Transcript Slide 1

Environmental Physics
Chapter 4:
Heat
Copyright © 2008 by DBS
Introduction
~20% of all the energy
in US is used for
heating and cooling
buildings
Residential sector uses
50% for space heating
Energy (conservation)
efficiency should be
first step in dealing
with environmental
impacts…
Figure 4.1: U.S. household energy consumption by
end use. 1 Quad = 1015 Btu.
Introduction
•
Thermodynamics – study of heat and work
Heat and Work and the First Law
•
Total Energy, E:
E = KE + PE + TE + chemical energy + electrical energy
•
Heat (Q) and work (W) are the only ways to add energy to an object to change its total E,
1st law of thermodynamics:
Won+ Qto = Δ(KE + PE + TE + chemical energy + electrical energy) = ΔE
•
Law of Conservation of Energy:
The work done on a system plus the heat added to it is equal to the change in the total energy of
that system
or Energyin = Energyout
Heat and Work and the First Law
•
Important discovery of the 18th century:
heat is the transfer of energy between two bodies due to temperature differences
•
Previously, heat was mistakenly thought to be a material fluid, called “caloric” that would flow from
a hot body into a cold one, causing an increase in temperature and mass
•
British physicist James Joule, in a series of highly accurate experiments, provided conclusive
evidence that heat is a form of energy in transit and that it can cause the same changes in a body
as work
Heat and Work and the First Law
•
Equivalence between mechanical work and
heat
•
Joule measured the increase in temperature
of a water bath when a paddle wheel was
turned
•
Observed the same effect (rise in water
temperature) either with the performance of
work or by addition of heat
•
Units are Joules or ft.lbs
(heat is a form of Energy)
Figure 4.2: Relationship between work and heat.
A temperature change in the water can be caused
either by letting the weight drop (causing the
blades to rotate) or by adding heat from the gas
burner.
Temperature and Heat
Temperature
•
Property of an object, much like color and shape
•
measurement of average KE of molecules
•
Cannot tell us the amount of energy in a substance, since it is independent of mass
Temperature and Heat
•
Melting point ice
Because the temperature scales have different zero
points, formulas must be used to carry out the
conversions
K = ºC + 273.15
ºC = K - 273.15
ºF=
ºC =
9 (ºC)
+ 32
or
1.8(ºC) + 32
or
(ºF - 32)
5
5
9
(ºF - 32)
1.8
Farenheit, Celcius and Kelvin Scales
Melting point ice
Example Temperature Conversions
1. Convert 350 oF to oC and K
oC
= (350 - 32 )(5/9) = (318)(5/9)
K = 177 + 273 = 450 K
2. Convert -40 oC to oF
oF
= (9/5)(-40) + 32 = 9(-8) + 32 =
-72 + 32= - 40o F
3. Convert 298 K to oC
oC
= 298 - 273 = 25 oC
= 177 oC
Temperature and Heat
Heat
•
measure of total energy content of vibrating molecules (KE and PE)
•
can tell us the amount of energy in a substance, since it is dependent on mass
•
governed by law conservation of energy – Joule’s exp.
Heat is energy that flows from one object to another when there is a difference in
temperature between the objects
Temperature determines the direction of heat flow
hotter → cooler object
Heat and Temperature
•
objects can have the same temperature but different amounts of heat
Steam burn – temp. is equal
but heat content is greater
Figure 4.4: Thermal energy. (a) If both brick assemblies
are heated in a kiln for several hours, they will have the
same temperature, but the larger array will store nine
times as much thermal energy as the smaller one.
Temperature and Heat
Specific heat capacity (c)
•
When heat is added to a substance, we usually find an increase in temperature
•
heat energy (joules) required to raise 1 g of a substance up by 1 °C (or 1 K)
•
different substances require different amounts of heat
•
Large c of water makes it an excellent coolant
•
substances with small specific heats absorb little energy when warming and give off little energy
when cooled
Why is c for H2O so much
more than Cu?
Heat and Temperature
Heat Capacity
When the samples are both heated by 1 °C, the addition to the KE (motion of molecules) is the same
For water, more energy must be added to the PE (energy from intermolecular forces) part of internal energy
Temperature and Heat
•
What factors are important?
