Solutions to Problems - Chapter 1

1. The effect of doing work is to: B) change the amount of energy stored in a system.
The amount of energy stored in a system can only be changed by energy transfer into or out of the system. Work is one way to transfer energy (along with heat, waves, etc.) so the effect of doing work on a system is to transfer energy into the system. For example, doing work to lift an object to a height h, changes the amount of energy stored as gravitational potential energy. Pushing on a box along the floor and causing it to speed up does work on the box and, in this case, the work done increases the amount of energy stored in the system (the box) as kinetic energy.

3. A wave on a rope has a wavelength of 0.25 m is observed to be moving at a speed of 3 m/s. What is the frequency of the wave?
The velocity of a wave is equal to the product of its frequency times its wavelength: frequency times wavelength = v. In this case, wavelength = 0.25 and v = 3 m/s, so  f = v/wavelength = 3/0.25 = 12 Hz.

4. What is the wavelength of a radio wave received at 100 megahertz on your dial?
A radio wave is an electromagnetic (EM) wave, and all EM waves have the same velocity c = 3 x 10⁸ m/s. (You should know this even though the problem does not specifically state it.) A frequency of 100 megahertz is 100 x 10⁶ Hz = 10⁸ Hz. The wavelength
is then wavelength = v/f = (3 x 10⁸ )/10⁸ = 3 m.

5. What is the period of a visible light wave having a wavelength of 500 nm?
The period (T) of a wave is the reciprocal of its frequency, i.e., T = 1/f. We are not given the frequency here, but we are given the
wavelength and we know the frequency is f = v/l. Since visible light is an E&M wave, v = 3 x 10⁸ m/s and, for a wavelengthl of 500 nm
(which is 500 x 10^-9 m = 5 x 10^-7 m), we have f = (3 x 10⁸ )/(5 x 10^-7 ) = 0.6 x 10¹⁵ = 6 x 10¹⁴ Hz. Now, we can find the period as T
= 1/f = 1/(6 x 10¹⁴ ) = 0.167 x 10^-14 sec = 1.67 x 10^-15 sec.

7. Two novice homebuilders are arguing over the packing of the glass wool insulation into the walls of the home that they are
building. One of the workers argues that it would be better to pack the insulation in tightly to fill all the space between the wall-boards.
The second worker argues that it would be better to pack the insulation loosely. With which worker do you agree? Explain
your thinking.
The insulation material is most effective when it contains the maximum amount of air trapped between its fibers, because air is a
very poor thermal conductor. If the insulation is packed very tightly, the trapped air would be "squeezed out" and the insulation
properties would be reduced. Thus, it would be better to pack the insulation loosely.

9. Do you think that a thermos bottle achieves its excellent insulating properties by inhibiting conduction, convection, and/or
radiation? Explain your thinking.
A thermos bottle has excellent insulating properties because it inhibits all three forms of heat transfer. The thermos bottle is dou-ble-
walled glass, with vacuum between the walls. The two inner glass surfaces facing each other are silvered. Recall that conduc-tion
is heat transfer that occurs as a result of collisions between neighboring atoms or molecules in a solid material. By definition,
a vacuum means that there is no material medium, i.e., there are no atoms or molecules that can transfer the energy by colliding
with one another. Similarly, convection is energy transfer carried by mass transport in gases and/or liquids’Äìthe wholesale mo-tion
of the material (say, air or water) carries the energy from one place to another. If there are no atoms or molecules to carry the
energy by their motion through space, there can be no convection. Finally, the silvered walls of the thermos bottle reflects the
electromagnetic waves that would normally carry energy out of the hot liquid back into the bottle so that it cannot escape into the
outside environment.

10. You hold a strip of aluminum so that one end is in an open flame until it becomes red hot. Describe which mechanisms of
heat transfer would be involved in this process.
Energy from the hot combustion zone in the flame is transferred into the aluminum strip by conduction. Once the aluminum strip
gets hot, it radiates away energy in the form of electromagnetic radiation. The fact that it is "red hot" is evidence that red visible
light waves are being radiated (along with lots of infrared which, however, you cannot see).

11. Water conducts heat about 20 times better than does air. If 70° air feels warm and comfortable to us, why does 70° water feel
cool when we swim in it?
Because water is a better conductor than air (about 20 times better, according to the problem), the heat from your body is conduct-ed
into the water better than when you are immersed in a "sea" of air. Because the water conducts your body heat away better than
air does, the body feels cooler. This is a very similar situation to the demonstration done in class involving the alternating wood
and aluminum rings wrapped in paper. Because aluminum is a better conductor than wood, the aluminum conducts the energy
away from the hot paper more effectively than the wood does. As a consequence, the paper remains cooler over the aluminum
rings and does not char or burn as rapidly as it does in the wood sections.

12. If you were caught in freezing weather with only your own body for a heat source, would you be warmer in an igloo or in a
wooden shack?
As discussed in class, the ice crystals that make up the igloo consists of alot of trapped air which is an excellent insulator. This
trapped air inhibits conduction of energy from your body ("body heat") through the walls of the igloo much more efficiently than
in the case in a wood shack. It is really the air in the igloo ice which is absent in wood, which makes the igloo a better insulator.