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5

No. You wouldn't say that pair of beams has a temperature. Temperature is defined by the zeroth law of thermodynamics, which states that if $A$ is in thermal equilibrium with $B$ and $B$ is in thermal equilibrium with $C$ then $A$ is in thermal equilibrium with $C$ and $A$, $B$ and $C$ are said to have the same temperature. Temperature is fundamentally a ...


4

To start with, "water freezes faster when it starts out hot" is not terribly precise. There are lots of different experiments you could try, over a huge range of initial conditions, that could all give different results. Wikipedia quotes an article Hot Water Can Freeze Faster Than Cold by Jeng which reviews approaches to the problem up to 2006 and proposes a ...


4

This happens due to cooling affect of evapourisation. As you must be knowing, the temperature of the lquid is a factor of evapourisation. So as the temperature of hot water is more, the rate of evapourisation is also more. Now this is where thwe cooling effect of evapourisation takes place. As the water evapourates, it takes away some heat thus cooling ...


4

When a cup of coffee is hot, the air molecules directly above it get hot as well. After some time, they reach equilibrium and no heat transfer (or maybe very little transfer) occurs. By blowing, you disturb that equilibrium and replace the hot air molecules directly above the cup with colder air and therefore create once again a steeper temperature gradient. ...


3

What is entropy, more than disorder. Mathematically, entropy is just a measure of spread of a probability distribution: The lower the entropy, the more spiked the distribution. In statistical mechanics, a state is generally only partially defined via some macroscopic constraints, and entropy is a measure of microscopic indeterminacy. Maximizing entropy ...


3

The showers I have used that have two knobs have something akin to a globe valve for each line As you unscrew the handle, there is more opening between the plug and the body, letting more water through. The resistance of valves like this is quite variable when the plug is near the body. Once the plug is withdrawn a certain amount the resistance is small. ...


3

Actually, in your rotating torus your are mimicking gravity, which is point outward. I.e. the outside of the torus acts as a floor. The centrifugal acceleration would be $g\approx\omega^2 R$. This $g$ plays the same role as the gravitational acceleration on liquid or gas pressures under normal gravity conditions, so you can say $\Delta p = \rho g h$, or in ...


2

PhotonicBoom is correct in saying that the airflow created by blowing across the top of the coffee will replace the coffee-heated air with cooler air that will absorb more heat from the coffee. It also allows more of the coffee to evaporate (which might seem like a bad thing, but evaporation is simply the hottest molecules becoming gaseous and leaving, so it ...


2

The equation you state is a very general expression related to heat transfer, and basically everything goes into that constant. Convection of course is one thing, but what about radiative cooling (often important), diffusive cooling (might be important), and heat resistance, since the temperature of your object is not uniform. All these contributions can be ...


2

What is entropy, more than disorder? Don't look at entropy as disorder. Thinking of it as disorder has long been a source of confusion. Many texts are moving away from using the disorder description. Macroscopically, it's better to think of entropy as a measure of energy dispersion rather than as a measure of disorder. Microscopically, it's better to think ...


1

For a system of atoms to have a meaningful temperature, I would say there has to be uncertainty in their state, and there must be a way (at least hypothetically) for the system to exchange energy with some other system. The first example you give of the two beams is an idealized state with no uncertainty, so assigning a temperature would be impossible. You ...


1

I think that you are trying to compare two situations which actually are quite different. In the solid/solid contact case, the two solids are in contact with each other for a shorter amount of time as you go faster. If you made slab 2 very very long so that slab 1 is always in contact with it and then moved it at different speeds, but doing all of them for ...


1

For (1): the energy required to vaporise a liquid is known as the enthalpy of vaporisation, or alternatively as the latent heat of vaporisation. For water at room temperature this is about 44kJ per mole, and a mole of water is 18g. For (2): the density of air at room temperature and pressure is about 1.2 kg per cubic metre, so 1kg of air is 1/1.2 or about ...


1

Christoph gives a good answer from the point of view of statistical physics, but the first context we actually encounter entropy is in classical thermodynamics. It is useful even without the interpretation of being "the measure of disorder". This got slightly out of hand and is now quite technical, but I think it is still digestible and provides a complete ...


1

When studying dynamical systems you consider a low-dimensional phase space that only includes macroscopic variables. In this phase space dissipation does indeed cause volume contraction - but only because the energy that has been lost has been transferred to the far bigger phase space including all the microscopic variables. In this space energy must be ...


1

For $N$ particles that can occupy $M$ different states $\left(M\geq N\right)$, it seems to me that the answer is $$M\cdot M-1 \cdot \dots \cdot M-(N-1)=M!/(M-N)!\ $$ if one imposes that each must occupy a different state. That is since, to the first particle, $M$ states are available. For the second, $M-1$. We continue thus until we run out of particles, ...


1

The characteristic modes can be excited by photons whose energy matches these modes. However, heating mechanisms are dependent on several other parameters, not the least of which is the surface shape. Take a look at the literature on black-body cavities and on ultra-dark roughened surfaces for some info on how to maximize radiative absorption.


1

It is because of convection effect. Convection is fluid (in our scenario) movement driven by temperature difference. In this case grater temperature difference at the beginning - grater speed of fluid at the end. Fluid is cooling down near dish walls. This causes cooled water to sink faster in this part of dish. Picture shows water movement in dish in ...


1

For simple conductive heat transfer, h is $\kappa$, the thermal conductivity, divided by the length over which the temperature gradient exists. You can look this up for a given material. For convective heat transfer, this constant will depend on the details of your problem, including the dynamics of the liquid in question (can't simply look it up, you'd ...


1

In principle, the gravitational potential energy should be included into total internal energy, but in practice, most often it is not. I know of two reasons. because for systems that are discussed in thermodynamics, it is believed that gravitational energy is negligible compared to electromagnetic potential energy of the constituting particles; because it ...


1

Your separation into potential energy of the system as a whole due to external force fields and energy contained within the system known as internal energy seems a bit arbitrary. Still, if you want to split the PE up this way gravitational interactions within the system would have to go into internal energy. Take the Solar System as an example. Everything ...


1

The gravitational potential for particle 1 is $V_1(r_{12}) = -Gm_2/r_{12}$ and for particle 2 it is $V_2(r_{12}) = -Gm_1/r_{12}$. $m_2$ is in $V_1$ and vice versa because the gravitational potential energy is the potential energy in a gravitational field per unit mass, and therefore only depends on the mass that is generating that gravitational field. When ...


1

This is a very difficult problem. I try to explain why. If we want to obtain the mathematical proof of the second law, we must consider the mathematical proof of the entropy first, as a state function. Clausius’ definition $dS=δQ/T$ cannot be proven in mathematics, as an exact differential, so the definition $dS=δQ/T$ must depend on imaginary reversible ...



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