Example 15-1 Cycling It Off
At the end of a 15-minute session on a stationary bicycle at the gym, the bike’s display indicates that you have delivered
165 kJ of energy to the bike in the form of work. Your heart rate monitor shows that you have “burned off” 165 food
calories of energy. How much energy has your body lost to your surroundings in the form of heat?
Set Up
In this problem your body is the thermodynamic
system. You do work on your surroundings (the
bicycle), so W is positive and equal to 165 kJ.
The 165 food calories (165 kcal) that you have
“burned off” represent a decrease in your body’s
internal energy, so U is negative and equal to
2165 kcal. We’ll use the first law of thermodynamics to determine the heat Q that flows out of
your body.
Solve
First convert U from kilocalories to kilojoules.
Rearrange Equation 15-2 to solve for the
quantity of heat Q that flows into your body. A
negative value of Q means that heat flows out
of your body.
First law of thermodynamics:
(15-2)
U = Q 2 W
Your body does work
on the bicycle: W > 0.
system =
your body
Heat flows out of
your body: Q < 0.
1 kcal = 4186 J = 4.186 kJ, so
U = -165 kcal a
From Equation 15-2,
4.186 kJ
b = -691 kJ
1 kcal
Q = U + W
= 2691 kJ + 165 kJ
= 2526 kJ
This is negative, so 526 kJ of energy flows out of your body in the
form of heat as you exercise.
Reflect
Let’s look at the energy “accounting” for this exercise session. Your body expended 691 kJ of internal energy, of which
165 kJ went into doing work and 526 kJ was lost in the form of heat. One way to look at these numbers is that only
1165 kJ2 > 1691 kJ2 = 0.239, or 23.9%, of the energy that you expended went into doing work, so your body has an
efficiency of 23.9% in this situation.
Another instructive number is that 3500 kcal is the energy content of one pound (0.45 kg) of fat. If all of the 165 kcal
that you expended came from stored fat, the net result of your exercise is that you will have lost an amount of fat equal
to 1165 kcal2 > 13500 kcal>lb2 = 0.047 lb 10.021 kg, or 0.75 ounce2. Losing weight requires a lot of exercise!