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Because the liquid would boil away. Boiling is what happens when the partial pressure of a liquid exceeds the ambient pressure. Liquids have higher partial pressure as they get hotter, so we usually associate boiling with high temperature. For example, water needs to be heated to 100°C to boil at 1 atmosphere ambient pressure. However, pressure is ...

4

If we want to examine gravitational collapse from a statistical mechanics point of view, we find that there's a tradeoff between the fact that a more spread-out collection of matter has more possible position states, whereas a more concentrated collection has more possible momentum states (because more of the system's potential energy has been converted to ...

3

The definition does not require an "atmosphere". Your "environment" can be vacuum. A liquid can boil in vacuum.

2

Actually one can flood the mines on an asteroid. The water will become boiling, but before it all boils out the water will freeze. As such, the scientists could say so only if they anticipated negativity in ice bulbs forming in the mines. But the process of freezing is very slow, so the water most likely would reach the bottom of the mines.

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No, if $S$ is really the only thing you know about your system then there is no way to know its energy. There is no relationship between the energy and the entropy that doesn't involve some other quantity such as temperature. ...but surely you know something about your system, other than its entropy? I mean, you must know something about what it's made of, ...

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There are some nice ideas in other answers, but they are overseeing some basics. Let's do some thermodynamics. The efficiency of a thermal engine is bounded by the Carnot efficiency: $$\eta \le 1 - \frac{T_c}{T_h}$$ Where $T_c$ is the temperature of the cold end and $T_h$ the heat source. Assuming we are in a cool environment, $T_c=0 C$, $T_h=37 C$, so: ...

1

"a circuit that has different resistors at extremely different temperatures" -- Each resistor independently puts out its own noise related to its own temperature. "one long resistive element that has a temperature gradient across the whole thing" -- That's actually the same thing again. Treat it as a large number N of resistors in series, each with ...

1

There are actually two questions here. At phase equilibrium, yes independent water molecules do enter and leave the liquid vapour interface. The rate of crossing of individual molecules from one phase to another is characterized by an Arrhenius type rate equation of the form: $$\alpha \exp \left[ - \frac{\Delta E}{kT} \right]$$ where $\Delta E$ is the ...

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It depends on your power supply. The power $P$ through a circuit element is always given by $$P_\text{thing} = I_\text{thing}V_\text{thing}$$ where $I$ is the current through and $V$ the voltage drop across the thing that you're interested in. If your circuit element obeys Ohm's Law $$V_\text{thing} = I_\text{thing} R_\text{thing}$$ then you can write ...

1

The dimensionless Rayleigh number characterizes buoyancy driven convection. When the Rayleigh number is below a critical value, heat transfer is primarily by conduction (e.g. no Benard convection cells). When the Rayleigh number is above the critical value, heat transfer is primarily by convection (e.g. Benard convection cells spontaneously form and ...

1

An ideal gas should consist of pointlike particles that are non-interacting, except if they collide, in which case they should do so elastically, without losing kinetic energy. I do not think there is any distinction here between a collision and a repulsive force. Any short-range repulsive force between particles (short-range compared with the average ...

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