Troubling Homework Problems from Ch. 5 - Ch. 7

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Under what conditions can we say that "a thermometer measures its own temperature"?
When it is at thermal equilibrium.
What pressure would you expect in a rigid container of
0°C gas if you cooled it to -273°C?
0
What happens to heat added to a system that doesn't
increase the temperature of the system?
It does external work if it leaves the system.
Which generally expands more for an equal increase in temperature: solids or liquids?
liquids
Consider two glasses, one filled with water and the
other half-full, both at the same temperature. In which
glass are the water molecules moving faster? In which is
there greater thermal energy? In which will more heat be
required to increase the temperature by 1°C?
Same, more thermal energy in the full glass, and more heat required for the full glass.
When air is rapidly compressed, why does its temperature
increase?
Work is done in compressing the air, which increases its thermal energy.
After a car is driven along a road for some distance, why
does the air pressure in the tires increase?
Friction between the tires and the road warm the air outside and inside of the tires, which increases the motion of the molecules, thereby increasing the overall pressure in the tires.
Does 1 kg of water or 1 kg of iron undergo a greater change in temperature when heat is applied? Defend your answer.
A greater change in temperature occurs for iron because it has a lower specific heat capacity.
Desert sand is very hot in the day and very cool at
night. What does this tell you about its specific heat
capacity?
Sand has a low specific heat
capacity, as evidenced by the relatively large temperature changes for small
changes in thermal energy. A substance with a high specific heat capacity, on
the other hand, must absorb or give off large amounts of thermal energy for
comparable temperature changes.
Why are incandescent bulbs typically made of very thin
glass?
Thin glass is used because temperature changes can be very sudden. If the glass were thicker, unequal expansions and contractions
would break the glass when sudden temperature changes occur.
If the winds at the latitude of San Francisco and Washington, DC, were from the east rather than from the west, why might San Francisco be able to grow only cherry trees and Washington, DC, only palm trees?
As the ocean off the coast of San Francisco cools in the winter, the lost heat warms the atmosphere it comes in contact with. This warmed air blows over the California coastline to produce a relatively warm climate. If the winds were easterly instead of westerly, the climate of San Francisco would be chilled by winter winds from dry, cold Nevada. The climate would be reversed also in Washington, DC, because air warmed by the cooling of the Atlantic Ocean would blow over Washington, DC, and produce a warmer climate in winter in that region.
Entropy is a measure of how energy spreads to disorder in
a system. Disorder increases and entropy increases. How
does this relate to opening a bottle of perfume in the corner
of a room?
The natural state of
the perfume molecules is to spread out, to reach a state of increased disorder
and increased entropy. Perfume molecules and their smell soon drift from
the corner to all parts of the room.
Suppose that water is used in a thermometer
instead of mercury. If the temperature is 4°C
and then changes, why can't the thermometer indicate
whether the temperature is rising or falling?
Water has its maximum density at 4°C;
therefore, either cooling or heating at this temperature results in an expansion
of the water. A small rise in the water level would be ambiguous and
make a water thermometer impractical in this temperature region.
What are the three common ways in which heat is transferred?
conduction, convection, radiation
How is a barefoot firewalker able to walk safely on red-hot wooden coals?
Wood is a good insulator even when hot.
By what means is heat transferred by convection?
By the movement of fluids.
Why isn't Millie's hand burned when she holds it above the escape valve of the pressure cooker?
Her hand is not in steam, but in a jet of condensed vapor that has expanded and cooled.
How does the peak frequency of radiant energy relate to the absolute temperature of the radiating source?
Peak frequency and absolute temperature are directly proportional:
f = T.
What is evaporation, and why is it a cooling process?
Evaporation is the change of phase from liquid
to gas. As fast-moving molecules in a liquid escape into the air, slower ones
on average are left behind, thereby cooling the water.
What is condensation, how does it differ from evaporation, and why is it a warming process?
Condensation
is the opposite of evaporation. Gas molecules near the surface of a liquid
are attracted to the liquid, strike it with increased KE, and thereby warm
the liquid.
Distinguish between evaporation and boiling.
Evaporation is a phase change at the surface of a liquid;
boiling is a phase change that occurs throughout a liquid, producing bubbles.
Is it the boiling of the water or the high temperature of the water that cooks food faster in a pressure cooker?
High temperature cooks food.
Why does decreasing the temperature of a liquid make it freeze?
Molecular motion slows, thus allowing molecules to bind
together.
Does a liquid release energy or absorb energy when it changes into a gas? When it changes into a solid?
A liquid absorbs energy when it changes into a gas; when a liquid changes into a solid, it gives off energy.
From greatest to least, rank the energy needed for these phase changes for equal amounts of water: (a) from ice to ice water, (b) from ice-water to boiling water, (c) from boiling water to steam.
C, B, A
Thermal equilibrium = ? = ?
temperature, KE
What does the high specific heat capacity of water have to do with the convection currents in the air at the seashore?
