Physics 161
Fall 2006
Announcements

First quiz is next Monday (10/23) and covers chapters 1-4,
homework #1 and #2. You can find a cheat sheet here - this
contains formulas for the quiz and will be the first page of the
quiz.

Please have HW#2 complete no later than 2 days late, that is, by
Sunday at 5:00 . . . It is due on Friday at 5:00pm, and you will
need to request an extension if want to to do it over the
weekend.
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Physics 161
Fall 2006
Heat Pumps and Refrigerators:
more entropy
Heat Pumps provide a means to very efficiently move heat
around, and work both in the winter and the summer
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Heat Pump Diagram
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Heat Pumps and Refrigerators:
Thermodynamics
Hot entity
(indoor air)
heat energy delivered
Th
Qh
Just a heat engine run
backwards…
delivered work:
W = Qh – Qc
conservation of energy
heat energy extracted
Cold entity
(outside air or refrigerator)
Qc
Tc
Qh heat delivered
efficiency =
=
W
work done
(heat pump)
Qc heat extracted
efficiency =
=
W
work done
(refrigerator)
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Heat Pump/Refrigerator Efficiencies


Can work through same sort of logic as before to see that:
 heat pump efficiency is: Th/(Th – Tc) = Th/T
in ºK
 refrigerator efficiency is: Tc/(Th – Tc) = Tc/T
in ºK
Note that heat pumps and refrigerators are most efficient for
small temperature differences
 hard on heat pumps in very cold climates
 hard on refrigerators in hot settings
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Example Efficiencies




A heat pump maintaining 20 ºC when it is –5 ºC outside has
a maximum possible efficiency of:
293/25 = 11.72
 note that this means you can get almost 12 times the heat
energy than you are supplying in the form of work!
 this factor is called the C.O.P. (coefficient of
performance)
A freezer maintaining –5 ºC in a 20 ºC room has a maximum
possible efficiency of:
268/25 = 10.72
 called EER (energy efficiency ratio)
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Example Labels (U.S. & Canada)
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Heat, Heat Transfer, Problems

Heat vs. temperature: heat is energy in motion and is related to
temperature change by heat capacity; temperature is a measure of
the average kinetic energy the atoms inside something have

Heat is energy in motion - we do not ask ‘how much heat does
something have in it’ (at least physicists don’t); it goes into the
energy balance described by the first law - the ‘conservation of
energy’

Controlling heat transfer is a key ingredient of ‘energy conservation’
and cooking. How is heat transferred?
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Heat Transfer: Conduction

Heat moves ‘from the hot end to the cold end’
Q = heat transferred in time t
A = cross-sectional area
= thermal conductivity
d = thickness of material
Metals, eg., copper: high thermal conductivity
Insulators, e.g., wood, low thermal conductivity
What are the units of thermal conductivity?
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Heat Conduction and Insulation R-factors



Ever shop for insulation? If so, you’ve run up against R-factors or R-values. These are
essentially d/, which is a normalized efficiency for insulation
Large R means good insulation: Q/t = A x T/R
Example: 6” of fiberglass insulation has an R-value of 19 in units of ft2-hr-oF/Btu.
With a temperature difference of 30 oF, what is the rate of heat flow through 100 square
feet of R-19 fiberglass?
Q/t = 100 ft2 x 30oF/19 ft2-hr-oF/Btu = 158 Btu/hr = 46 Watts
This ignores other forms of heat transfer. . .
Water balloon demo . . . Huh?
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Heat Transfer by Radiation

This is what we called Blackbody Radiation a last week:
F = T4 in Watts per square meter  = 5.6710-8 W/ºK4/m2

Except we did not talk about emissivity e, which is a measure of how efficiently
something radiates; black things radiate efficiently and have emissivity of ~1, white
and shiny things do not and have emissivity below 0.1.

