QUESTION: Can changes of heat capacity produce a temperature difference and create heat-engine?
All details here:
ANSWER: Based on the weak effects you mention vs real temperature changes, this system (though it is not shown doing any actual work) will not create enough heating to actually move that piston. There's a ridiculous amount of energy involved in heat transfer, and further in phase changes...this system you describe on your wordpress site will basically just sit there. :( Neat concept, though! You get points for an original type of perpetual motion device.
---------- FOLLOW-UP ----------
QUESTION: Thank for your answer.
I disagree about perpetual motion device, because unpaired electrons with energy produce magnetic field. Also this device does not violate second law of thermodynamic. I would call it as a converter of internal energy into mechanical oscillations.
You're absolutely right the effect is very weak. However, It's just a concept to show how to use magnetic intensity difference to produce mechanical oscillation.
I have one more question about this device.
During magnetic spin polarization, the substance stops fluctuation on one vibrational degree of freedom. This changes a heat capacity of substance and temperature goes up. Also in reverse mode, when the paramagnetic element will go away from magnetic field then the substance will start fluctuations on this vibration degree of freedom and temperature will go down. Is
It good comparison with law of momentum conservation which is working on nuclear level?
ANSWER: The idea is fine, but any oscillation that happened if you built such a device probably wouldn't even be visible to the naked eye unless you did it under weird ultra-low gravity conditions and such.
As far as your further question goes, perhaps you could explain the first sentence about fluctuation on a vibrational degree of freedom in more detail?
---------- FOLLOW-UP ----------
QUESTION: The gravity field could be excluded if device will work in horizontal position.
A neodymium permanent magnet exhibits magnetic field in few Tesla. This is enough to change temperature of polycrystalline Ni-Mn-Ga and a Gadolinium alloy in few Kelvin. The curie temperature of alloy of Gadolinium is 293 K. In higher temperature it will be used as paramagnetic element. Also, If use a liquid with low point boiling same as used for "drinking bird" toy then it would be possible build a workable model for demonstration.
The previous question was about mechanism of heat capacity changes for substance into magnetic field. Could be compared redistribution of fluctuations inside a substance with law of momentum conservation?
I don't think you understand completely. An Nd magnet has a maximum of about 1 Tesla right at the surface, far less over any distance at all. The Curie temprature of the best alloy known is apparently only 173 K, not 293 K (if you have a reference, I'm all ears). But that's not the problem. Even if you design it with clever tricks to maximize the effect, you need something to get the gallium in between the magnets (compressing the piston) in the first place. So if you just push it in on its side, it'll heat up and compress the gas, pushing the piston back out. But on its way in, it'll start giving off heat through the piston, so your lose energy. Then on its way out, it will cool down and the air will simultaneously decompress...basically it will slow to a stop on the way out, but there will be nothing to make it go back in. If you want to use the whole momentum of the piston to make some mild oscillations, that's the only thing that will cause oscillations. And it can do that with no magnets and no gallium alloy. This is really just overcomplicating a simple oscillator by adding thermal damping to the process.
Anyhow, the redistribution of magnetic moments, not fluctuations, inside the substance is a quantum phenomenon that is not really comparable with something as simple as conservation of momentum. The two aren't the same thing.