Solved: The level of liquid helium (temperature ) in its

Chapter 18, Problem 91GP

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The level of liquid helium (temperature \(\approx 4 k\)) in its storage tank can be monitored using a vertically aligned niobiumtitanium (NbTi) wire, whose length  spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current  at all times in the NbTi wire and a voltmeter monitors the voltage difference  across this wire. Since the superconducting critical temperature for  is , 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  is in the normal state. Define \(f=x / l\) to be the fraction of the tank filled with liquid helium (Fig.  and \(V_{0}\) to be the value of  when the tank is empty \((f=0)\). Determine the relation between  and  (in terms of \(V_{0}\) ).

Equation transcription:

Text transcription:

approx 4 k

f=x / l

(f=0)

V{0}