Does ambient temperature affect temperature of heat source?

[stuffandthings]

If a Stirling engine was operating with a heat source on one end and ambient temperature on the other end, increasing the ambient temperature would obviously increase the temperature on the "cold" end.
However, would increasing ambient temperature increase the temperature of the "hot" end, which is a metal plate, by an equal amount?

If it would, I could increase both ends of the engine by an equal amount to simulate an increase in ambient temperature.


Thanks.

[deleted-2131]

Hi stuffandthings,

No. To see why, consider a simplified thought experiment. For example, let's say the hot end of your engine is 100 C and the cold end is 20C. The ambient temperature is also 20C. (I'm picking random temperatures here). Finally, the surroundings (at ambient temperature) are much, much more massive than the engine. In that case, the cold end of the engine is in thermal equilibrium with the surroundings. The hot end is "trying" to reach thermal equilibrium, so the hot end would cool as heat diffuses from the hot end to the cold end and from the hot end into the surroundings. If left for long enough, the hot end, the cold end, and the surroundings would all evolve to the same temperature, at a rate that depends on the thermal gradient (difference in temperature) and mode of heat transport.

Now, a second scenario. Imagine we have the same starting conditions. But, shortly after starting the experiment, we suddenly increase the temperature of the surroundings to 50C. The cold end's temperature will increase to equilibrate with the ambient surroundings. But, the ambient conditions are still cooler than the hot end. The hot end's temperature will still decrease, not increase, although the rate of temperature decrease will be slower, since the thermal gradient between the surroundings and hot end is smaller. The temperature of the cold end will increase, and the temperature of the hot end will decrease, at different rates and by different amounts.

If the temperature of the surroundings were increased to 120C, instead of 50C, then the temperature of the hot end and cold end would both increase, at different rates and by different amounts, to reach thermal equilibrium with the surroundings.

If there is a heat source at the hot end that produces enough heat to keep the temperature of the hot end constant, then the situation is somewhat different. But, the change in temperature and rate of change in temperature of the two ends of the engine will still be different.

[stuffandthings]

Is there any realistic scenario that would increase the temperature of both ends of the engine by an equal amount?

And the hot end does have a heat source.

[deleted-2131]

Hi stuffandthings,

I supposed if you put each end in close contact with something that was X degrees warmer than that particular end, then both ends would increase in temperature by X degrees, if the heat source is large enough and the thermal conductivities and specific heats of the two ends of the engine are the same.

If you are trying to simulate an increase in ambient temperature (i.e. the temperature of the engine's surroundings), then it may not be necessary to increase the temperature of both ends by the same amount. If you increase ambient temperature, the two ends of the engine will be affected to varying degrees, rates, and directions (up/down), depending on the change. They will not both increase in temperature by the same amount. So, if you are looking at the effect of ambient temperature on your engine, then you don't want to increase the temperature of the two ends by the same amount. That isn't a realistic representation of what increasing the ambient temperature does to the engine. Instead, you could increase the ambient temperature by some fixed amount, and tracking the responses of the hot end and cold end to that change.

[stuffandthings]

I supposed if you put each end in close contact with something that was X degrees warmer than that particular end, then both ends would increase in temperature by X degrees, if the heat source is large enough and the thermal conductivities and specific heats of the two ends of the engine are the same.

Why couldn't that something be air?

When I increased ambient temperature of the engine by about 25 degrees C, the temperature of both ends increased by 10 degrees C (give or take a degree or two). Was that merely coincidence?

[deleted-2131]

Hi stuffandthings,

Air works just fine.

I'm a bit confused as to what you mean by the "ambient temperature of the engine". Are you referring to the temperature of the air surrounding the engine? As to your results, the degree or two difference may be significant, if it reproducible. The timescale of your measurements also matters in interpreting your results. Interpreting your results will require a bit more information. To help me help you better, can you please explain more about the heat source the one end of the engine is in contact with? What is the temperature of the hot end? What is the temperature of the heat source? Is the heat source in physical contact with the hot end? What is the temperature of the cold end? What was the increased ambient temperature? How large is the engine? How long did you let the engine equilibrate with the increased ambient temperature in the surroundings? Did you repeat the experiment several times? If so, were the temperature differences of "a degree or two" consistent?

