Heat convection in liquid nitrogen

[OrangeYogi]

Hello,
I am trying to achieve a range of temperature (below 0 degC) by heating up liquid nitrogen (77K) with an electric heater (100W) inserted into a copper block. How do I calculate the time taken (t) for the nitrogen vapour to reach temperature T (say 100K). The liquid nitrogen is poured into a 34 litre polystyrene box (420mmx320mmx250mm).

Let me know if you have any questions.

Thank you in advance.

 

[mfb]

For the ideal case of a uniform temperature: Calculate the energy needed to boil the nitrogen, calculate the amount of nitrogen in the box after that is done, calculate the energy needed to heat this nitrogen. Divide by the heating power. Take into account that some nitrogen will escape out of the box in the process or ignore that.

Unless this is a homework question this approach will fail, because your heater is way too powerful to lead to a uniform temperature distribution. The nitrogen around the heater will exceed 100 K long before the rest of the box reaches this temperature.

 

[OrangeYogi]

For the ideal case of a uniform temperature: Calculate the energy needed to boil the nitrogen, calculate the amount of nitrogen in the box after that is done, calculate the energy needed to heat this nitrogen. Divide by the heating power. Take into account that some nitrogen will escape out of the box in the process or ignore that.

Unless this is a homework question this approach will fail, because your heater is way too powerful to lead to a uniform temperature distribution. The nitrogen around the heater will exceed 100 K long before the rest of the box reaches this temperature.

Thank you for your answer.

I see your point about temperature gradient. I think extra time is required to achieve a uniform temperature throughout the box after switching off the heater (and by using a lower power heater).

Would you suggest an alternative arrangement in achieving a range of temperature (below 0degC) using liquid nitrogen?

Thank you.

 

[mfb]

It depends on what you want to do, your requirements and your budget. There are certainly commercial solutions, those are typically the best but also the most expensive options.

Some material with a boiling point around the target temperature is great, ventilating boiled off nitrogen (after passing a heater) over your sample might work as well. If your temperature range does not have to be too precise, a pool of liquid nitrogen at the bottom and some heating (or just an open box) on top could work as well.

Things get much easier if you don't want to keep the temperature for a longer time, then you can just attach temperature sensors to your experiment, and measure when the setup has the right temperature.