– Mass (m)
– Temperature change, T = Tf –Ti
– I.D. of substance, steel, water, (specific heat capacity, c)
•
Heat gained or lost,
Q = mcT
Iron’s ability to store heat is less than
waters
Question
What is more effective in cooling your cup of coffee, 100 g aluminum or 100 g milk?
Aluminum has lower c than milk (which is mostly water). The aluminum absorbs less heat
from the coffee for each degree of temperature that it changes than the milk does.
Question
Calculate the heat energy required to raise the temperature of 24.5 g of mercury from
5.0 oC to 35.2 oC
T = 35.2 - 5.0 = 30.2
m = 24.5 g
c = 0.14 kJ
kg K
T = 35.2 - 5.0 = 30.2
Q = mcT
Q = (0.14 kJ) (0.0245 kg) (30.2 K ) = 0.10 kJ
kg K
Question
A kettle full of water is rated at 2 kW and starting at room temperature (25 ºC) takes 4
minutes to boil.
(i) How much energy is used?
(ii) How much water was boiled?
2 kW = 2 kJ / s
E = Pt = 2 kJ / s x 240 s = 480 kJ
Q = mcT
Q = 480 kJ = (m) (4.2 kJ ) (75 K )
kg K
 m = 1.5 kg
Question
Which object experiences the greatest temperature change?
Assume equal masses and heat losses.
Substance
Specific Heat
Capacity
Marble
0.88
Aluminum
0.91
Copper
0.380
ΔT = Q
mc
Temperature and Heat
•
•
Adding heat may not
increase the temperature!
May change state of matter
At the boiling / melting temperature, adding
heat energy changes state WITHOUT
RAISING THE TEMPERATURE
Temperature and Heat
Latent Heat
•
Latent heat = energy needed to change state
(solid, liquid, gas) without affecting temperature
e.g. Energy needed to evaporate water is released when water condenses
e.g. Energy needed to melt ice is released when water freezes
•
Sensible heat = heat that results in temperature change
Substance
Latent heat
fusion
(kJ / kg)
Latent heat
evaporation
(kJ / kg)
Water
335
2260
Lead
23
858
Latent heats are high
compared with specific
heat capacity
– intermolecular bonds
must be broken
Aluminum
393
10,500
Q = m Lf
Question
How much thermal energy in joules must be absorbed by 50 g of ice at 0 ºC to melt it?
Q = m Lf
= 0.050 kg x 334 kJ/kg = 16700 J
How much thermal energy will be released when
50 g of water freezes?
16700 J
Temperature and Heat
Heat liberated
Heat absorbed
At the boiling / melting temperature, adding heat energy changes state
WITHOUT RAISING THE TEMPERATURE
Question
If the specific heat capacity of ice is 2.1 kJ kg-1 K-1, how much heat would have to be added
to 200 g of ice, initially at -10 °C to raise the ice to the melting point and completely melt the
ice?
Total energy = Qraise + Qmelt
Total energy = mc T + m Lf
= (0.200 kg x 2.1 kJ kg-1 K-1 x 10 K) + (0.200 x 334 kJ kg-1)
= 4.2 kJ + 66.8 kJ = 71 kJ
End
• Review
Heat Transfer Principles
Figure 4.7: Heat flows when
there is a temperature
difference ΔT.
In this case,
ΔT = 70° − 50° = 20°F
Heat Transfer
• One of two ways in which energy can be transferred to a body
• Occurs when there is a temperature difference
• Occurs through conduction, convection and/or radiation
Heat Transfer Principles
Conduction
•
Conduction – movement of heat through a solid
substance, exchange of thermal energy between
atoms
•
Most important in solids
•
Block demonstration
Figure 4.8: Heat is transferred by conduction
through the metal spoon from the hot coffee to
the colder fingers.
Demo
Why does B melt the ice quicker than the
warm block?
Metal conducts heat more readily than wood,
so more heat flows from your hand into the
metal than the wood. Since contact with the
metal cools your hand more rapidly the metal
block feels colder.
