Could Both Carnot and Tom be Correct?
Posted: Wed Aug 14, 2024 4:39 am
Could Both Carnot and Tom be Correct?
I've always suspected the following, but just figured it out. Heat is being rejected in a nonmagical but different way than through the cold plate.
The question is why are both Carnot and Tom correct? The answer is buffer pressure. The derivations I've provided in the past, are valid for both an engine running in a vacuum or with a buffer pressure. Tom is working exclusively with a buffer pressure. Although the efficiency equations are not affected. the heat gets rejected in different ways depending on having a buffer pressure or not.
The fact that an isothermal power stroke is 100% efficient, heat in equals work output, only applies to zero buffer pressure, and a single stroke. Many derivations, using calculus, assumes integration to zero pressure. And or zero Kelvin. Running an atmosphere or buffer pressure, the zero in calculus now becomes the buffer pressure. Easily recalculated, should someone care to do so. Adds a simple subtraction of buffer pressure.
Buffer pressure 15 psi. Plus of minus 5 psi. 15/5 = 0.3 or 30%.
A nonzero buffer means the power stroke is no longer 100%. Example, say 30%. 70% of the heat coming in goes out as work through the piston into the cold sink known as the atmospheric pressure. This energy is lost directly to the outside air. It is gone. It doesn't get rejected as heat through the cold plate. In fact the cold plate gets colder during this stroke if insulated. The gas, by definition, isothermal, stays hot.
The regenerator and displacer change the gas temperature to cold Tc, while saving that energy difference and using zero work (constant volume).
It gets worse for the return stroke. The work lost during the power stroke, is returned by atmospheric pressure. The gas adiabatically heats from the retuned work. It heats less than the work from the power stroke, because the gas is colder than for the expansion power stroke. The cold plate might be slightly colder than the atmosphere. The air rushing back into the piston cylinder could also be slightly colder. They are subjected to hysteresis. That cold air is pulled into and through Tom's insulation, further cooling the cold side of the engine and reducing the work needed and returned.
The displacer and regenerator return the energy back to the gas, becoming hot Th.
In other words, for a 80% Carnot rule engine, the buffer pressure eats 70% of the rejected heat as atmospheric work. Leaving 10% or less to come out of the returning piston and cold plate.
10W Qh, 2W power output max, 7W heat removed by working the atmosphere directly. 1W removed by the cold plate, which is fanned by the piston pushing air in and out through the insulation.
Now just imagine how those figures would decrease if the engine could only absorb 1/10 or 1/100 that amount of power?
It may very well reject more heat with insulation than not, for atmospheric LTD engines, running unloaded, only.
If anything, Tom's experiment verified Carnot. It still needs measurement of work output to confirm that theory. Thanks Tom.
I've always suspected the following, but just figured it out. Heat is being rejected in a nonmagical but different way than through the cold plate.
The question is why are both Carnot and Tom correct? The answer is buffer pressure. The derivations I've provided in the past, are valid for both an engine running in a vacuum or with a buffer pressure. Tom is working exclusively with a buffer pressure. Although the efficiency equations are not affected. the heat gets rejected in different ways depending on having a buffer pressure or not.
The fact that an isothermal power stroke is 100% efficient, heat in equals work output, only applies to zero buffer pressure, and a single stroke. Many derivations, using calculus, assumes integration to zero pressure. And or zero Kelvin. Running an atmosphere or buffer pressure, the zero in calculus now becomes the buffer pressure. Easily recalculated, should someone care to do so. Adds a simple subtraction of buffer pressure.
Buffer pressure 15 psi. Plus of minus 5 psi. 15/5 = 0.3 or 30%.
A nonzero buffer means the power stroke is no longer 100%. Example, say 30%. 70% of the heat coming in goes out as work through the piston into the cold sink known as the atmospheric pressure. This energy is lost directly to the outside air. It is gone. It doesn't get rejected as heat through the cold plate. In fact the cold plate gets colder during this stroke if insulated. The gas, by definition, isothermal, stays hot.
The regenerator and displacer change the gas temperature to cold Tc, while saving that energy difference and using zero work (constant volume).
It gets worse for the return stroke. The work lost during the power stroke, is returned by atmospheric pressure. The gas adiabatically heats from the retuned work. It heats less than the work from the power stroke, because the gas is colder than for the expansion power stroke. The cold plate might be slightly colder than the atmosphere. The air rushing back into the piston cylinder could also be slightly colder. They are subjected to hysteresis. That cold air is pulled into and through Tom's insulation, further cooling the cold side of the engine and reducing the work needed and returned.
The displacer and regenerator return the energy back to the gas, becoming hot Th.
In other words, for a 80% Carnot rule engine, the buffer pressure eats 70% of the rejected heat as atmospheric work. Leaving 10% or less to come out of the returning piston and cold plate.
10W Qh, 2W power output max, 7W heat removed by working the atmosphere directly. 1W removed by the cold plate, which is fanned by the piston pushing air in and out through the insulation.
Now just imagine how those figures would decrease if the engine could only absorb 1/10 or 1/100 that amount of power?
It may very well reject more heat with insulation than not, for atmospheric LTD engines, running unloaded, only.
If anything, Tom's experiment verified Carnot. It still needs measurement of work output to confirm that theory. Thanks Tom.