Because of the high specific heat capacity of water, sunshine warms water much less than it warms land. As a result, air is warmed over the land and rises. Cooler air from above the cool water takes its place and convection currents are formed. If the land and water were heated equally by the Sun, such convection currents (and the winds they produce) would not occur.
Give two reasons why pouring a cup of hot coffee into a saucer results in faster cooling.
Hot coffee poured into a saucer cools because (1) the greater surface area of the coffee permits more evaporation to take place, and (2) by the conservation of energy, the thermal energy that heats up the saucer comes from the coffee, cooling it.
If all the molecules in a liquid had the same speed, and some were able to evaporate, would the remaining liquid be cooled? Explain.
Evaporation would not cool the remaining liquid because the energy of exiting molecules would be no different from the energy of molecules left behind. Although the thermal energy of the liquid would decrease with evaporation, the energy per molecule would not change. The temperature of the liquid would not change. (The surrounding air, on the other hand, would be cooled. Molecules flying away from the liquid surface would be slowed by the attractive force of the liquid acting on them.)
When can you add heat to a substance without raising its temperature? Give an example.
You can add heat without raising the temperature
when the substance is undergoing a change of phase. Small amounts of heat added to 0°C ice or to 100°C water, for example, don't increase the temperature.
AC units contain no water whatever, yet it is common to see water dripping from operating air conditioners poking outside homes on a hot day. Explain.
No water leaks from inside the unit because water vapor in warm air condenses on its low-temperature metal surface. That's the water that drips.
When you are near an incandescent lamp, turn it on and off quickly. You feel its heat, but you find when you touch the bulb that it is not hot. Explain why you felt heat from the lamp.
The heat you felt was caused by radiation, which travels at the speed of light. Heating the glass, however, takes longer.
T or F: A good reflector is a poor radiator of heat, and a poor reflector is a good radiator of heat.
True.
What does an AC have in common with a refrigerator?
Both remove thermal energy from one place and put it in another by the phase change of a refrigerant.
If you wish to save fuel and you're going to leave your cool house for a half-hour or so on a very hot day, should you turn the AC thermostat up a bit, turn it off altogether, or let it remain at the room temperature you desire?
Turn the air conditioner off altogether to keep T small. Heat leaks at a faster rate into a cold house than into a not-so-cold house. The greater the rate
at which heat leaks into the house, the greater the amount of fuel consumed by the air conditioner.
Why is a tub of water placed in a farmer's canning cellar in cold winters to help prevent canned food from freezing?
Every gram of water that freezes releases 80 cal of thermal energy to the cellar. This continual release of energy by the freezing water keeps the temperature of the cellar from going below 0°C. Sugar and salts in the canned goods prevent them from freezing at 0°C. Only when all the water in the tub freezes will the temperature of the cellar go below 0°C and then freeze the canned goods. The
farmer must, therefore, replace the tub before or just as soon as all the water in it has frozen.
Distinguish between mass density and weight density.
Mass density is
mass per volume; weight density is weight per volume.
How does the pressure exerted by a liquid change with
depth in the liquid? How does the pressure exerted by a liquid change as the density of the liquid changes?
According to
the formula liquid pressure = density * depth, pressure increases with
an increase in depth and pressure increases with an increase in density.
Why does buoyant force act upward on an object submerged
in water?
Because pressure is greater against the bottom where water is deeper.
State Archimedes' principle.
An immersed body is buoyed up by a force equal to the weight of the fluid displaced.
If a 1-L container is immersed halfway in water, what is
the volume of the water displaced? What is the buoyant
force on the container?
0.5 L, 4.9 N
Think about what happens to the
volume of an air-filled balloon on top
of water and beneath. Then rank the
buoyant force on a weighted balloon
in water, from most to least, when
the balloon is (a) barely floating with its top at the surface, (b) pushed 1 m beneath the surface,
and (c) 2 m beneath the surface.
a, b, c
Rank the buoyant force supplied by the atmosphere on
the following, from greatest to least: (a) an elephant,
(b) a helium-filled party balloon, and (c) a skydiver at
terminal velocity.
a, c, b
Why are people who are confined to bed less likely to
develop bedsores on their bodies if they use a waterbed
rather than a standard mattress?
A person lying on a waterbed experiences
less body weight pressure because more of the body is in contact
with the supporting surface. The greater area reduces the support pressure.
Why will a block of iron float in mercury but sink in water?
Mercury is more dense (13.6 g/cm3) than iron. A block of iron will
displace its weight and still be partially above the mercury's surface. Hence
it floats in mercury. In water it sinks because it cannot displace its weight.
When the wooden block is placed in the beaker that is brim filled with water, what happens to the scale reading after water has overflowed? Answer the same
question for an iron block.
In the case of the wooden block, the weight on the scale doesn't change. The weight of the brim-full beaker is the same whether or not a block floats in it, because the block's weight equals the weight of water that
overflows. But not so with an iron block that sinks in the water and is heavier than the water displaced. The scale reading increases when the iron block is in the beaker.
