalorie, or, as it is sometimes referred to, one “small” calorie. The calorie is therefore a measure of energy. It
is equal to about 4.186 J. Using the definition above, the caloric content of the average banana is 80,000 calories. A
more useful unit to measure food calories is called the “big” calorie, which equals 1000 “small” calories. Thus, the
average banana contains 80 “big” calories, or 80 food calories.
1000 small calories= 1 f ood calorie= 4186 J→ 1. 00 kcal= 1. 00 kC= 4186 J.Check Your Understanding
Your doctor recommends an average caloric intake of 2,000 calories per day.
How many joules is this?
Answer: Since 1 food calorie equals 4186 J:( 2000 C)( (^4186) CJ) = 8 , 372 , 000 → 8. 372 × 106 J
Illustrative Example 13.1.1
a. How long can a 60 W light bulb burn if supplied with 8. 372 × 106 J?
Answer: 60 W is the same as 60Js. Thus ,a 60 W light bulb uses 60 J every second.
If 8. 372 × 106 Jare available, then^8.^372 ×^10
(^6) J
60 Js =^139 ,^533 →^140 ,^000 s. Since there are 86,400 seconds in one
day,^13986 ,, 400533 = 1. 6149 → 1. 61 days, or close to 39 hours.
b. To what height could a 70.0 kg person climb using this much energy? SeeFigure13.4
FIGURE 13.4
A vertical climbAnswer:We know that 2,000 kcal equals 8. 372 × 106 J. So, 20% of this is 0. 20 × 8. 372 × 106 = 1. 674 × 106 J
Recall that the net work done by a climber of weight mg over a vertical displacement of∆his equal to the change in
his potential energy:
∆PE=mg∆h(Assuming the change in his kinetic energy is zero.)