# A heating element in a container with low pressure gas?

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1. May 8, 2015

### randombill

This is just a qualitative question but feel free to show an equation if possible.

Basically if you have a container with a heating element, lets say 500 W with a temperature of 2500 Kelvins and inside this box is a low pressure ideal gas, something like 1/100 of an atmosphere. Also imagine that the walls of the container do not let heat escape. The question I have is what would be the final temperature of the low pressure gas (after a considerable time), higher than the temperature of the heating element at 2500 Kelvin or just the same. I'm assuming a Maxwell-Boltzmann distribution would describe the speeds of the particles and the temperature of a particle is (3/2)K_bT.

2. May 8, 2015

### Staff: Mentor

What are your thoughts on this? Would the heater be left on after a long time, or shut off?

Chet

3. May 8, 2015

### randombill

Let's imagine that the heater would only stay on at 2500k. The reason I ask this is because of the experiment at UW call the Madison plasma dynamo experiment. They use LaB6 as the heating element with a max temperature around 2500k and in the Madison experiment they plan on heating Sodium to a temp much higher than that, like 30k Kelvin. I'm just not sure how that would be achieved?

4. May 8, 2015

### Staff: Mentor

What do you think would happen with the heating element if you kept it on at 500 W after the temperature in the chamber reached 2500 K?

Chet

5. May 8, 2015

### randombill

My guess is the heater would stay at whatever temp that's equivalent to 500 w and the gas in the container would start to go above 2500 kelvin, but I'm sort of lost as to how to explain this using only convection; the average electron temps would definitely increase over 2500k.

6. May 8, 2015

### Staff: Mentor

The first law of thermodynamics tells me that if you keep supplying thermal energy via the heating element (electrical energy being converted to heat), and since the container is rigid so no work is being exchanged with the surroundings, the internal energy of the container contents will keep rising. In order for the heating element to supply heat to the gas, its temperature must be higher than the gas. So, if you keep supplying 500 W to the heating element, its temperature will rise above 2500. (What made you think that it wouldn't?). How much higher its temperature can get before burning out is what needs to be addressed.

Chet

7. May 9, 2015

### randombill

I don't disagree with your statement, the last part.

"How much higher its temperature can get before burning out is what needs to be addressed."

Is what I'm confused by simply from the standpoint that the melting point of the heater is 2500 Kelvin, therefore the gas around the element shouldn't ever reach anything above that, yet they're supposedly getting 30k Kelvin just by stirring the plasma? I'm confused now.

8. May 9, 2015

### Staff: Mentor

Well, the heater is not going to be able to do it, so something else must supply the required energy. Maybe viscous heating from the stirring could do the trick, but it might take a long time (if the stirrer is magnetic so that heat couldn't be conducted out along the shaft).

Chet