# Tag Info

## Hot answers tagged thermodynamics

28

Firstly, to make a valid comparison between how water and air 'feels' on your skin, two conditions would need to be met: Both water and air would have to be at exactly the same temperature. That temperature would have to be lower than human body temperature (strictly speaking skin temperature). If those conditions are met then water would certainly feel ...

9

I think there is a misunderstanding. You are perfectly right when you write that the total micro canonical entropy of a combined system will be $$S_\textrm{combined}(2E) = k_B\ln \sum_x \Omega(x)\Omega(2E-x)$$ The micro canonical entropy ought to be a function of only the total energy, total amount of matter and total volume of ...

7

It's an interesting video but I wouldn't describe what's happening as 'explosions', more like rapid deflagrations. Explosions require prior containment (like in a bomb shell) before violent energy release. What I suspect is happening is the following. When strongly heated Pyrite undergoes an oxidation reaction, reacting with oxygen in the air and/or the ...

6

If there is friction (air resistance), that friction will extract energy from the spinning fan, thus slowing it to a stop. If you extract energy in any other way, you are also applying friction to the fan, again slowing it to a stop. In other words, yes you can extract energy from the fan, but no more than the rotational energy that the fan possesses: ...

6

Major edit: In @gatsu's answer, it is pointed out that only the amount of energy should matter, which is correct, as there's no such thing as distinguishable microstates with only rearranged energy (think stars-and-bars-type entropy calculations). So, I've edited out that part of the first paragraph and equations (in the first draft, I dropped that part of ...

5

The entropy $S$ is extensive as long as you're consistent about what you mean by entropy. In your case you've mixed up two different definitions. One definition of the entropy has the system at fixed energy $E$ -- the other, a fixed temperature $T$. Fixed-E entropy For a system with fixed energy $E$ the entropy is defined to be $$S = \log\Omega(E) ... 5 The energy of an electrical wave certainly undergoes energy loss through heat, so in that way is entropic. This is a result of the material's resistivity through which the electricity is conducted. The mechanism is primarily scattering of the energy through electron-phonon interactions, but electron-electron interactions do also occur. In metals, the main ... 5 Bubbles are formed when the pressure in the fluid is less than the saturated vapor pressure of the liquid at that temperature, modified by surface tension effects. Surface tension actually increases the pressure inside a gas bubble in water; the approximate increase in pressure is \Delta P = \frac{2\sigma}{r} (see for example this earlier answer). The ... 4 It is all a matter of engineering balance, between the water circulating in the radiator circuit of the car, which enfolds the engine and with water-metal contact which takes heat away at a certain rate. In automobiles and motorcycles with a liquid-cooled internal combustion engine, a radiator is connected to channels running through the engine and ... 4 Edited because I had misread the question If the goal is to keep the tea hot, you add the milk first. This will bring the temperature of the tea down by some amount \Delta T, and the cooler tea will now lose heat more slowly while you dissolve the sugar. I am assuming that since you cannot see the sugar in the milky tea, you will do what I do - you add ... 4 Three processes are involved: Conduction: Heat flows from the object to its environment. Removal rate of heat from the interface further away from the object is proportional to the coefficient of conductivity (0.024 for air, 205 for aluminum -see http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html). Convection: The interface between the object ... 4 Are all heaters (same wattage, electric to thermal, no geothermal or other extra energy source) exactly as efficient as each other? No. Let's focus just on electrically powered heaters. If you have a heater that basically consists of a resistor with a current passing through it, you have 100% efficiency of electrical energy to heat energy conversion. ... 4 An arbitrary speed is tricky, but the ultra relativistic case is easier. If you look at this What's the max speed a man-made satellite can travel in space before its circuitry stopped working? SE answer, I noted that the *specific intensity * (in W m^{-2} sr^{-1} Hz^{-1} of the CMB radiation is boosted by a factor z^3, where z is the usual ... 4 If the processes are instantaneous, and you drink the tea at once after that, then it doesnt matter. A more interesting question would be, when to put the milk in the tea. Now it does matter if you wait first and then add the milk and drink - or if you add it at once and then wait and drink. Do you see, why? Also, in your formulation "you were asked to ... 3 These are conjugate variables. 3 We do observe spontaneous symmetry restorations in nature. This is called an emergent symmetry. See e.g. this post. A system posses an emergent symmetry if it appears symmetric at large (coarse-grained) scales although the apparent symmetry is explicitly broken by the microscopic description (typically the Hamiltonian or Lagrangian). I can give two examples ... 3 It is reversible in the first case because it satisfies the reversibility definition. A thermodynamic process is called reversible if an infinitesimal change of the external condition reverses the process. Consider a system at temperature T in thermal contact with a thermal reservoir at same temperature. By an infinitesimal increase dT of the reservoir's ... 3 Consider the virial theorem, which says (ignoring complications like rotation and magnetic fields) that twice the summed kinetic energy of particles (K) in a collection of particles (could be the gas in a star, could be stars in a star cluster) plus the (negative) gravitational potential energy (\Omega) equals zero.$$ 2K + \Omega = 0$$Now you can ... 3 Basically, it's a consequence of negative heat capacity. Gravitationally bound systems can (often do) behave such that adding energy results in reducing temperature, and vice versa. You can understand this intuitively if you consider a simple two-body system: adding energy to the system causes the orbits to expand, and bodies on larger orbits move at lower ... 3 The answer to this question depends on various aspects. For instance when you say white object, do you mean perfectly white? or white with respect to only visible light? Same happens for a mirror too. The most direct way to look into the problem would be following. Mirrors are nothing but extremely fine and optically flat white surfaces at the back of ... 3 At the power station electricity is generated as work from a heat engine. Work is entropy free, so we have an entropy free electron-gas at the point of generation. However, a thermodynamic gas will always equilibrate to the available degrees of freedom. In this case it is the electronic states of the conductor in the transmission wire. There will be a ... 3 Wikipedia says at above 1.416785\times 10^{32}~\rm{K}, all theories breakdown. So, that is theoretical limit. In actuality, 7.2 trillion deg F is the highest known temperature, and that is in Large Hadron Collider (LHC) when they smash gold particles together. In terms of motion of atoms, the limit would be much lower because, the atoms will fly away as ... 3 There's something called the "Planck Temperature" that is the current limit of how hot something can be before the physics we use to describe it breaks down. The Planck Temperature is about 1.4 \times 10^{32}~\rm{K}. Above this temperature, we can't describe the behavior of a substance because we don't have a working theory of quantum gravity. Of course, ... 3 A hotter black body emits more radiation than a colder black body at all wavelengths. The hotter body will have the peak of its spectrum at a shorter wavelength, but it outshines the colder body everywhere. The intensity of the radiation from a black body is given by:$$ B(\lambda,T) = \frac{2\pi ...

