Randall D. Knight — Work, Heat, and the First Law of Thermodynamics: Problem 67

Liquid helium, with a boiling point of 4.2 K, is used in ultralow-temperature experiments and also for cooling the superconducting magnets used in MRI imaging in medicine. Storing liquid helium so far below room temperature is a challenge because even a small “heat leak” will boil the helium away. A standard helium dewar, shown in FIGURE P19.67, has an inner stainless-steel cylinder filled with liquid helium surrounded by an outer cylindrical shell filled with liquid nitrogen at –196°C. The space between is a vacuum. The small structural supports have very low thermal conductivity, so you can assume that radiation is the only heat transfer between the helium and its surroundings. Suppose the helium cylinder is 16 cm in diameter and 30 cm tall and that all walls have an emissivity of 0.25. The density of liquid helium is $125 \text{ kg/m}^3$ and its heat of vaporization is $2.1 \times 10^4 \text{ J/kg}$. a. What is the mass of helium in the filled cylinder? b. In how many hours will half the helium boil away?