Lecture-23-11

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Temperature and Heat
Heat and Mechanical Work
Heat is another form of energy.
James Joule used a device similar
to this one to measure the
mechanical equivalent of heat:
One kilocalorie (kcal) is defined
as the amount of heat needed to
raise the temperature of 1 kg of
water from 14.5° C to 15.5° C.
Heat Capacity
The heat capacity of an object is the amount of heat
added to it divided by its rise in temperature:
Heat capacity tells you how
much heat flow for a given ΔT
Q = C ΔT
Q is positive if ΔT is positive; that is, if heat is
added to a system.
Q is negative if ΔT is negative; that is, if heat
is removed from a system.
Specific Heat
The heat capacity of an object depends on its
mass and on a property of the material itself:
the specific heat
“heat capacity per kilogram”
Specific heats of various materials
Heat capacity is
mass x specific heat
C = mc
A ceramic coffee cup, with c=1090 J/(kg K) and m =116 g, is initially at room
temperature (24.0 °C). If 225 g of 80.3 °C coffee and 12.2 g of 5.00 °C cream are
added to the cup, what is the equilibrium temperature of the system?
Assume that no heat is exchanged with the surroundings, and that the specific heat of coffee and
cream are the same as the specific heat of water.
cwater = 4186 J / (kg K)
Heat Transfer Mechanisms
Thermal equilibrium is reached by means of thermal contact, which
in turn can occur through three different mechanisms
conduction : it occurs when objects at different temperature are in
physical contact (e.g. when holding a hot potato). Faster moving
molecules in the hotter object transfer some of their energy to the
colder one
convection : this occurs mainly in fluids. In a pot of water on a
stove, the liquid at the bottom is heated by conduction. The hot
water has lower density and rises to the top, cold water from the
top falls to the bottom and gets heated, etc.
radiation : any object at non-zero temperature emits radiation (in the
form of electromagnetic waves). The effect is more noticeable when
standing next to a red-hot coal fire, or in the sun rays
Conduction
Conduction is the flow of
heat directly through a
physical material
The amount of heat Q that flows through a rod:
• increases proportionally to the cross-sectional area A
• increases proportionally to ΔT from one end to the other
• increases steadily with time
• decreases inversely with the length of the rod
The constant k is called
the thermal conductivity
of the material
Some Typical Thermal Conductivities
Substances with high
thermal conductivities
are good conductors of
heat; those with low
thermal conductivities
are good insulators.
Two metal rods—one lead, the other copper—are connected in series, as shown.
Note that each rod is 0.525 m in length and has a square cross section 1.50 cm on a
side. The temperature at the lead end of the rods is 2.00°C; the temperature at the
copper end is 106°C.
(a) The average temperature of the two ends is 54.0°C. Is the temperature in the
middle, at the lead-copper interface, greater than, less than, or equal to 54.0°C?
Explain.
(b) find the temperature at the lead-copper interface.
kPb = 34.3 W / (kg-m)
kCu = 395 W / (kg-m)
Two metal rods—one lead, the other copper—are connected in series, as shown.
Note that each rod is 0.525 m in length and has a square cross section 1.50 cm on a
side. The temperature at the lead end of the rods is 2.00°C; the temperature at the
copper end is 106°C.
(a) The average temperature of the two ends is 54.0°C. Is the temperature in the
middle, at the lead-copper interface, greater than, less than, or equal to 54.0°C?
Explain.
(b) find the temperature at the lead-copper interface.
kPb = 34.3 W / (kg-m)
kCu = 395 W / (kg-m)
Assumptions:
•The
end points are infinite heat reservoirs... so their temperature doesn’t
change for this exercise
•The temperature is constant in time at every point. This is not true at
moment of thermal connection. We are solving the “steady state”
condition, when the temperature at each point doesn’t change.
Two metal rods—one lead, the other copper—are connected in series, as shown.
Note that each rod is 0.525 m in length and has a square cross section 1.50 cm on a
side. The temperature at the lead end of the rods is 2.00°C; the temperature at the
copper end is 106°C.