Heat Transfer Principles
Conduction
•
•
Depends on temperature gradient, size of conductor and conductivity
Rate of heat transfer by conduction (Qc/t)
Where Q = heat (J) transferred in time t (s), k = thermal conductivity (W m-1 K-1), A =
surface area, δ = thickness, T1 and T2 are temperatures on each side
Heat Transfer Principles
Conduction
•
Rate of heat transfer by conduction (Qc/t)
Q = kA(T2 – T1)
t
δ
•
Good insulators e.g. polystyrene, wool jumpers
rely on incorporating air into structure
Substance
Thermal
Conductivity
W m-1 K-1
Diamond
1000
Copper
401
Aluminum
210
Iron
76
Glass
1.1
Brick
0.13
Water
0.62
Air
0.024
Heat Transfer Principles
Conduction
•
Rate of heat transfer by conduction (Qc/t)
Q = kA(T2 – T1)
t
δ
•
To reduce heat loss:
– Reduce T2
– Reduce A
– Increase δ
Figure 4.10: Percentage of energy saved by lowering the
thermostat from 72°F to the values shown on the curved
lines, for the time periods shown.
Heat Transfer Principles
Convection
•
Gases and fluids molecules are too far apart for heat to conduct
Figure 4.11: Convection currents in water.
Heat Transfer Principles
Convection
Demo
•
Galilean thermometer
– Liquids change density when heated
Transmission of Heat
Convection
•
•
Warm fluid expands,
density decreases and
it tends to rise
Ocean currents and
winds redistribute heat
from the tropics to the
poles
Heat Transfer Principles
Convection
•
May be natural (density differences) or assisted by wind
Figure 4.12: Heat transfer through a double-pane
window.
Heat Transfer Principles
Convection
•
Convection currents are important in some types of solar heating systems
Figure 4.13: Solar air heater for use in a window.
Transmission of Heat
Radiation
•
EM radiation is transferred not through matter, but through electrical and magnetic
fields
-Self propagating as it moves
through space
- Electrical charges are
accelerated
- Carries energy and momentum
which may be imparted on
interaction with matter
- does not require a medium in
which to travel
http://www.edumedia.fr/a185_l2-transverse-electromagnetic-wave.html
Transmission of Heat
Radiation
3 Hz
•
Classified according to frequency
v=fλ
Where:
v = speed of light = 3 x 108 (m/s),
f = frequency (Hz or cycles s-1),
λ = wavelength (m)
Different types of EM radiation all have the same
velocity in a vacuum
3.0 x 108 m/s = 1.1 billion km/h = 671 million mph
1 Hz
Question
What is the wavelength of a cell phone using the microwave frequency (GHz)?
f x λ = 3.0 x 108
λ = 3.0 x 108 /109 = 0.3 m
Figure 4.15: The electromagnetic spectrum, shown as a function of wavelength.
Fig. 4-15, p. 112
Transmission of Heat
Radiation
•
•
•
•
All objects above absolute zero (0 K) emit radiation
Amount of energy emitted from an object is proportional to its temperature
Humans, animals, the Earth etc. and basically anything < 1000 °C emit IR
Sun’s surface ~ 6000 °C emits primarily visible radiation + some IR and UV
cf.
Sun emits majority
short-wave (SW)
radiation = visible
Earth emits majority
long-wave (LW) radiation
= Infra-red
Stefan-Boltzman
and Wien’s laws
Transmission of Heat
Radiation
•
For a body to maintain a certain temperature, Energyin=Energyout
At night a body continues
to radiate heat
– radiative cooling
Figure 4.17: The equilibrium temperature of an object is
maintained if the energy input is equal to the energy output.
•
•
•
Convection – movement of heat through a fluid (liquids and gases) brought about by changes
in temperature affecting density
Conduction – movement of heat through a solid substance, exchange of thermal energy
between atoms
Radiation – transfer of heat energy via electro-magnetic waves through a vacuum
Figure 4.18: A hot-water radiator as an illustration of heat transfer via
conduction, convection, and radiation.
Fig. 4-18, p. 115
End
• Review
Heat Engines
•
“heat engines” – devices in which heat is converted into useful work
e.g. automobile, electrical generating plant
•
Requires a source of heat, e.g. burning a fuel, nuclear, solar etc.
•
The flow of heat proceeds through the “working fluid” (gas or liquid)
Heat Engines
•
Energy flow diagram for a heat engine:
Since energy is conserved heat leaving the source (QH) is equal
to the heat entering the sink (QC) plus work done (W)
QH = QC + W
and
W = QH - QC
•
Higher TH and lower TC the higher the work output
•
Energy available for work comes from a decrease in the
total energy of the working fluid
Figure 4.19: A heat engine
transforms heat into work.
