Download Temperature Heat Internal Energy The calorie First Law of

Temperature
The calorie
We have previously considered the microscopic interpretation
of temperature as the average kinetic energy of the random
motion of molecules. Two objects have the same temperature
when they have the same average kinetic energy per molecule.
A calorie is the amount of heat that is required to increase
the temperature of one gram of water by one degree Celsius.
We would expect that for a fixed amount of
water, a larger amount of heat would result in
a larger temperature increase. In addition,
we know that it takes more heat to increase
the temperature of a large pot of water than
for a small pot of water.
Just as water in a pipe seeks a
common level, the thermometer and
its immediate surroundings reach a
common temperature.
Internal Energy
The total microscopic energy of the molecules in
an object is called its internal energy. It is not
the ordered macroscopic kinetic or potential energy
of the object as a whole, but the net energy of the random
motion of all the molecules in the object. The molecules can
have translational, vibrational, rotational and electronic
energy. As the temperature of the object increases, the
internal energy also increases. The internal energy, like the
temperature, is a property of the system. The internal
energy is sometimes called the thermal energy.
Heat
Heat is the energy that flows between two objects because
they are at different temperatures. It is energy in transit
due to a temperature difference.
So the amount of heat Q required to raise the temperature
of m grams of water by an amount ΔT must be proportional to
both m and ΔT;
cal
Q = m ΔT × 1.0
g °C
How much heat is required to raise the temperature of
400 g of water from 20°C to 30ºC?
How much heat is associated with an 8°C drop in the
temperature of 500 g of water?
Because the stove element has a higher
temperature that the pot of water, heat flows
from the stove to the water increasing the
thermal energy and temperature of the water.
7.1
PHYS 1010Q
© D.S. Hamilton
Work
Heat is not the only way to change the temperature of
something. Try rubbing your hands together. There is a
temperature rise, but no heat flow (between two objects at
different temperatures).
In the paddle-wheel apparatus used by James
Joule to compare heat with mechanical work,
the weights fall, giving up potential energy
which is transformed into the work done on
the water by the paddle-wheel. This leads to
a temperature increase of the water. Joule
showed that 1 calorie of heat was equivalent
to 4.2 Joules of mechanical work.
If you mix food in a blender, the electric motor
does mechanical work on the contents. How much
work is done if the blender motor runs at a power
of 100W for 8s. How many calories of thermal
energy are produced?
7.2
PHYS 1010Q
© D.S. Hamilton
The first law of thermodynamics is just a more general
statement of the conservation of energy.
What is the net change in the internal energy of the food in
the blender from the previous problem if 60 cal of heat
leaves the system while the electric motor is running?
Specific Heat
The quantity 1.0 cal/g°C is called the specific heat of water.
But different types of molecules partition up the internal
energy in different ways, not all of it going into the kinetic
energy. So the resulting temperature change for the same
amount of heat can be different for different molecules.
Q = cm ΔT
water
ice
aluminum
air
First Law of Thermodynamics
So we now know how to increase the internal energy of a
system by two different ways. We can either heat the
system or do work on it. The result is the same. The change
in the internal energy is due to a heat flow in or out of the
system and when work is done on or by the system.
1.00 cal/g°C
0.50 cal/g°C
0.215 cal/g°C
0.24 cal/g°C
The specific heat for
different materials
(see K&F, table 13-1)
How many calories would it take to raise the temperature of
a 400-g aluminum pan from 20°C to 30ºC?
ΔU = Q(in) + W(on)
7.3
PHYS 1010Q
© D.S. Hamilton
7.4
PHYS 1010Q
© D.S. Hamilton
Change of State
Conduction
It can happen that the addition of heat does not change the
temperature of a material, but instead there is a change of
state, sometimes called a phase change or phase transition.
Thermal conduction is the transfer of thermal energy by the
collisions of molecules within a substance or at an interface.
The tile floor feels colder than the furry rug,
even though both materials are at the same
temperature. This is because tile is a better
conductor than the rug, and thus heat is more
readily conducted away from the foot in
contact with the tile, ie it “feels” colder.
Convection
The thermal energy that is released or gained per unit mass is
known as the latent heat,
Q = mL
To freeze or thaw water, it takes about 80 cal/g (334 kJ/kg)
at 0°C, and about 540 cal/g (2260 kJ/kg) to boil or condense
water at 100°C. Note that temperature of the material does
not change, the energy is involved with doing work against the
cohesive forces between the atoms and molecules.
How much heat energy would be needed to melt
a 30 gram ice cube at 0°C?
Thermal convection is the transfer of
thermal energy in fluids by the physical
movement of the fluid. The warmer fluid
(air) above the radiator is less dense and
moves upward through the more dense and
cooler fluid around it. One often speaks of
convection currents for the fluid motion.
Radiation
The random jiggling motion of the electrons in atoms and
molecules cause them to emit electromagnetic waves. The
wavelength or “color” of this EM radiation changes with
the temperature of the object. The red-orange color of
the heating element on an electric stove suggest it is
cooler than the yellow light from a star like our sun.
The dominate wavelength emitted by a cozy
fireplace is in the infra-red. The emission from
hot objects such as human bodies or car engines
can be viewed with special "night glasses".
7.5
PHYS 1010Q
© D.S. Hamilton
7.6
PHYS 1010Q
© D.S. Hamilton
Thermal Expansion
Modeling the Temperature of a “Naked” Earth
As the temperature of an object is raised, its molecules jiggle
faster and faster and tend to move farther apart. The result
is an expansion in the dimensions of the object. With a few
exceptions, all forms of matter expand with increasing
temperature and contract with decreasing temperature. (The
interesting exception of this rule is water between 0°C and
4°C.) The fractional change in length depends on the size of
the temperature change and the type of material.