(a) The average temperature of the two ends is 54.0°C. Is the temperature in the
middle, at the lead-copper interface, greater than, less than, or equal to 54.0°C?
Explain.
(b) find the temperature at the lead-copper interface.
kPb = 34.3 W / (kg-m)
kCu = 395 W / (kg-m)
(a)
- The heat (per unit time) through the
lead must equal that through the copper
- The lead has a smaller thermal
conductivity than the copper
The lead requires a larger temperature difference across it
than the copper, to get the same heat flow. So TJ > 54o C
Two metal rods—one lead, the other copper—are connected in series, as shown.
Note that each rod is 0.525 m in length and has a square cross section 1.50 cm on a
side. The temperature at the lead end of the rods is 2.00°C; the temperature at the
copper end is 106°C.
(a) The average temperature of the two ends is 54.0°C. Is the temperature in the
middle, at the lead-copper interface, greater than, less than, or equal to 54.0°C?
Explain.
(b) find the temperature at the lead-copper interface.
(b)
kPb = 34.3 W / (kg-m)
kCu = 395 W / (kg-m)
Convection
Convection is the flow of fluid due to a difference
in temperatures, such as warm air rising. The
fluid “carries” the heat with it as it moves.
Radiation
All objects give off energy in the form of radiation, as
electromagnetic waves (light) – infrared, visible light,
ultraviolet – which, unlike conduction and convection,
can transport heat through a vacuum.
Objects that are hot
enough will glow – first
red, then yellow, white,
and blue.
The surface of the Sun has a temperature of 5500 oC.
(a) Treating the Sun as a perfect blackbody, with an emissivity of 1.0, find the
power that it radiates into space. The radius of the sun is 7.0x108 m, and the
temperature of space can be taken to be 3.0 K
(b) the solar constant is the number of watts of sunlight power falling on a
square meter of the Earth’s upper atmosphere. Use your result from part (a) to
calculate the solar constant, given that the distance from the Sun to the Earth is
1.5x1011 m.
The surface of the Sun has a temperature of 5500 oC.
(a) Treating the Sun as a perfect blackbody, with an emissivity of 1.0, find the
power that it radiates into space. The radius of the sun is 7.0x108 m, and the
temperature of space can be taken to be 3.0 K
(b) the solar constant is the number of watts of sunlight power falling on a
square meter of the Earth’s upper atmosphere. Use your result from part (a) to
calculate the solar constant, given that the distance from the Sun to the Earth is
1.5x1011 m.
(a)
(b)
emissivity
Heat Conduction
Given your experience of
what feels colder when you
walk on it, which of the
surfaces would have the
highest thermal
conductivity?
a)
b)
c)
d)
a rug
a steel surface
a concrete floor
has nothing to do with
thermal conductivity
Heat Conduction
Given your experience of
what feels colder when you
walk on it, which of the
surfaces would have the
highest thermal
a)
b)
c)
d)
a rug
a steel surface
a concrete floor
has nothing to do with
thermal conductivity
conductivity?
The heat flow rate is k A (T1 − T2)/l. All things being
equal, bigger k leads to bigger heat loss.
From the book: Steel = 40, Concrete = 0.84,
Human tissue = 0.2, Wool = 0.04, in units of J/(s.m.C°).
Chapter 17
Solids
Phase Changes
Thermal Processes
We’ve been dealing with fluids (gases or liquids), but this chapter
describes some behaviors from the solid phase of matter as well.
Solids
(The topics are not so deep, but thy are on the MCAT...)
Solids and Elastic Deformation
Solids have definite shapes (unlike fluids), but
they can be deformed. Pulling on opposite ends
of a rod can cause it to stretch:
Stretching / Compression of a Solid
The amount of stretching
will depend on the force;
Υ is Young’s modulus
and is a property of the
material:
The stretch is proportional to the
force, and also to the original length
The same formula works for
stretching or compression (but
sometimes with a different Young’s
modulus)
Note: Larger modulus = smaller change
(for same force)
Shear Forces
Another type of deformation is called a shear
deformation, where opposite sides of the object
are pulled laterally in opposite directions.
The “lean” is proportional to the force,
and also to the original height
Shear Modulus
S is the shear modulus.
