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15

updated calculations - based on neutrino energy escaping and vapor inhalation risk Your math is close but not quite right. First - the number of tritium atoms. There are 1000/(16+3+3) = 45 moles (as you said) This means there are 45*2*$N_A$ = $5.5 \cdot 10^{25}$ atoms of Tritium Now the half life is 12.3 years or 4500 days, that is $3.9\cdot 10^8 $s. ...


6

Actually that's not an impossible task as long as you don't constrain the problem by not allowing energy input to the filter. The problem is the famous Maxwell 's Demon, but in the end you have to pay the demon. His efforts don't come free. The Hilsch tube, originally thought to house the demon fails the challenge as it takes excessive energy to separate hot ...


6

Compare to the energy that the Earth surface receives from the sun, how much power comes from the inner melted core ? Very little. The Earth's surface emits about 503 watts per square meter (398.2 W/m2 as infrared radiation, 86.4 W/m2 as latent heat, and 18.4 W/m2 via conduction/convection), or about 260 petawatts over all of the Earth's surface ...


6

Yes there is, using electrostatic forces. See the details here: Electrostatic Fluid Accelerator I should add that it can't lead to a high compression ratio like a mechanical compressor, but technically it does compress the gas in the vicinity of the charging source. And that leads to flow. A perhaps more interesting followup question: can you conceive some ...


4

Recall two things... First that the 1st law is conservation of energy. Second that temperature is a non-decreasing function of internal energy. So if we take two identical samples of gas and add the same heat $Q$ to each (increasing their internal energies), but allow one to do work $W$ on the surrounding while the other does none, then the sample doing ...


4

Let us take the example of the Hubble primary mirror. It has a diameter of 2.4 m and a mass of 828 kg. It is actually made in a sandwich structure - glass-honeycomb-glass - making it about 30 cm thick (for stiffness) but light. The mirror is coated with an aluminum coating of thickness t = 65 nm, with a 25 nm MgF2 protective coating on top. Coefficient of ...


4

In statistical mechanics, at least when you can ignore the spin of the particles you're dealing with, the occupation number of a quantum state (that is, the number of particles in the state, or probability of a particle being found in the state) is proportional to $e^{-E/kT}$, where $E$ is the energy of the state. If you have a harmonic oscillator at ...


4

The heat flow (per unit area) through some thin layer, e.g. a boundary layer of water, is given by: $$ \frac{dQ}{dt} = \frac{K\Delta T}{d} $$ where $K$ is the thermal conductivity, $d$ is the thickness of the layer and $\Delta T$ is the temperature difference between the two sides of the layer. So a high thermal conductivity does indeed mean a high heat ...


3

The rapidity of heat loss from black body radiation depends only on the temperature of the body and the difference to the temperature of the environment according to the Stefan-Boltzmann law. which describes the power radiated. This will happen in any case for any body immersed (first version of question) in a supercooled liquid if its temperature is higher ...


3

Spilling supercooled liquid on your skin would actually be less painful than spilling a similar liquid that wasn't supercooled. This is because when a supercooled liquid freezes it gets warmer due to the latent heat of crystallisation released by the liquid to solid transition. So suppose we had some supercooled water and some other hypothetical fluid at ...


3

First of all you can directly write $p$ as a function of $V$ without solving a quadratic equation: $$ p = \frac{N k_B T}{V- N b } - a \frac{N}{V} $$ Then you take a look at the interesting points $$\left(\frac{\partial p}{\partial V}\right)_{T,N} = 0 $$ The solutions to this equation tell you where the bulk modulus (or its inverse, the compressibility) ...


2

Today I heard a thermodynamic argument for about this. Since there is little work done by the system in solid and liquid phase. The heat capacity must be (roughly) same for the solid and liquid phase. This one does not convince me at all. Especially, because no work is done by the system in the case one considers the constant volume heat capacity ...


2

In the supercritical state the difference between liquid and gas vanishes. The sharp distinction between liquid and gas only exists up to a critical pressure and temperature at which the energy needed to vaporize the liquid vanishes and the densities of the liquid and the gas get equal, above this points no different liquid and gas phases exist. In other ...


2

You will probably find the Stirling approximation useful here. For your purposes it will be sufficient to use the form $\ln N! \approx N\ln N - N$, which is valid for $N\gg 1$.


2

Entropy is a state variable. That means for every state you have a single value for entropy of that state. So the entropy difference of two states does not depend on the process that takes you from one state to the other. Therefore you can use this formula if the initial state is $(T_0,V_0)$ and final state is $(T,V)$. However the change in the Entropy of ...


