# Calculating the boil-off rate of liquid helium

• NZPhysics
In summary, the problem involves an aluminum rod of 0.500 m length and 2.60 cm2 cross-sectional area being inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 340 K, with a thermal conductivity of 3,100 W/m · K at 4.20 K and a specific heat of 0.215 cal/g · °C and density of 2.70 g/cm3. The density of liquid helium is 0.125 g/cm3. The question asks for the approximate boil-off rate of liquid helium in litres per second after the lower half of the rod has reached 4.20 K, assuming the circular surface of the upper
NZPhysics

## Homework Statement

An aluminum rod 0.500 m in length and with a cross-sectional area of 2.60 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at340 K. (Aluminum has thermal conductivity of 3,100 W/m · K at 4.20 K; ignore its temperature variation. Aluminum has a specific heat of 0.215 cal/g · °C and density of 2.70 g/cm3.The density of liquid helium is 0.125 g/cm3.)

(a) If the circular surface of the upper end of the rod is maintained at 340 K, what is the approximate boil-off rate of liquid helium in litres per second after the lower half has reached 4.20 K?
___________ litres/s

## Homework Equations

ΔL/L0 = αΔT, I'm not really sure what else would be applicable.

## The Attempt at a Solution

I honestly have no idea where to start with this question so any help would be really appreciated.

Thanks

Unless you are expected to solve the diffusion equation using Fourier series, I would assume that only the lower tip of the rod is in the helium. So it becomes a question about rate of conduction of heat along a rod with the ends at fixed temperatures.

## 1. What is the boil-off rate of liquid helium?

The boil-off rate of liquid helium refers to the rate at which liquid helium, a cryogenic liquid with a boiling point of -269°C, transitions into its gaseous form at room temperature. This process is known as the boiling or evaporation of liquid helium.

## 2. Why is it important to calculate the boil-off rate of liquid helium?

Calculating the boil-off rate of liquid helium is crucial for the proper storage and handling of this valuable and expensive resource. It helps scientists and researchers determine the necessary storage capacity and usage rates for liquid helium, as well as plan for refilling or replenishing the supply.

## 3. How is the boil-off rate of liquid helium calculated?

The boil-off rate of liquid helium can be calculated using the following formula: R = (V x H)/T, where R is the boil-off rate in liters per hour, V is the volume of liquid helium in liters, H is the latent heat of vaporization (which is 21.79 kJ/mol for helium), and T is the time in hours.

## 4. What factors can affect the boil-off rate of liquid helium?

The boil-off rate of liquid helium can be influenced by several factors, including the temperature difference between the liquid helium and its surroundings, the insulation of the container holding the liquid helium, and the purity of the liquid helium itself. Other factors may include the pressure and flow rate of the surrounding gas and any external heat sources.

## 5. How can the boil-off rate of liquid helium be minimized?

To minimize the boil-off rate of liquid helium, it is essential to properly insulate the storage container and maintain a consistent and low temperature. Additionally, using high-purity liquid helium and reducing the pressure and flow rate of the surrounding gas can also help minimize the boil-off rate. Regular monitoring and refilling of the liquid helium supply can also help to keep the boil-off rate at a manageable level.

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