3

Energy stored as heat, by itself, is neither low- nor high-quality. What matters is the temperature at which the heat is stored, and the relationship of that temperature compared to the heat sink that will absorb the excess energy in the process. To be more specific, say you have a heat sink at $T_S=20°\:\mathrm C$, such as the atmosphere for a car engine. ...

3

The (long-term) temperature of an object depends on the heat transfer between it and all of the environment. Air isn't a great conductor of heat. So if there is little air movement, the radiation environment may dominate the heat transfer. A cold calm day may feel quite balmy under full sunlight. On a cold evening, the sky may have a radiation ...

3

One benefit of scaling the heat capacity with another extensive variable is that you end up with an intensive property -- heat capacity per # of particles. Similarly specific heat refers to the heat capacity per unit mass so that the value of the intensive property can be compared between samples of the same material but with different sizes or geometries ...

2

Your second thesis is right. At least the result. The explanation not, as the example in the answer of Diracology might illustrate. Assume, that the piston does not move (we fix it). So $V$ didn't change on either side. Obviuosly, $n$ didn't change on either side. Therefore, $p$ is proportional to $T$ (in each side separately!). So if $T$ rises by the same ...

2

Let $T_{20}$ be the initial temperature of tank 2 and $T_{10}=T_{20}+\Delta T$ be the initial temperature in tank 1. Let $\delta T$ be the equal rise in the temperature of both thanks. Assuming that the piston does not move, we would have $$p_{2f}=p_2\frac{T_{20}+\delta T}{T_{20}}$$and$$p_{1f}=p_1\frac{T_{20}+\Delta T+\delta T}{T_{20}+\Delta T}$$ Since ...

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