Uniform Compression
Under uniform pressure, an
object will shrink in volume
Here, the proportionality constant,
B, is called the bulk modulus.

Stress and Strain
The applied force per unit
area is called the stress,
and the resulting
deformation is the strain.
They are proportional to
each other until the
stress becomes too
large; permanent
deformation will then
occur.
Phase Changes
Kinetic Theory and
Ideal Gases
Isotherm
PiVi = PfVf
= N Kav
The square root of (v2)av is called
the root mean square (rms) speed.
Maxwell Distribution
of molecular speed at
a given temperature
Distribution of Molecular Speed
Some molecules will have speeds exceeding the
planetary escape velocity!
Lighter molecules will have higher speeds (at the
same temperature) and so will leave the planet more
quickly.
This is why less massive planets
have thin, or no, atmosphere...
and why earth has little H2 in the
atmosphere, but Jupiter has
plenty
Evaporation
Molecules in a liquid can sometimes escape
the binding forces and become vapor (gas)
Phase Equilibrium
If a liquid is put into a sealed container so that there
is a vacuum above it, some of the molecules in the
liquid will vaporize. Once a sufficient number have
done so, some will begin to condense back into the
liquid. Equilibrium is reached when the numbers in
each phase remain constant.
Vapor Pressure
The pressure of the gas when it is in equilibrium with
the liquid is called the equilibrium vapor pressure,
and will depend on the temperature.
A liquid boils at the temperature at which its vapor
pressure equals the external pressure.
Boiling Potatoes
Will boiled potatoes cook
faster in Charlottesville or in
Denver?
a) Charlottesville
b) Denver (the “mile high” city)
c) the same in both places
d) I’ve never cooked in Denver, so
I really don’t know
e) you can boil potatoes?
Boiling Potatoes
Will boiled potatoes cook
faster in Charlottesville or in
Denver?
a) Charlottesville
b) Denver (the “mile high” city)
c) the same in both places
d) I’ve never cooked in Denver, so
I really don’t know
e) you can boil potatoes?
The lower air pressure in Denver means that the water
will boil at a lower temperature... and your potatoes will
take longer to cook.
Phase Diagram
The vapor pressure curve is only
a part of the phase diagram.
There are similar
curves describing the
pressure/temperature
of transition from
solid to liquid,
and solid to gas
When the liquid reaches the critical point,
there is no longer a distinction between liquid
and gas; there is only a “fluid” phase.
Fusion Curve
The fusion curve is the
boundary between the solid
and liquid phases; along that
curve they exist in equilibrium
with each other.
One of these two fusion curves has a
shape that is typical for most materials,
but the other has shape specific to water.
Curve 1
Which is which?
(a) Curve 1 is the fusion curve for water
(b) Curve 2 is the fusion curve for water
(c) Trick question: there is no fusion curve
for water!
Curve 2
Fusion Curve
The fusion curve is the
boundary between the solid
and liquid phases; along that
curve they exist in equilibrium
with each other.
One of these two fusion curves has a
shape that is typical for most materials,
but the other has shape specific to water.
Curve 1
Which is which?
(a) Curve 1 is the fusion curve for water
(b) Curve 2 is the fusion curve for water
(c) Trick question: there is no fusion curve
for water!
Curve 2
Ice melts under pressure!
This is how an ice skate works
Fusion curve for water
Phase Equilibrium
The sublimation curve marks the boundary
between the solid and gas phases.
The triple point is where all three phases are
in equilibrium.
Heat and Phase Change
When two phases coexist, the temperature
remains the same even if a small amount of heat
is added. Instead of raising the temperature, the
heat goes into changing the phase of the
material – melting ice, for example.
Latent Heat
The heat required to convert from one phase to
another is called the latent heat.
The latent heat, L, is the heat that must be added
to or removed from one kilogram of a substance
to convert it from one phase to another. During
the conversion process, the temperature of the
system remains constant.
Latent Heat
The latent heat of fusion is the heat needed to go
from solid to liquid;
the latent heat of vaporization from liquid to gas.
