Talk Topics Due Wednesday March 5
HW-2 Problem #1
HW-2 Problem #2a
2. Calculate the Joule-Thomson coefficient for a gas which obeys
a. the ideal gas law: pv=nRT
1. An ideal Linde liquefier runs on air between 1 atm. and 200
atm. at 20 C. What is the liquefaction rate y (2 significant figures)?
H 1 − H 2 6.7 − (−1.8)
=
H1 − H f
6.7 − (−97)
Ans: y = = 0.082 = 8.2%
(Reference source: Thomas M. Flynn, “Cryogenic Engineering”,
second edition, New York: Marcel Dekker, p. 394, 2005.)
HW-2 Problem #2b
b. For the Dieterici equation of state: p(v-b)exp(a/vRT)=RT, where a and b are
constants, find
we define
a
=u
vRT
You try to get the answer:
HW-3 Problem #3
Ans:
With normal hydrogen liquid in dewar, it consists 75% ortho and
25% para. The ortho fraction after 24 hours is
x=
µ JT =
1
CP
⎡ ( v − b )( a + vRT ) ⎤
− 1⎥
⎢ 2
⎢⎣ v RT − a ( v − b ) ⎥⎦
a
=u
vRT
a is associated with the interaction
between molecules and b takes into
account the finite size of the molecules,
similarly to the Van der Waals equation.
So the total fraction of para-hydrogen present after 24 hours is 1x=37.64%
(Reference source:
1. Thomas M. Flynn, “Cryogenic Engineering”, second edition,
New York: Marcel Dekker, p. 193-202, 2005. )
Thermometry
OUTLINE
1. Goals
2. Thermometry
3. Temperature Ranges
of Application
4. Constant Volume
Thermometer
5. Thermocouples
6. Thermometer Time
Response Data
7. 4 Terminal Resistance
Measurement
1
= 62.36%
1.33 + 0.0114 × 24
Thermometer Characteristics
8. Pt (pure metal)
Thermometer
9. Typical Resistive Thermal
Sensor
10. Typical Resistance and
Sensitivity Curves
11. Thermal Regulation
12. Data
Collection/Wheatstone
Bridge
1
Temperature Ranges of Application
Constant Volume Thermometer
•Named after Sir Fancis
Simon
•Helium is an ideal gas
down to 5 K
•Modern versions use in
situ pressure gauges at
low T with electrical readout (no gas line from RT
to Low T)
Thermocouples
Wires of 2 different
metals (pure or alloy)
when joined and
connected to a volt
meter produce a
voltage related to
temperature.
At right is the sensitivity
of various common
thermocouples,
perhaps the simplest,
least expensive, and
most common
thermometer in use.
Usually a reference
junction in an ice bath is
used to make the
measurement absolute.
RT
Gas line
Low T
Helium
gas
Thermometer Time Response Data
Differences between wet / dry can be exploited for level detection
Calibrations are tabulated (e.g. type K)
Figure adapted from Cryogenic Engineering by Thomas M. Flynn, Dekker:NY (1997), p. 530
Figure adapted from Cryogenic Engineering by Thomas M. Flynn, Dekker:NY (1997), p. 495
4 Terminal Resistance Measurement
Meter at RT must have high input impedance
Thermometer
at low T
Leads from RT to
Low T must have
low heat leak (alloy)
4 Terminal Resistance Measurement
The purpose of a 4-terminal measurement of
resistance is:
A. To provide extra wires in case of breakage
B. To make it easier to hook up the measurement
instruments
C. To make sure the current only flows in one direction
D. To make it a Wheatstone bridge
E. To avoid contact and lead resistance
Current source must be stable and reversible. Average
of readings with current flowing in opposite directions
gives correct voltage drop, canceling thermal emfs.
Often, low frequency ac source is used, with lock-in
detector as volt meter, to improve sensitivity.
2
Pt (pure metal) thermometer
Typical Resistive Thermal Sensor
•Resistance thermometer—use 4 terminal set-up
•R is almost proportional to T:
Callender-VanDusen Equation: R(T)=R0[1+AT+BT2+C(T-10)T3]
(0 K<T<300K)
Other calibrations available down to 20 K
•Purity determines calibration (A, B, C)-no individual calibration required
•Transfer standard used by NIST
Cross-section:Details of
construction showing
strain-free mounting of chip
Latest sensors are 300 µm
(#4) inside hermetically
sealed container
Photo of sensor with leads
Figure adapted from Cryogenic Engineering by Thomas M. Flynn, Dekker:NY (1997), p. 512
Typical Resistance and Sensitivity Curves
Thermal Regulation
106
Resistance (Ω)
105
104
Ge on GaAs substrates
Heat treatment produces
sensitivity in desired T range
TTR-G
TTR-D
103
PID Heater
Response
Dewar
102
101
0.01
0.1
1
10
Temp.
Monitor
100
Dimensionless Sensitivity (S)
Temperature (K)
TTR-G
3
TTR-D
Temperature
Input-set point
2
1
0
0.01
0.1
1
10
Heater
Thermometer
Computer data acquisition
board may be used for all
electronics
100
Temperature (K)
Data Collection/Wheatstone Bridge
Computer
with data
acquisition
board
InputCurrent
level
Computer board
Break-out box
source
detector
Resistor
Thermometer
Temperature
sensor
Decade
Resistor
Temperature
Temperature measurement
and control are easily
automated
Decade Resistor
10k Resistor
Resistor
R
R
3