Our Sun is the energy source that drives the temperature and
climate on the Earth. The solar radiation falling on the Earth
is about 1,400 W/m2.
Calculate the power incident on the Earth assuming that the
solar radiation is distributed over an area of πR2 where R is
the radius of the Earth (= 6.37x106 m).
The Greenhouse Effect
About 30% of this power is reflected back into space. This
reflective property of the Earth is called its albedo (=a). The
reflected power is a P and the absorbed power is (1-a)P.
Glass is transparent to the
short wavelength radiation
from the Sun but reflects
longer wavelengths. The
reradiated energy from the
plant is at a longer wavelength
because the plant has a much
lower temperature.
What is the solar power absorbed by the Earth for a = 0.3
A similar greenhouse effect happens in
the Earth’s atmosphere. Carbon dioxide
transmits the incoming solar energy and
then reflects the reradiated energy from
the Earth. Without the greenhouse
effect, the Earth’s temperature would be
about -20°C.
Our present environmental concern is that excess CO2 in the
atmosphere traps too much energy which will significantly
increase the temperature of the Earth.
7.7
PHYS 1010Q
© D.S. Hamilton
This diagram shows the
power balance for a model
of the Earth that does
not have an atmosphere.
In thermal equilibrium,
the absorbed incoming
power is balance by the
outgoing thermal radiation
of the Earth.
To find the outgoing thermal radiation, we note that for any
object at absolute temperature T, the radiated power is
Prad = σAT4 where A is the surface area of the object and σ is
the Stefan-Boltzmann constant (5.67x10-8 W/m2K4).
7.8
PHYS 1010Q
© D.S. Hamilton
Measured and Calculated Temperatures
10.5
Land average temperature, with 95% confidence interval
Simple fit based on CO 2 concentration and volcanic activity
The black curve shows the increase
in the surface temperature of the
Earth between 1750 and 2010. The
solid red curve is the predicted
temperature based on measured CO2
concentrations and volcanic activity.
10
9.5
9
8.5
8
7.5
Global Land Surface Temperature
12−Month Moving Average ( °C )
Use this model to estimate the equilibrium temperature of
an earth that does not have an atmosphere.
7
Berkeley Earth Surface Temperature
6.5
1750
1800
1850
1900
1950
2000
Climate Change
One obvious result of this
temperature increase is the
melting of the polar ice and
the rise of sea level. Some of
the damage of the 2012
hurricane Sandy was due to
this sea level effect.
Add in the Atmosphere of the Earth
The diagram is now more
complex with power
being absorbed directly
from the Sun and
additionally from the
greenhouse radiation.
Weather vs. Climate
Determining the net solar power absorbed by the Earth and
its resulting equilibrium temperature is a more involved
problem whose solution requires input from physicists,
chemists, mathematicians, and atmospheric scientists.
7.9
PHYS 1010Q
© D.S. Hamilton
The difference between the terms “weather” and “climate” is
subtle yet important to understanding their respective
implications. Simply put, the distinction between the two is
time. Weather refers to the behaviors of the Earth’s
atmosphere over a short period of time. Hurricanes, wind,
winter storms, and a really hot day in August are examples of
weather. Climate, however, refers to the long-term behavior
of the atmosphere that goes beyond individual events.
7.10
PHYS 1010Q
© D.S. Hamilton
Global Climate Change
What Climate Change Means for Coastal CT
According to the Intergovernmental Panel on Climate Change
(IPCC) 2014 Fifth Assessment Report, warming of the earth’s
climate system is unequivocal. Human activities play a
dominate role by increasing the atmospheric concentration of
greenhouse gases from burning fossil fuels and land-use
changes, including deforestation.
There are many aspects of climate change that could
influence the severity of coastal hazards, but the primary
concerns are the implications of sea level rise, potential
changes in storm activity and the combined effect of the
two. In this light, climate change can be viewed as a “coastal
hazards multiplier.” Rising seas and potential changes in
storm activity can make both flooding and erosion much
worse. Consider the following findings:
"There is very high confidence that the net effect of human
activities since 1750 has been one of warming... Most of the
observed increase in global average temperatures since the
mid-20th century is due to the observed increase in
anthropogenic GHG [greenhouse gas] concentrations. There
has been significant anthropogenic warming over the past 50
years averaged over each continent (except Antarctica).”
Boston and Atlantic City can expect a coastal flood
equivalent to today’s 100-year flood every two to four years
on average by mid-century and almost annually by the end of
the century.
Anthropogenic warming of the climate is expected to continue
and perhaps accelerate in the 21st century, depending on
greenhouse gas (GHG) emissions: "Continued GHG emissions at
or above current rates would cause further warming and
induce many changes in the global climate system during the
21st century that would very likely be larger than those
observed during the 20th century.”
7.11
PHYS 1010Q
© D.S. Hamilton
New York City is projected to face flooding equivalent to
today’s 100-year flood once every decade on average under
the IPCC higher-emissions scenario and once every two
decades under the IPCC lower-emissions scenario by
century’s end.
References and Reading
www.ct.gov/deep State of Connecticut Department of Energy
and Environmental Protection
www.climate.nasa.gov National Aeronautics and Space
Administration
7.12
PHYS 1010Q
© D.S. Hamilton