Boiling Potatoes
Will potatoes cook faster if the
water is boiling faster?
a) Yes
b) No
c) Wait, I’m confused. Am
I still in Denver?
Boiling Potatoes
Will potatoes cook faster if the
water is boiling faster?
a)
Yes
b)
No
c)
Wait, I’m confused.
Am I still in Denver?
The water boils at 100°C and remains at that temperature until all
of the water has been changed into steam. Only then will the
steam increase in temperature. Because the water stays at the
same temperature, regardless of how fast it is boiling, the
potatoes will not cook any faster.
Follow-up: How can you cook the potatoes faster?
You’re in Hot Water!
Which will cause more severe
burns to your skin: 100°C
water or 100°C steam?
a) water
b) steam
c) both the same
d) it depends...
You’re in Hot Water!
Which will cause more severe
burns to your skin: 100°C
water or 100°C steam?
a) water
b) steam
c) both the same
d) it depends...
Although the water is indeed hot, it releases only 1 cal/(gK) of heat
as it cools. The steam, however, first has to undergo a phase
change into water and that process releases 540 cal/g, which is a
very large amount of heat. That immense release of heat is what
makes steam burns so dangerous.
Phase Changes and Energy Conservation
Solving problems involving phase changes is
similar to solving problems involving heat
transfer, except that the latent heat must be
included as well.
Water and Ice
You put 1 kg of ice at 0°C
a) 0°C
together with 1 kg of water
b) between 0°C and 50°C
at 50°C. What is the final
c) 50°C
temperature?
– LF = 80 cal/g
– cwater = 1 cal/g °C
d) greater than 50°C
Water and Ice
You put 1 kg of ice at 0°C
a) 0°C
together with 1 kg of water
b) between 0°C and 50°C
at 50°C. What is the final
c) 50°C
temperature?
d) greater than 50°C
– LF = 80 cal/g
– cwater = 1 cal/g °C
How much heat is needed to melt the ice?
Q = mLf = (1000 g)  (80 cal/g) = 80,000 cal
How much heat can the water deliver by cooling from 50°C to 0°C?
Q = cwater m T = (1 cal/g °C)  (1000 g)  (50°C) = 50,000 cal
Thus, there is not enough heat available to melt all the ice!!
Ice Cold Root Beer
You have neglected to chill root
beer for your son’s 5th-birthday
party. You submerge the cans
in a bath of ice and water as you
start dinner. How can you hurry
the cooling process?
a) Add more ice to the icewater
b) add salt to the icewater
c) hold the icewater in an
evacuated chamber
(vacuum)
d) Jump in the car and drive to a
nearby convenience store
Ice Cold Root Beer
You have neglected to chill root
beer for your son’s 5th-birthday
party. You submerge the cans
in a bath of ice and water as you
start dinner. How can you hurry
the cooling process?
a) Add more ice to the icewater
b) add salt to the icewater
c) hold the icewater in an
evacuated chamber
(vacuum)
d) Jump in the car and drive to a
nearby convenience store
Not a), because ice water at 1 atm is zero degrees, no matter the
proportion of water and ice
Not c), because ice is less dense than water so you will raise the melting
point when you reduce the pressure. This will allow the water to get a
little warmer than 0o
Not d), because you’ll forget your wallet and it will end up taking more
time
b) because salt interferes with the formation of ice. This barrier to the
solid phase lowers the fusion temperature, and so reduces the
temperature of the ice water. (This is why you salt the sidewalk in winter.)
Again: explaining why putting the ice/water under
vacuum won’t help the root beer chill faster
Fusion curve
for most stuff
remember: water is weird: it melts
under pressure, and freezes under
vacuum, when near the fusion curve
Fusion curve for water
The larger ΔT, the more heat transfers
per unit time. Thus, the colder the ice
bath, the faster the root beer will chill,
and the warmer the bath, the slower the
root beer will chill
1
ΔP
2
ΔT
When two states exist in the same
system (like, ice and water), the
system MUST be on the equilibrium
curve (in the case, the fusion curve).
Fusion curve for water
As pressure goes lower, the ice/water
mixture will ride the fusion curve from
point 1 to point 2.
This implies that temperature goes up.
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