Heat Engines
•
Open cycle – working fluid is exhausted into environment
e.g. 4-stroke gasoline
– Intake
– Compression
– Power (volume expansion of gas)
– Exhaust
Heat Engines
•
Closed cycle – working fluid is sent back to the heat source to start the cycle over
e.g. steam turbine – working fluid = water
QH
Heat into plant
(fuel combustion)
=W
= net work out
(electricity)
+ QC
+ net heat out
(of condenser)
W comes from dec. in
ΔE of the steam,
condenser provides
low-temp. sink
Heat Engines
Types of heat engines:
Working fluid
changes state
Working fluid
remains a
gas (air)
Heat Engines
•
Ocean Thermal Conversion (OTEC)
Figure 4.20: Ocean Thermal Energy Conversion (OTEC). The
temperature difference between waters on the top of the water and
down deep allows one to construct a heat engine.
The Second Law of Thermodynamics
•
•
Why doesn’t book lying on a table take thermal energy from the table and convert it into kinetic
energy (work)?
1st law of thermodynamics doesn’t prevent this form happening!
Figure 4.21: Impossibilities according to the second law of thermodynamics.
(a) Heat withdrawn from the table is converted into mechanical energy—the
kinetic energy of the block, (b) Heat from sea water is converted into
electrical energy (the resulting ice cubes are discarded).
The Second Law of Thermodynamics
•
Second law of thermodynamics:
for any spontaneous process, the entropy (disorder) of an isolated system can only increase or stay
the same, but never decrease
•
Important statements that follow from the second law:
– Heat can flow spontaneously only from a hot source to a cold source
– No heat engine can be constructed in which heat from a hot source is converted entirely to
work. Some heat has to be discharge to a sink at a lower temperature (cf. previous examples)
The Second Law of Thermodynamics
•
The efficiency (η) of an energy conversion process is defined as:
η = Eout/Ein x 100 %
•
Principle of conservation of energy says that the work output (energy out) equals the heat input
minus the heat transferred out (W = QH – QC):
Efficiency = W = QH – QC
QH
QH
= 1 – (QC / QH)
x 100%
x 100%
If some heat is transferred out to a cold sink, then we can never have a 100% efficient process
Therefore we will never have perpetual motion machines…
The Second law of Thermodynamics
Maximum Efficiency
•
If some heat has to be discarded, what is the best we can do?
The Second law of Thermodynamics
Maximum Efficiency
•
•
Upper temperature limit is 500 ºC (restricted by engineering, pollution and corrosion), exhaust
temperature 100 º C
Max possible efficiency for a heat engine (Carnot efficiency):
η = TH – TC x100 %
TH
= 1 – TC/TH
x100 %
η = 61% (must be computed in K)
•
•
•
Theoretical upper limit, other losses (e.g. friction, heat loss from boilers, transmission losses)
At best we can convert 35 % of the thermal energy in burning fossil fuels to mechanical/electrical
More than ½ lost as waste heat
Question
A heat engine takes in 1200 J of heat from the high temperature heat source in each cycle
and does 400 J of work in each cycle. What is the efficiency of the engine? How much heat
is released to the environment in each cycle?
η = W/QH = 400 J / 1200 J = 33%
From 1st law:
W = QH - QC = 1200 J - QC = 400 J
QC = 800 J
Question
Calculate the efficiency of a power station located in a colder climate (Tc = 0 ºC). Why wouldn’t it
be beneficial to generate power in colder climates for use in warmer areas?
η = 69 %
The Second law of Thermodynamics
Available Energy
•
It is impossible to convert a given quantity of heat energy completely into work. In an energy
conversion process, energy is always degraded in quality, so that its ability to do work is reduced
Summary
•
•
•
•
•
•
1st law – energy is conserved, QH = W + QC (heat in = work and heat out)
Heat engines make use of a flow of heat from hot to cold in order to do work
2nd law limits the amount of work obtainable from a heat engine
Heat energy that flows from the hot source cannot be entirely converted into work; some heat has
to be discharged into the environment
Maximum efficiency may be calculated using the Carnot efficiency equation
Total entropy of a system increases in a physical process