Transcript Physics 141 Mechanics Yongli Gao Lecture 4 Motion in 3-D

Physics 141
Mechanics
Lecture 24
Heat and Temperature
Yongli Gao
• So far we have concentrated on mechanical energy,
including potential and kinetic energy. There are
other forms of energy and energy may change from
one form to another.
• Heat is a form of energy. It is associated with the
microscopic random motion of atoms and
molecules.
• The unit of heat is calorie (cal).
1 cal = 4.186 J =3.969 x 10-3 Btu
• Temperature measures the intensity of the
molecular random motion.
• The unit of temperature is kelvin (K) in so called
absolute temperature scale.
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Measurement of Temperature
The lowest temperature possible is 0 K (absolute
zero), at which all the atoms are frozen to minimum
vibration.
The frozen temperature of water is 273.15 K = 0
degrees celsius (°C), and the boiling temperature is
373.15 K = 100 °C, both at the atmosphere pressure
(1x105 Pa). Celsius scale is internationally used in
daily life. T(K )  (T(C)  273.15)K
In the US, we use Fahrenheit scale in the unit of
degrees fahrenheit (°F) in daily life.
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T(F)  T(C)  32 F
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Room temperature 72.0 °F = 22.22 °C = 295.37 K
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Thermal Expansion
As the temperature of an object increases, the
random motions of the molecules also increase. As
a result, the average distance between molecules
increases, resulting the expansion of the object in all
directions.
Typically, liquids expand more than solids, and
gases much more than liquids.
For a solid of length L, the change of length, DL, due
to thermal expansion after temperature increase DT
is DL=aLDT
where a is the coefficient of linear expansion,
typically in the order of 10-5-10-6.
The volume expension
DV  DL3  3L2 DL  3L2aLDT  3aL3 DT
 DV  3aVDT
0th Law of Thermodynamics
• The zeroth law of thermodynamics states that two
systems are in thermal equilibrium when they are of
the same temperature T.
• Thermal equilibrium <=> molecular random motion
of the same intensity <=> the same temperature.
Heat Capacity
• When you put heat DQ into an object, its
temperature increases by DT, DQ  CDT
• The coefficient C measures the amount of heat
energy necessary the temperature of the object by
one temperature unit, and is termed heat capacity.
• The heat capacity of one unit mass of a material is
called the specific heat c of the material,
DQ  cmDT
where m is the mass of the object. The typical unit
of c is cal/gK, but in SI it is J/kgK.
• Another common unit for specific heat is called
molar specific heat, in which the amount of
material is measured by mole (mol) instead of mass
• l mole = 6.023 x 1023 (atoms or molecules)
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Heat Transfer
There are three modes of heat transfer, conduction,
convection and radiation.
Conduction is the transfer of heat by touching or
through a heat conductor. Microscopically, it is heat
transfer by the collisions of molecules such that the
random molecular motions propagate.
Convection is the transfer of heat by macroscopic
flow of a fluid, such as cooking with a gas heater,
drying hair with a hair dryer.
Radiation is the transfer of heat by electromagnetic
(EM) waves, such as infrared or visible light. We
get energy from the sun by radiation heat transfer.
Conduction
• Suppose we have a heat conductor. When steady,
the heat conducted across, DQ, is proportional to the
time taken Dt, the cross section A, the thermal
gradient DT/Dx. The heat flow equation for the rate
of transfer H
DT
DQ
DT
DQ  A
Dt  H 
 kA
Dx
Dt
Dx
where k is the thermal conductivity of the
conductor, and the "-" sign means that DQ is from
high T to low T.
• The unit for thermal conductivity k is W/mK, and
the value is from 401 (Cu) to 0.024 (PUT foam).
• In industry, the insulation is expressed by R=Dx/k,
where Dx is the thickness of the conductor
(insulator). In the State of New York, the outer wall
of a house must have R≥13. H   A DT
R
The First Law of Thermodynamics
• The first law of thermodynamics states that the
heat absorbed by a system in a process, DQ, equals
to the sum of internal energy increase, DE, and the
work done by the system during the process, DW.
DQ  DE  DW
• This is in fact the conservation of energy.
Entropy
• In winter if you stand outside and take off your coat,
you'll feel cold because heat is dissipated from you
to the environment. Why doesn't the net heat flow
the other way around?
• The process above is irreversible. The heat lost to
the environment is lost, it cannot come back to you
by itself. There are also reversible processes. A
reversible process is such that at any moment the
system is in equilibrium so that it can go either way.
• To determine whether a process is irreversible, we
need to know entropy, which is a quantity
describing the status of a system in a way as energy,
temperature, pressure, volume, etc.
The 2nd Thermodynamic Law
• Entropy is defined as
dQ
SA  
 S0
0 T
• The second thermodynamics law is that for an
isolated system in any process, the change of its
entropy is non-negative, DS≥0
• For example, consider a system with a hot reservoir
Th and a cold reservoir at Tl. In a contact of the two,
DQ goes from the hot reservoir to the cold one but
not the other way around.
f dQ
DQ DQ
Tl  Th
DS  S f  Si  


 DQ
0
i T
Th
Tl
Th Tl
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Statistical Definition of Entropy
• Entropy is in fact a measurement of disorder. The
2nd law of thermodynamics is in fact stating that by
itself, any system prefers more randomness.
• If W denotes the multiplicity of the system, or the
number of possible configurations, entropy of the
system can also be defined as
S=kB lnW
• The 3rd law of thermodynamics states that as the
temperature goes to zero, the entropy approaches a
constant, regardless how it reaches zero. From the
statistical point of view, it is the fact that at zero
temperature, the system falls into its ground state
with a certain number of possible configurations
W0.
T  0  S  S0  kB ln W0