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Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of information content, how can these two principles be compatible? I don't think there's anything inherently quantum-mechanical about this paradox. The same ...

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Based on some "google research" I get the impression that the popularity of the perfume thought experiment stems from a 1975 Scientific American article written by David Layzer called The Arrow of Time. The article featured this figure visualizing the thought experiment: Of course, the notion that the second law of thermodynamics implies an asymmetry ...

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Ahh, I spent quite some time reading this problem, the problem with applying Dalton's Law of Partial Pressures is that we shouldn't be multiplying moles of $CO2$ with the total Pressure, rather we should multiply the mole fraction of $CO2$ with the total Pressure, in this case however, since the initial quantity/moles of oxygen is not known, it is not ...

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The key step in this derivation is the assumption of isotropy of particle velocities. Think of the velocity vector of each particle as a randomly selected direction in space, in combination with a randomly selected speed from a specified distribution of speeds. The result of such a random sampling is that on average $\langle v_x\rangle=\langle ... 2 The main assumption used here is that the direction of the velocity is distributed uniformly. This means that if I take a particle at random, the probability of its velocity pointing in any particular direction is the same for every direction; that is, no direction is more likely than the rest. Now suppose I take a whole bunch of particles and measure ... 2 Your requirement that the measurement be made with equipment available in a kitchen is a severe constraint as I can't think of any way of measuring the electrical power supplied. If it's impossible to measure the electrical power in then the only other approach is to measure the thermal power out - i.e. measure the heat produced by the appliance. Given that ... 2 The Second Law of Thermodynamics states that the entropy of the universe always increases or stays constant. This means that we can reduce the entropy of the gas in the box (gas compressed from the whole box to half the box at constant temperature), only if we increase the entropy somewhere else. For example, we can compress the gas, doing work on it, and ... 2 There has been a new approach that you may consider. Your question involves the energy conversion between heat energy and Gibbs free energy. Since the two both are non- conserved quantities, the changes in heat energy and both Gibbs free energy can be divided into the two parts: one is the fluxes, the other one is the productions. For heat energy,$\delta Q$... 2 If you fill a bottle with hot water, the water in contact with the sides cools quickly. This sets up convection currents, which help to cool the whole bottle, and ensure its temperature is rather uniform. The syrup is viscous, so this doesn't happen. The syrup in the centre of the bottle remains hot - maybe 80 C after half an hour. The coldest part of ... 2 Yes, it's boiling. The clue is that you said some of the air above the liquid was sucked out, so the pressure is significantly lower than normal atmospheric. Boiling happens when the gas pressure at the surface of a liquid is lower than the liquid's vapor pressure. When boiling something in a open container, we heat it to make it boil. Water boils at ... 2 I think you will find more useful material by rather looking for "heat pumps" instead of refrigerators. If you teach them about the basic ideas of thermodynamics used in a heat pump first, understanding refrigerators becomes trivial. Three useful links that I just found: Physics of heat pump How heat pump works The basic physics of heat pumps 2 Strictly in the sense of physics, the entropy is less free than it might seem. It always has to provide a measure of energy released from a system not graspable by macroscopic parameters. I.e. it has to be subject to the relation $${\rm d}U = {\rm d}E_{macro} + T {\rm d} S$$ It has to carry all the forms of energy that cannot be expressible macroscopically, ... 2 There are (at least) two things going on. Perhaps the easiest place to start is with the temperature as estimated from the radiation in the universe - possibly what you are referring to when you say the temperature is approaching 0K? The radiation in the universe takes the form of thermal blackbody radiation. It is emitted by material in thermal equilibrium ... 2 The heat capacity of an Einstein solid is given by $$C = Nk \left(\frac{\epsilon}{kT}\right)^{2} \frac{e^{\epsilon/kT}}{(e^{\epsilon/kT}-1)^{2}},$$ where$N$is the number of degrees of freedom. So the value of the energy quantum$\epsilon$, or more precisely the ratio$x\equiv\epsilon/kT$matters! The above equation tends to the ... 1 Now we have the second law of thermodynamics, that says that entropy always increases. Second law does not say exactly that. It has more formulations, some of which use the concept of entropy. One such formulation is When thermally insulated system changes its state from one equilibrium state to another, its entropy cannot decrease. This statement ... 