2

There is also, a gas of photons in the right side. It was trapped there when you assembled your box, and since you are assuming a perfectly zero emissivity, these photons must be perfectly reflected from all surfaces. That means they are blue shifted if the wall moves toward the right and red-shifted if the wall moves toward the left. Result: If you ...


2

Planck published several works on the theory of blackbody radiation based on different ideas, but generally the use of integer counting of energy he meant to be used for the energy of material oscillators. He did not believe the quantization applied to light itself - he assumed Maxwell's theory with its differential equations and derived his spectral ...


2

Heat if you remember from 8th grade science transfers by convection, conduction and radiation. Convection is by the flow of a fluid which cannot go faster than light, conduction is caused by molecules colliding with neighboring molecules, conductive heat equations are only for after a steady flow has been established and do not treat transient effects so can ...


2

A state is thermodynamically stable when its Gibbs free energy is at a minimum. $$G=U-TS+PV$$ Holding all variables but $P$ and $V$ fixed, it means that: $$dG=dP V+PdV=0 \implies {dP\over dV}=-{P\over V}$$ Since neither of $P$ nor $V$ could be negative ${dP\over dV}$ must be negative.


2

The incoming waves will terminate against each other in the corners of the square pipe, meaning there is a deficit of heat in the faces of the square. If that's true, we should add more corners, and waste less material. A square has 4 corners, with not a lot of heat on the center of the faces. An octagon has 8 corners, with $ 1 \over 2 $ of the ...


1

You can pump heat from cold objects to hot objects if you pay some more energy (that's what your refrigerator is doing) and that doesn't violate second law of thermodynamics. You should note as you heat object, its thermal radiation will increase. Intensity (that is power per unit surface area) of thermal radiation is proportional to $T^4$ so when the ...


1

Assuming we can treat the air in the room as an ideal gas, it will obey the ideal gas equation of state: $$ PV = nRT \tag{1} $$ where $n$ is the number of moles of the gas. The question tells us that the pressure is constant, and obviously the volume of the room is constant, so the only things that can vary are $T$ and $n$. The question tells us that $T$ ...


1

Water is a complicated phase. I would expect a simplistic analysis to break down because water is really a quasi-crystal at loser temperatures. It tends to form cage-like structures because of hydrogen bonding. Like @SebastianRiese I think the argument that "there is little work done by the system in solid and liquid phase. The heat capacity must be ...


1

The equation: $$ dS = \frac{dQ}{T} $$ only applies to reversible processes. For an irreversible process $dS \gt dQ/T$. To see this start with the expression for the change in internal energy: $$ dU = dQ - dW $$ The internal energy is a state function, so this equation always applies whether the process is reversible or irreversible. So for a reversible ...


1

The sign is governed by the convention - whether the volume is of your system in consideration or not. If you decrease the volume of your system - you increase the energy of your system, so you require for total energy change to be positive. If the volume is describing your system then $ dV <0 $ and so $dE=-PdV>0$ is the correct expression If the ...


1

the shape and area of the cross section of the pipe can change flow property along the stream. The fluid velocity in a pipe changes from zero at the surface because of the no-slip condition to a maximum at the pipe center. In fluid flow, it is convenient to work with an average velocity which remains constant in incompressible flow. Laminar flow in a round ...


1

I suspect you are looking at the steady state solution of the set of partial differential equations that model heat dynamic heat conduction. The dynamic equations will show that the heat is NOT propagating at an infinite rate. Using the steady state solution to infer dynamic response is not proper.


1

The Landau model for ferromagnetism has the following expression for the free energy density, as a function of temperature $T$ and magnetization $M$: $$F(T,M)=F_0(T)+\dfrac{a}{2}(T-T_C)M^2+\dfrac{b}{4}M^4+\dfrac{c}{6}M^6+\mathcal{O}(M^6)$$ First order phase transition occurs when the first derivative of $F$ (namely, the entropy) is discontinuous as $T\to ...


1

What effect [does] heating have on [the electrical conductivity of] metals? Conductivity drops as temperature rises See How Does Temperature Affect the Conductivity of a Conductor? Note, this graph plots resistivity not conductivity, vs temperature. Temperature obviously affects the thermal velocity of free electrons and this affects the rate of ...


1

Let us understand Brownian motion in liquids before we look at the motion in solids. If you observe a glass of water at rest on a table, it "appears" to be motionless. However, all we need is a magnifying glass to observe the random, incessant motion of water on the surface. This random motion is a manifestation of heat. The same thing happens in a solid. A ...



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