The level of liquid helium (temperature = 4 K) in its storage tank can be monitored using a vertically aligned niobium- titanium (NbTi) wire, whose length l spans the height of the tank. In this level-sensing setup, an electronic circuit Constant I maintains a constant electrical current I at all times in the Helium NbTi wire and a voltmeter monitors the voltage differ- ence V across this wire. Since the superconducting critical temperature for NbTi is 10 K, the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above 10 K) is in the normal state. Define f = x/l to be the fraction of the tank filled with liquid helium (Fig. 18–38) and Vo to be the value of V when the tank is empty (f = 0). Determine the relation between fand V (in terms of Vo). vapor (>10K) Liquid helium (=4K) FIGURE 18–38 Problem 91. Superconducting Normal

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The level of liquid helium (temperature = 4 K) in its storage
tank can be monitored using a vertically aligned niobium-
titanium (NbTi) wire, whose length l spans the height of
the tank. In this level-sensing setup, an electronic circuit
Constant I
maintains a constant electrical current I at all times in the
Helium
NbTi wire and a voltmeter monitors the voltage differ-
ence V across this wire. Since the superconducting critical
temperature for NbTi is 10 K, the portion of the wire
immersed in the liquid helium is in the superconducting
state, while the portion above the liquid (in helium vapor
with temperature above 10 K) is in the normal state. Define
f = x/l to be the fraction of the tank filled with liquid
helium (Fig. 18–38) and Vo to be the value of V when the
tank is empty (f = 0). Determine the relation between
fand V (in terms of Vo).
vapor
(>10K)
Liquid
helium
(=4K)
FIGURE 18–38 Problem 91.
Superconducting
Normal
Transcribed Image Text:The level of liquid helium (temperature = 4 K) in its storage tank can be monitored using a vertically aligned niobium- titanium (NbTi) wire, whose length l spans the height of the tank. In this level-sensing setup, an electronic circuit Constant I maintains a constant electrical current I at all times in the Helium NbTi wire and a voltmeter monitors the voltage differ- ence V across this wire. Since the superconducting critical temperature for NbTi is 10 K, the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above 10 K) is in the normal state. Define f = x/l to be the fraction of the tank filled with liquid helium (Fig. 18–38) and Vo to be the value of V when the tank is empty (f = 0). Determine the relation between fand V (in terms of Vo). vapor (>10K) Liquid helium (=4K) FIGURE 18–38 Problem 91. Superconducting Normal
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