In reality, F = e T4 and power = P = e T4 A

Black vs silver radiation demo
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Heat Transfer by Convection
Transfer of heat due to the actual motion of a fluid. You’ve seen this above your
toaster or a hot parking lot.
On-shore vs. off-shore breezes.
Convection often entails ‘rolls’ of fluid motion, with cool fluid being warmed and thus
having its density lowered in a localized region. It then rises locally, but falls elsewhere.
It is often the dominant mechanism of heat transfer in everyday life.
Geothermal convection drives plate tectonics as well as many astrophysical phenomena.
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Heat Transfer Summary

Controlling heat transfer requires careful design, taking into account
conduction, radiation, and convection.

Building codes have evolved a lot over the past several decades to require
better and better insulation - old houses lose a lot of heat compared to new
houses

On a global scale, heat transfer by convection and radiation are key
ingredients of atmospheric physics. So are latent heats . . .
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Latent Heat: Heat Associated with a Phase Change

Add heat to a solid, e.g., ice, and the temperature rises
according to the material’s specific heat: Q = m cice T

When the ice melts, the temperature remains constant
at 0oC while a latent heat of fusion of 80 cal/g is
added and the ice changes to water.

Adding additional heat to water again raises the
temperature according to the heat capacity of Q = m
cwater T

At 100oC, the water boils and the latent heat of
vaporization of 540 cal/g must be added to produce
water vapor

Adding additional heat to water vapor will raise the
temperature according to Q = m cvapor T
Latent heat of vaporization of water is unusually high. This energy play a key role in
powering hurricanes. You don’t need to boil the water – it just needs to evaporate
from the warm Gulf of Mexico to acquire the extra latent heat, which reappears when
clouds form.
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Quiz Format

10 short answer questions, similar (in some cases identical) to those in the
‘questions’ sections at the end of the chapters in the text

6 multiple choice, probably some a little bit numerical (e.g., a unit change)

2 numerical problems like those on the homework sets.

Bring a calculator.
A good way to study will be to look at the ‘questions’ and ‘problems’ sections in
chapters 1-4. If you can do all of those that can be done simply, you will be
fine.
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More. . .

A flashlight lamp connected to a battery that provides 1.4 V
draws a current of 0.10 A. What power is used by the lamp?

What is the resistance of the bulb’s filament?
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More . . .

How much mass is lost in the fission of the nuclear fuel in a
power plant in one year if the reactor operates at 1000 MW?
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More . . .
A 100 Watt light bulb has a tungsten filament with an area of
100 mm2. Estimate the temperature of the filament when
the bulb is on. (P =  T4 A;  = 5.67x10-8 W/(m2 K4), A =
area, T = absolute temperature)
Tungsten melts at ~4000K. How much power could the light
bulb handle before the filament melts?
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More . . .
100 liters of water is heated from 0oC to 100oC. How much
heat does this require? (heat capacity of water is Cp = 1
Cal/(kg oC); 1 Cal = 4.2 kJ, density of water is 1 kg/l)
How much does the mass of the water change?
If we used a 500 Watt immersion heater to heat the water,
how long would it take?
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More . . .
How much power does an adult with a surface area of 2 m2
radiate?
Assuming the heat capacity of a human is the same as that of
water (1 Cal/(kg oC)) and that the only heat loss is by radiation,
how long would it take for a 70 kg adult located in a very cool
environment to cool by 10oC?
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More . . .
A river 100 m wide, 2 m deep, and flows at 1 m/s has a
hydroelectric dam 100 m high. What is the maximum power
this dam could produce?
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More . . .
A conveyor belt delivers 100 kg of coal/minute to a height
of 20 m. How much power is required?
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More . . .

An alpha particle (helium nucleus with no electrons) is
accelerated through a potential difference of 5000 V. What is the
change in potential energy of the alpha? Give your answer in J.

How fast is the alpha particle traveling?
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Ahem . . .

Is it possible to cool your kitchen down by leaving the
refrigerator door open? I mean, the whole kitchen and for an
extended period of time.
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