1 I'm not sure how one can know that the half maximum corresponds to$kT/\epsilon \approx 1/3$without resorting to the formula for the heat capacity. Still, notice that there are only two energy scales, i.e.,$\epsilon$and$kT$, in the problem. Then, whatever (dimensionless) number that determines whether the equipartition holds or fails has to be the ratio ... 1 Are not we simply saying that things more likely to occur, occur more times? Isn't it then, that the second law is simply an inmense tautology? No, this argument doesn't suffice to prove the second law. This argument only proves that thermal fluctuations away from equilibrum should be rare and short-lived. That's a statement that doesn't have anything ... 1 You have not specified how the pressure is controlled in the two systems. If they are each at the triple point pressure of 611.73 Pa there is no reason for heat to exchange and all will stay constant. If the pressures are different from this (and not on the freezing curve) energy can be released if there is heat flow by transferring heat between the ... 1 No. As @Jim said, the heat would weaken the rock, which would cause a tunnel collapse before any sublimation could occur. Also, remember that the air in the tunnel would generally be at the same temperature as the rock (unless a large cooling system was put in), so thermal equilibrium would be maintained without any sublimation. 1 Liquids evaporate at any temperature - not just at their boiling point. This is the reason, for example, why wearing a wet shirt on a windy day makes you so cold: the water evaporates, and in the process "takes some heat with it". The explanation for this is simple when you think about statistical thermodynamics. You have a lot of molecules whose energies ... 1 Henri Poincaré, in discovering limit cycles, used a thought experiment containing a box with a partition. One side had a gas, and the other didn't. When the partition was removed, the gas would diffuse through the opening and occupy both sides of the container. He first published works describing limit cycles somewhere in 1881-1882. I am unsure if he ... 1 As a rule, when the initial temperature difference is the same, the system that rejects heat at the lowest temperature will be the more efficient. That is because this involves the least amount of entropy. So without doing the math, I would say that case (b) will give rise to the greater amount of extracted work - which is also your conclusion. And yes, ... 1 The expansion takes place when the pressure is changed suddenly and drastically modifying the initial equilibrium state, remember that at difference of the reversible case the pressure is not changed infinitesimally. So in the formula$P \Delta V$use the final pressure. The other questions you set up are very interesting, I recommend you this paper that ... 1 Volcanic eruptions release both stratospheric ash, which reduces insolation at the ground, and carbon dioxide, which has a long-term warming effect. The ash falls out of the atmosphere after a few years, but the extra carbon dioxide is brought from underground into the biological carbon cycle more or less in the same way as the carbon from fossil fuels. My ... 1 It depends on the eruption, location, magnitude , timing etc. Have a look at the great Krakatoa eruption in 1883. In the year following the eruption, average Northern Hemisphere summer temperatures fell by as much as 1.2 °C (2.2 °F).[9] Weather patterns continued to be chaotic for years, and temperatures did not return to normal until 1888. Note, the ... 1 You can only measure a part of EU compliance. By using your utility meter and measuring the difference between the power consumed over say 10 minutes with the appliance on and off (with everything else in the house as off or steady as possible), you can measure consumed power. However, that's just one part of EU compliance. The other is power factor. ... 1 The area of the manometer tube makes no difference. All that matters is the difference in the heights of the two ends (labelled$x\$ in your diagram). That's why pressure units like the torr exist that are (or rather were) defined as the pressure difference when the difference in height of a mercury manometer is 1mm. All that matters is the height difference. ...

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A certain volume of space with a uniform distribution of particles has maximum entropy. That is correct for non-interacting particles, but wrong for particles with the gravitational interaction. When gravity condenses these particles, it increases the entropy of the system, not decreases it, at least when the Jeans instability condition is satisfied. ...

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It has not be proven that The Second Law of Thermodynamics is physically derived from other basic physical principles. The H-Theorem is predicated upon some pretty serious, yet plausible, assumptions about how our universe works. To my knowledge, these assumptions have not themselves been explained using other principles and/or experimental verifications of ...

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