Many Biomedical applications require very strong magnets. Just two examples are the magnets used for the medial imaging technique Magnetic Resonance Imaging (MRI) and Nuclear Magnetic Resonance Spectroscopy (NMR), which may be used as a technique for the characterization of metabolites.

The above figure, depicts a so called superconducting magnet. At the core of this magnet is a metal- coil, which is used to store a very strong electrical current. This requires that the current is kept at a temperature of 4K, which is achieved by immersing this coil into liquid Helium. Since liquid Helium is very expensive, the vessel containing the lHe must be thermally insulated. Thermal insulation occurs through various levels: 1. A vacuum chamber surrounding the lHe vessel. 2. A chamber containing liquid Nitrogen surrounding the vacuum chamber, 3. A chamber containing insulation materials such as glass fibers surrounding the liquid-Nitrogen chamber.

Despite all efforts the Helium is not perfectly insulated.

We consider a system where liquid helium is evaporating and leaving an MRI magnet at a rate of 50 ml of liquid Helium/hour. The Helium gas is leaving the magnet at room temperature.

In order to decrease the boil-off of helium, the manufacturer of the Magnet considers the following modification: The chamber containing the liquid nitrogen is replaced with a metal- shield, which is cooled to 10K using a so-called cold head, which requires electrical work. The heat transfer coefficient between the helium-reservoir and the cold shield at 10K is the same as the heat transfer coefficient between the helium reservoir and the liquid nitrogen reservoir.

Calculate the improved Helium consumption after the introduction of the cold-head.