If you have repeated the experiment and obtained the same data, then the results are unlikely a coincidence. But, without these details, it is difficult for me to know how to interpret your results. I suspect there is something in your setup that I'm missing or misunderstanding. So, any other details you can provide about your setup will be very helpful.

[stuffandthings]

Are you referring to the temperature of the air surrounding the engine?

I am referring to the air around both ends of the engine by ambient temperature.

I want to experiment the effect of increasing the temperatures of both ends of the engine by an equal amount, and I previously thought that this could be done by increasing ambient temperature.
For this actual experiment, I will be using a hot plate as a heat source for some tests and dry ice as a "cold" source for other tests.

To separately test if increasing ambient temperature would increase the temperature of both ends of the engine by an equal amount, I placed the engine about two inches above a candle first in room temperature and then in a freezer at -2 degrees Celcius.
I let the temperature equilibrate with the change in ambient temperature until the temperature reached a constant value. The temperature of the heat source was too high for my thermometer to measure, but the temperature of the hot end was 77 degrees Celcius in room temperature and 66 Celcius in the freezer. The temperature of the cold end was 34 degrees at room temperature and 24 degrees in the freezer.

This is the engine I'm using:
https://lh3.googleusercontent.com/-CgoO ... engine.jpg

The pressure chamber is about a centimeter from top to bottom.

I haven't repeated this side test and have instead started my main experiment.

And a side question: Is an engine's Carnot efficiency directly related to its actual efficiency?

[deleted-2131]

Hi stuffandthings,

Thanks for the info - that engine is definitely not the picture I had my head!

Are the hot and cold ends the red triangles in the picture you posted? The red metal is not very thick, so I expect conduction to be fairly rapid (characteristic timescales on the order of 10 to 10s of minutes, depending on the metal type).

One way to interpret your data from the freezer and candle (although I'm still not clear on the exact geometry involved, which matters) is that the waste heat from the engine dominates the thermal budget of the engine. Now, I'm not convinced of that myself, but it's one way of looking at the data.

RE: Carnot efficiency: the Carnot efficiency is the highest efficiency a heat engine can possibly have. The actual efficiency of a heat engine will be less than the Carnot efficiency.

[stuffandthings]

The ends of the engine are the blue metal plate at the bottom and the red metal directly above.

One way to interpret your data from the freezer and candle (although I'm still not clear on the exact geometry involved, which matters) is that the waste heat from the engine dominates the thermal budget of the engine. Now, I'm not convinced of that myself, but it's one way of looking at the data.

That's what I thought too.

I know the actual efficiency is always less than the Carnot efficiency, but is it a set percentage of the Carnot efficiency?

[deleted-2131]

Hi stuffandthings,

The difference between the Carnot efficiency and the actual efficiency of an engine depends on the nature of the engine cycle, along with other factors. So, not every single engine in the wide, wide, world operates at (picking a random number) 90% of its Carnot efficiency. The following Wikipedia article describes the engine cycle efficiency for several different types of engines. Also take a look at the section on "Other Inefficiencies" to get a feel for factors (besides engine cycle) that may vary from one engine to another and definitely affect efficiency.

http://en.wikipedia.org/wiki/Thermal_efficiency

[stuffandthings]

Terik Daly I know that.
But if an engine's efficiency is currently, say, 50% of its Carnot efficiency.

If its Carnot is doubled, would the real efficiency also be doubled?

[deleted-2131]

Hi stuffandthings,

Thank you for pointing out what you do and do not know. The more information you provide in your posts, the more likely it is that you will get helpful responses. We Experts don't know your background knowledge, etc. unless you tell us what it is. So, thank you.

The Carnot cycle is the most efficient engine cycle for converting a given amount of thermal energy to work. The equation for the Carnot efficiency depends only on T_hot and T_cold. Changing the Carnot efficiency therefore requires changing T_hot and T_cold. As far as I know, changing T_hot and T_cold in such a way as to double the Carnot efficiency does not automatically double the real efficiency of the heat engine.

[stuffandthings]

I realize it probably won't be by the same percentage, but will increasing the Carnot efficiency of an engine always result in improved real-life efficiency (unless it involves some mechanical factors that change with temperature, but this would depend purely on the construction of the engine)?

[deleted-2131]

HI stuffandthings,

Sorry for the protracted delay in getting back to you. I suspect it will vary on a case-by-case basis. However, it would not surprise me if changing the engine cycle to one with a higher Carnot efficiency usually increases "real-life" efficiency.