Download PX121: Thermal Physics Lecture 2

PX121: Thermal Physics
Lecture 2
http://www2.warwick.ac.uk/fac/sci/physics/
teach/module_home/px121/
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Room P447
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Introduction VII
Equilibrium - Le Chatelier’s Principle
“A system in equilibrium reacts to a (small) externally imposed change in one of
its state variables by readjusting its internal condition so as to reverse the
change.” (Henri Louis le Chatelier, 1844)
E.g.
If there is a small heat flow into a gas in equilibrium with its
surroundings, its temperature will increase. However, the temperature
will now be higher than that of the surroundings, so heat will flow out of
the gas, and its temperature will decrease again.
Thermal equilibrium
Definition:
two systems are in thermal
equilibrium if their state variables (p, V, T)
do not change when they are put in contact
via a diathermal wall.
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S1
S2
Introduction VIII
Leads to “Zeroeth Law of Thermodynamics:
“If systems S1 and S2 are separately in thermal equilibrium with system S3 then
they are in thermal equilibrium with each other.”
Results in the idea that there is something you could measure separately about
S1 and S2 which would be the same. This “something” is temperature.
The concept of temperature
Look at the website and copy “The temperature connection” to your notes.
Temperature is a variable of state .
- it is a physical property related to the kinetic and potential energies of
the atoms and molecules in a system.
- it is measured using a thermometric scale which has one or more
fixed reference points.
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Introduction IX
The concept of temperature / contd.
U is the internal energy of the system
Infra-red (IR)
U1
which is the sum of the translational,
vibrational and rotational energies of its
components (we will return to this later).
If, for example, we bombard an isolated
system with IR then:
- its internal energy increases through
the addition of heat Q
T2  T1
T1
+Q
U 2  U1
U2
T2
- its temperature increases
The temperature of a system is only dependent on its internal energy
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Temperature and Heat I
Young and Friedman (Y & F) Ch. 17
Thermometry - measurement of temperature.
Consider 3 systems S1, S2, and S3.
Let S3 have some observable property which scales (ideally linearly) with
temperature.
If S3 is placed in contact with S1 and then with S2 and the observable does not
change, then S1 and S2 have the same temperature.
S3 is a thermometer.
Suppose that the property is X. Then, we would like:
where X0 and c are constants.
X T   X 0  cT
Need two fixed reference points to find X0 and c - i.e. for calibration.
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Temperature and Heat II
Thermometry / contd.
The two fixed points should be easy to reproduce, e.g.:
- Ice point :
liquid and solid water in equilibrium at 1 Atmosphere
define as 0 on Celsius scale
- Steam point :
liquid water and water vapour in equilibrium at 1 Atmosphere
define as 100 on Celsius scale
Measure X at each fixed point then
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T
100  X  X ice  o
C
X steam  X ice
Temperature and Heat III
Thermometry /contd.
Examples of X
- expansion of solids or liquids ~ cT (e.g. mercury thermometer)


V  V0 1  T  1T 2   2T 3  ...
where V0 is volume at some “zero” temperature,  is the volume
coefficient of expansion, and T is temperature.
V  V  V0   V0 T
to first order
(differentiate)
- change in electrical resistance (e.g. thermistor, platimum resistance
thermometer)


R  R0 1  T   1T 2   2T 3  ...
hence (to first order)
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R  R0 T
Temperature and Heat IV
Thermometry /contd.
- Seebeck effect (thermocouple)
(potential difference across a junction between dissimilar metals)
T2
metal 1 (e.g. chromel)
metal 2 (e.g. alumel)
T1 = reference temperature
T1  0 o C
T1  0 o C
T2 = temperature to measure
V  1  70 VK -1
Reference junctions usually done electronically these days.
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Temperature and Heat IV
Thermometry /contd.
- Measurement of the wavelength of emitted em radiation (pyrometer)
(Can be used remotely - e.g. for stars)
Based on the Wien displacement law: mT  2.9  10
3
where m is the wavelength of at the peak of the spectral
emittance curve for a black body
Read section 39.5 (Continuous Spectra) in Y & F and copy
fig 39.32 (Spectral emittance) into your notes
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mK
Temperature and Heat V
Thermometry /contd.
- pressure of a gas (e.g. constant volume gas thermometer)
based on the ideal gas equation
pV  nRT
where n is the number of moles of gas and R is the universal gas constant
use He at low pressure to get ideal behaviour
Open to
atmosphere
Constant
temperature bath
h
Fixed
point
p p h
at
Hg
Gas at
temperature T
Flexible
connection
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p T
Temperature and Heat VI
Thermometry /contd.
Absolute zero and the constant
volume thermometer
Series of straight lines for different n
extrapolate to a common point absolute zero temperature
p
n1
 nR 
p   T
V 
n2
n3
o
absolute zero  273.15 C  0 K
-273.15
0
T / ºC
 need only 1 fixed reference point
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100
Temperature and Heat VII
Absolute zero / contd.
Reference point:
triple point of water
(solid/liquid/vapour all in equilibrium at 0.01 ºC and 610 Pa)
Ttr  273.16 K
Then, where ptr is the pressure of the gas at Ttr in the gas thermometer
Note: pressure of the gas in the thermometer at,
Ttr not pressure of the equilibrium mixture whose
temperature is being measured.
Effect of non-ideality of gas on
measurement of steam point:
T / K  273.16 Lim
ptr 0
p
ptr
p/MPa
0.08
H2
He
Air
O2
He at low pressure approaches the
ideal behaviour
T/K
373.15
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373.5
Temperature and Heat VIII
Gas thermometer - worked example (Y & F17.8)
A gas thermometer registers an absolute pressure corresponding to 325 mm
Hg when in contact with water at the triple point. What pressure does it read
when in contact with water at the normal boiling point?
p
 const.
T

ptr pbp

Ttr Tbp
 pbp  Tbp
ptr
Ttr
 373.15
325
273.16
 444 mm Hg
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N.B. Use Kelvin scale for
almost all thermodynamic
calculations!