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9

This is a bit of a soft question (get it?). Intuitively, the ice cream and bowl will move towards a state of equal temperature (second law of thermodynamics). When you stir the ice cream you are doing at least four things: you are 'encouraging' the heat to become more uniformly distributed (as you suspected), causing the ice cream to come into contact ...


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 $u_0$ = ...


8

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 ...


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.


6

Sound is attenuated in air - this is an irreversible, lossy process that results in the heating of the air. You can conclude that it is not an isentropic process. See my recent answer to another question for some of the math behind this - showing that while the amount of heating is very small, it is not zero. For practical purposes (for example, for ...


6

Sound waves do generate changes in temperature because the propagation of sound is an isentropic process. Keep in mind though that changes in static temperature can very well occur without the generation of heat. Moreover, the pressure changes associated with sound waves are of such a small magnitude that the observable temperature changes are minimal (but ...


5

Put more simply: sound waves are attenuated as they propagate through air (this is more easily measured for very short wavelengths, e.g. ultrasound). This means they lose energy - which is turned into heat of the air. The amount of heating, however, is very very small. Let's do the math. A sound wave of 120 dB (really loud) has energy of only $1 ...


4

See e.g. Landauer's principle http://en.wikipedia.org/wiki/Landauer's_principle and capacity of noisy channels http://en.wikipedia.org/wiki/Channel_capacity. Not everybody agrees with these limits, but to me they seem fairly reasonable based on relatively straight forward noise arguments. In an ideal world (i.e. temperature T=0), there is no lower limit ...


4

The premise is true if the object is in thermal equilibrium. See, for example, this Wikipedia article. Besides radiation, heat can be transferred by conduction and convection.


4

A breeze at 35°C and 90% humidity (typical conditions in Houston, Texas) doesn't cool you off. It just makes you feel even more miserable. A breeze at 40°C and 20% humidity (typical conditions in Phoenix, Arizona) doesn't cool you off, either. It, too, just makes you feel even more miserable. Your body cooled because the air velocity was much lower than the ...


4

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 ...


3

Just to give an account of some of the most popular approaches that I have met so far about out of equilibrium thermodynamics and corresponding generalized definitions of entropy and thermodynamic potentials. On one end of the spectrum, on can follow a statistical inference approach to statistical mechanics in its very foundation (as it has been proposed ...


3

Heat corresponds to random movements of atoms and molecules. It travels only through conduction - slowly. Sound consists of ordered movements, travelling through a medium as a wave (although it can also stand still, as in a standing wave). Large numbers of atoms or molecules move back and forth in synchrony. Sound eventually becomes random, as it is ...


3

First, a comment. Radiative heat transfer is oftentimes a non-factor for everyday objects encountered here on Earth. Radiative transfer is important for objects that can't exchange heat conductively or convectively, and for objects whose temperatures differ by a marked amount. That said, the rest of this answer will focus on radiative heat transfer. If ...


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 ...


3

The microcanonical ensemble is the (maximum entropy) probability distribution for a given specified total energy. What you've calculated is actually the maximum entropy distribution with no constraints on the energy, which is the same as the canonical distribution at infinite temperature ($\beta = 0$). To correctly calculate the microcanonical entropy, ...


3

Isentropic processes are ones with constant entropy. Since entropy is defined as dS = dQ/T, then a reversible adiabatic process with dQ = 0 is an isentropic process. Need to take a step back to understand this. First, the physics of waves in gases come from the fluid equations. These include conservation of mass, momentum and energy. These three ...


3

You're problem is not fully defined, but let's begin to define it. Firstly, you're looking for something with a high emissivity $\epsilon$, so that it will absorb most of the incident light. This factor is simple: the higher $\epsilon$, the swiftlier you can transfer heat to your stone. As long as the stone doesn't get too hot, the rate of absorption ...


3

The following are postulates of thermodynamics (Callen, Thermodynamics, 1st ed.) I. There exist particular states (called equilibrium states) of simple systems that are chracterized by their internal energy $U$, their volume $V$, and the particle numbers $N_1, \dots, N_r$ of their components. III. The entropy is a monotonically increasing function ...


2

i have pondered this theory before. with ac the change in refrigerant state causes a high and low pressure range. when a car needs gas topped up its because the high pressure is not reaching the required pressure so when the state is changed it is cold. if this would be possible with water would certainly interesting. to throw another theory into the ...


2

The change in electronic excitation represents both a potential and a kinetic energy term in classical physics, but there is no simple correspondence to classical physics terms, when you are looking at quantum systems. All we really care about is the total energy difference between electronic states. Those energy differences correspond to the energies at ...


2

What constituent of internal energy does an electron excitation represent? You can think of electrons as just like planets orbiting the sun and get the correct answer to this question. An electron in a higher energy level has less kinetic energy, but more potential energy as it is (generally) farther from the nucleus. The net result is more energy. ...


2

It is reasonably easy: the balloon will want to maintain pressure equilibrium with its surroundings, i.e. $P_{in} = P_{out}$. This occurs because any pressure imbalance can be redressed on the sound-crossing time scale, i.e. the time it takes a sound wave to cross the balloon's diameter. This can easily be checked to be less than a millisecond, thus on ...


2

Phase transitions are a many-body effects. You can not generate sharp transition with a finite number of degrees of freedom (or particles). However as you add particles the features of the system may become sharper. In the limit of infinitely many particles (thermodynamic limit) you get a truly discontinuous transition. In practice nothing is infinite. The ...


2

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 ...



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