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20

First, strictly speaking a neutron star is not a nucleus since it is bound together by gravity rather than the strong force. Measuring a surface temperature for any star is deceptively simple. All that is needed is a spectrum, which gives the luminous flux (or similar quantity) as a function of photon wavelength. There will be a broad thermal peak somewhere ...


9

Earth can lose heat to space through radiation. The earth behaves roughly as a blackbody and so radiates electromagnetic radiation into space at a rate of roughly 120 PW.


8

First of all, there are no Moon-sized asteroids in the (sufficiently inner) Solar System. The largest asteroid has radius 450 km which is about 4 times smaller (64 times smaller volume) than the Moon. Moons of planets are not counted as asteroids. A collision with a Moon-sized object would of course be a terminating catastrophe for the Earth. If you look at ...


8

Dimensionless equations have the advantage that they work for any value of the parameters. They are scale invariant. So the solution in terms of a single dimensionless variable applies to all values of $D$ and $t$. It also allows the definition of characteristic values for the dynamic variables. In your example, one could say $u_0$ = ...


7

Let's say your goal is to describe the shape of some object, such as a box. You could create a completely arbitrary ruler and measure the three axes of the box, coming out for example with lengths of 11.72, 23.44, and 35.16 of your arbitrary ruler units. Or you might look at your results more closely and think hmm, something is going on here, since the ...


7

It's the water itself that forms the lens. Lenses work via refraction. The refractive index of water is about 1.333, which is different from the refractive index of air (about 1.0), so rays of light bend at the junction of the air and the water.


7

If carefully interpreted and converted to mathematics, the passages are not contradicting one another. The uncertainty principle guarantees that there is some zero-point energy that can't be eliminated (the second passage) – it is the energy of the ground state of the physical object (atom or a macroscopic piece of a material). On the other hand, the ...


7

This is a very interesting question. In fact liquid helium-4 exhibits this property of "thermal superconductivity". What happens is that when one tries to establish a thermal gradient a "temperature wave", also referred to as second sound, propagates. This gives it effectively an infinite thermal conductivity or as you put it, thermal superconductivity. My ...


6

Your question, I think, is best answered by separately addressing its many directly and indirectly implied questions. You are mixing up a lot of different notions together in your question as you've phrased it. So to clarify, I thought I would pull all of the pieces apart. To start: Do atoms have nonzero kinetic energy at absolute zero? Yes, they still ...


6

Here's an intentionally more conceptual answer: Entropy is the smoothness of the energy distribution over some given region of space. To make that more precise, you must define the region, the type of energy (or mass-energy) considered sufficiently fluid within that region to be relevant, and the Fourier spectrum and phases of those energy types over that ...


5

In terms of the temperature, the entropy can be defined as $$ \Delta S=\int \frac{dQ}{T}\tag{1} $$ which, as you note, is really a change of entropy and not the entropy itself. Thus, we can write (1) as $$ S(x,T)-S(x,T_0)=\int\frac{dQ(x,T)}{T}\tag{2} $$ But, we are free to set the zero-point of the entropy to anything we want (so as to make it convenient)1, ...


4

You have to check if the temperature is small compared to the chemical potential. In heavy ion collisions, the chemical potential is rather low but the temperature is very high, so one have to stick with thermal field theory. In compact stars the densities and therefore the chemical potential is at the MeV scale whereas the temperature is at the keV scale so ...


4

The total radiative power emitted by the Sun is equivalent to the total radiative power emitted by an ideal black body with a temperature of 5778 K and a surface area equal to that of the Sun. This 5778 K is the Sun's effective temperature. The spectrum of the Sun is very close to that of a 5778 K black body, but there are deviations. Some are due to ...


4

It matters what's on fire. If it's a flammable material that floats, like oil or gasoline, some fraction of it will remain on or return to the surface and you may have flames on the water. (This is basically the only thing that I remember from watching Black Beauty as a kid.) If it's a flammable material that sinks, the water will probably extinguish the ...