The Falkirk Wheel in Scotland (see Figure 5.17) rotates
with the same low energy no matter what the weight of
the boats it lifts. What would be different in its operation
if instead of carrying floating boats it carried scrap metal
that doesn't float?
The low energy required to rotate
the Falkirk Wheel is due to balanced caissons, which weigh the same as long
as the water in them has the same depth. If nonfloating material is carried,
then balance and the associated low energy input would be problematic.
This is because only in floating does an object displace a weight of water that
matches the weight of the floating object.
A ship sailing from the ocean into a freshwater harbor
sinks slightly deeper into the water. Does the buoyant
force on it change? If so, does it increase or decrease?
The buoyant force does not
change. The buoyant force on a floating object is always equal to that object's
weight, no matter what the fluid.
The "pump" in a vacuum cleaner is merely a high-speed
fan. Would a vacuum cleaner pick up dust from a rug on
the Moon? Explain.
A vacuum cleaner
wouldn't work on the Moon. A vacuum cleaner operates on Earth because
the atmospheric pressure pushes dust into the machine's region of reduced
pressure. On the Moon there is no atmospheric pressure to push the dust
anywhere.
Drinking through a straw is slightly more difficult on top
of a high mountain. This is because the reduced atmospheric pressure is less
effective in pushing soda up into the straw.
Drinking through a straw is slightly more difficult on top
of a high mountain. This is because the reduced atmospheric pressure is less
effective in pushing soda up into the straw.
Why is it so difficult to breathe when snorkeling at a
depth of 1 m, and practically impossible at a depth of 2 m?
Why can't a diver simply breathe through a hose that
extends to the surface?
One's lungs, like an inflated balloon, are compressed when submerged in water, and the air
within them is compressed. Air will not of itself flow from a region of low
pressure into a region of high pressure. The diaphragm in one's body reduces
lung pressure to permit breathing, but this limit is strained when nearly 1 m
below the water surface. The limit is exceeded at more than 1-m deep.
Breathing through a hose that extends to the surface can't occur because air
will not move from low pressure at the surface to higher pressure below in
your lungs.
A steel tank filled with helium gas doesn't rise in air, but
a balloon containing the same helium easily does. Why?
An object rises in air only when the buoyant force exceeds
its weight. A steel tank of anything weighs more than the air it displaces, so
it doesn't rise. A helium-filled balloon weighs less than the air it displaces
and rises.
It is said that a gas fills all the space available to it. Why,
then, doesn't the atmosphere go off into space?
Some of the molecules in Earth's atmosphere do go off into
outer space—those like helium with speeds greater than the escape speed. But the average speeds of most molecules in the atmosphere are well below
the escape speed, so the atmosphere is held to Earth by Earth's gravity.
The force of the atmosphere at sea level against the outside
of a 10@m2 store window is about 1 million N. Why
doesn't this shatter the window? Why might the window
shatter in a strong wind blowing past?
The force of the atmosphere is on both sides of the window; the
net force is zero, so windows don't normally shatter under the weight of the
atmosphere. In a strong wind, however, pressure is reduced on the windward
side (Bernoulli's principle) and the forces no longer cancel to zero. Many
windows are blown outward in strong winds.
You're having a run of bad luck, and you slip quietly into
a small, calm pool as hungry crocodiles lurking at the
bottom are relying on Pascal's principle to help them to
detect a tender morsel. What does Pascal's principle have
to do with their delight at your arrival?
Part of whatever pressure you add to the
water is transmitted to the hungry crocodiles, via Pascal's principle. If the
water were confined—that is, not open to the atmosphere—the crocs would
receive every bit of the pressure you exert. But even if you were able to slip
into the pool to quietly float without exerting pressure via swimming strokes,
your displacement of water raises the water level in the pool. This ever-so-slight
rise, and the accompanying ever-so-slight increase in pressure at the
bottom of the pool, is an ever-so-welcome signal to the hungry crocodiles.
If you bring a bag of potato chips aboard an airplane,
you'll note that the unopened bag puffs up as the plane
ascends to high altitude. Why? And why is this effect
opposite to what happens to the drum in the preceding
question?
If the bag is airtight, then
whatever air is inside the bag when it is on the ground expands against the
decreased cabin pressure when the plane is aloft. The air pressure in the bag is
greater than the surrounding atmospheric pressure.
Your study partner says he doesn't believe in Bernoulli's
principle and cites as evidence how a stream of water can
knock over a building. The pressure that the water exerts
on the building is not reduced, as Bernoulli claims.
What distinction is your partner missing?
Your partner isn't distinguishing
between the internal pressure in a fast-moving fluid and the external pressure
that fluid can exert on something in its way. Bernoulli's principle refers to the
internal pressure changes in a fluid, not to pressures the fluid may exert when it
interacts with objects in the fluid. (This distinction eludes many people!)