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There are two parts to your question, and I'll address them individually, assuming that the room+ball system is an isolated system, i.e. no work is being done on the system, and no energy is being added / removed. Part I: How cold will it get? This depends on the size of the room, the materials that everything in the room is made of, the size and material ...


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[As requested, I convert my comment into an answer, as it might also be useful for other people.] There is a very interesting series of works by Lieb and Yngvason on entropy and the second law of thermodynamics, based on the kind of axiomatic approach you seem to be interested in. You can start with this introductory paper, or this, this or this more ...


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A number of factors go into determining the optimum daytime temperature settings for cooling: one of them is humidity. An air conditioner doesn't 'cool', it removes the heat, through the heat of the liquid refrigerant vented to the atmosphere. More humidity means in a residential setting without a lot of tonnage of air being moved is more 'wattage' is ...


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Ultimate physical motivation 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 ...


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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 ...


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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


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The heat capacity of an Einstein solid is given by \begin{equation} C = Nk \left(\frac{\epsilon}{kT}\right)^{2} \frac{e^{\epsilon/kT}}{(e^{\epsilon/kT}-1)^{2}}, \end{equation} 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 ...


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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 ...


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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 ...


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Thermodynamically entropy is defined by \begin{equation} \mathrm{d}S = \frac{\mathrm{d}Q_{rev}}{T} \, ,\end{equation} where $\mathrm{d}Q_{rev}$ is the heat, transferred reversibly. As you point out it can be shown that this quantity is a function of state. This implies that the entropy of any thermodynamic system has, up to a constant, a well defined ...


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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 ...


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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 ...


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The main thing you want the air conditioner to do is to remove the heat that enters the apartment and eject it to outside. The rate that the heat enters depends on the thermal conductivity of the apartment (which we assume to be fixed) and the temperature difference between the inside and the outside. The greater the heat difference, the greater the heat ...


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Heat Capacity is well defined: $C = \frac{\Delta Q}{\Delta T}$ see: http://en.wikipedia.org/wiki/Heat_capacity Heat Transfer by Holman. It is a property that refers to the amount of energy required to increase the temperature of an object. This is slightly different than specific heat $C_p = \frac{\Delta Q}{\Delta T \times m}$ see: ...


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Heat capacity is the ability of a material to store heat, higher the heat capacity higher the amount to heat stored by the material. Heat transfer usually varies inversely with heat capacity, i.e heat transfer will decrease with increase in heat capacity and vice versa. Thermal diffusivity is the ratio of thermal conductivity to the heat capacity, it says ...



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