Thermodynamics question

Amhran Nua

I wonder if someone could settle a discussion being had elsewhere: If you have a room temperature heat reservoir and one at 3 k, and a thermoelectric engine between the two, what happens as regards the temperature of the cold reservoir?

I mean as I see it, if you put in heat energy x you get out electricity y plus whatever heat wasn't converted to electricity in the gradient, plus I guess entropy. Therefore the cold reservoir should increase in temperature very very slowly if you have a highly efficient thermoelectric engine and a high gradient, would that be about right?

And what happens with the entropy, is that just wear and tear on the engine or what?

d'Oracle

How big are the reservoirs?
Are they thermally isolated?
How much heat is lost by the engine?
What type of engine?

It seems like you are kind of talking about a theoretical and real situation side by side here.

If you start with a theoretical problem and then apply real conditions to it, the rabbit hole can go very deep indeed.

Amhran Nua

d'Oracle wrote: »

How big are the reservoirs?
Are they thermally isolated?
How much heat is lost by the engine?
What type of engine?

Eh well assuming they are thermally isolated, the hot reservoir would produce around 50 kilowatts at 300 k or around room temperature, the cold one would be around say ten thousand tons at 3 k, which would make the Carnot limit on efficiency 99%, unless I picked that up wrong, which is entirely possible. We were looking at these guys, and projecting maybe a 95% efficiency potentially possible in future. The temperature rise of the cold reservoir over a few months would be fairly negligible surely?

d'Oracle

I'm not sure really.

I mean in practical terms, regardless of the observed efficiency of the engine, if the temp of cold side reservoir wasn't constant (i.e. the increase in temp due to heat from the engine was negligible as you suggest) then the system would be of self defeating purpose. Which is to say that the efficiency would decrease as the cold side got warmer.

Amhran Nua

d'Oracle wrote: »

Which is to say that the efficiency would decrease as the cold side got warmer.

Yes, sorry to clarify what I'm trying to pin down here, the purpose of the exercise is to establish that the larger cold reservoir (around a thousand times larger) would not increase in temperature by much over the course of say four months, and that interposing a thermoelectric engine between the hot and cold reservoirs will in fact reduce the overall temperature of the system, rather than increasing it, since the thermal energy gradient is transferred to electrical energy, which is then presumably stored in a battery.

The discussion is bogged down in whether or not such an engine would in fact increase the overall temperature, which makes no sense to me, since that means thermal energy x is going in, and electrical energy z plus thermal energy (x plus y) are coming out.

Amhran Nua

Over two hundred views and only one opinion ventured? Anyone? I guess its the case that eventually the heat total would have to increase as batteries would be discharged doing some sort of work, but would they not apply a cooling effect in the interim.