4

You are missing the fact that when I have a lot of air in a tight space, and I then heat it up, I get really high pressure. You have to draw yourself a diagram of pressure vs volume - compressing the cold gas requires a certain $\int P \cdot dV$ of work, but then I heat the gas and the subsequent expansion takes me along a different curve where the work ...


3

I believe that in the top you'll find it's the saturated vapor pressure of water. http://en.wikipedia.org/wiki/Vapour_pressure_of_water (80 F ~27 C vapor pressure of about 27 mmHg or 27mm/760 mm * 14.7 = 0.52 psi.. not bad.


3

Taking an intuitive guess here: The pressure above the water column is indeed very low, and water molecules at the surface may escape - but they are also held back by the surface tension of the water (is your meniscus concave or convex?). There is an equilibrium here, and the temperature is low enough that the water won't boil off all at once. So at room ...


3

The statement "the internal energy is known to be a relative quantity, with no unique zero" refers probably to the fact that for common systems of thermodynamics that do not lose or gain matter, the First law of thermodynamics implies the internal energy is a function of temperature $T$ and volume $V$ such that addition of a constant independent of them has ...


3

As far as dimensional analysis goes, temperature and energy are separate and independent physical dimensions. However, there is a more or less unique way to translate temperatures into energies and vice-versa, which is by means of Boltzmann's constant $$k_\text{B}=1.380×10^{−23}\:\text{J}/\text K.$$ Any given temperature $T$ has an associated ...


3

why does it seem improper to add many speeds (or velocities)? Adding speeds is ofttimes inappropriate even in Newtonian mechanics. Suppose Mark is moving 3 m/s eastward with respect to Bob, and John is moving 3 m/s westward with respect to Mark. The relative velocity between Bob and John is zero rather than the 6 m/s suggested by adding speeds. You can ...


3

Your question, as of right now, seems confused to me. An extensive property of a system is one that scales with the system size. An intensive property is independent of the system size. For example, consider a system $A_1$ with $N$ particles in a volume $V$, with density $\rho=\frac{N}{V}$. Now, we consider two of these systems separately, $A_1$ and $A_2$, ...


3

In a metal the Fermi energy is somewhere in an unfilled band. At any temperature above absolute zero (which you can never reach) there are states available for electrons to get to and result in conduction at the Fermi surface. This will occur in any metal. Superconductivity is a separate phenomena that I won't touch on here.


3

The entropy of a system is the amount of information needed to specify the exact physical state of a system given its incomplete macroscopic specification. So, if a system can be in $\Omega$ possible states with equal probability then the number of bits needed to specify in exactly which one of these $\Omega$ states the system really is in would be ...


3

You can set the entropy of your system under zero temperature to zero in compliance with the statistical definition $S=k_B\ln\Omega$. Then the S under other temperature should be $S=\int_0^T{\frac{dQ}{T}}$.


3

Much of the vapor you see at that stage is unburned material, not a true "smoke" which would be ashes or non-burnable material. A true solid is very difficult to burn. Most fuels instead volatilize as the temperature rises, increasing the surface area. This material coming from the heated fuel appears similar to smoke. A visible flame is the burning of ...


3

Have a look at this chapter THE THERMODYNAMICS OF THE HUMAN BODY AND THE BIOPHYSICAL FEATURES OF THE THERMAL ENERGY In effect the main cooling method for the human body once the outside temperature gets larger than the body temperature is evaporation of sweat which is increased by fanning oneself with make do fans, as the humid air is pushed away and less ...


3

These solutions are preferred because they directly embody the scale invariance of the equation. In general, when a physical problem has some sort of symmetry - like the parabolic dilation invariance of the heat equation - then this establishes a corresponding action of the symmetry group on the solutions. The canonical forms based on dimensionless ...


3

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 ...


3

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 ...


3

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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