Hot answers tagged

47

Can we compare alive cells with heat engines at all? No, not really, because the living being isn't only a heat engine. There are three main points I want to make here. 1. Homeostasis Requires Constant Energy Input This statement is especially true and obvious of homeotherms Mammals (Mammaliaformes, descended from the Therapsid Synapsid Amniotes), and ...


27

I'm really winging this one because the last time I did an equilibrium calculation was 35 years ago! But I'm fairly sure of a partial answer (see discussion at end). A gas's solubility in water (or liquid generally) almost always decreases with increasing temperature. This phenomenon is explained in a way very like the explanation of the increase in ...


23

What I fail to see is how moving too quickly could also impair cooling performance as stated in a lot of online forums. One argument I clearly remember from reading about this a while back was: and: You shouldn't crank the pump speed too fast or the water won't have time to pick up the heat from the waterblock as well. The latter statement you quoted ...


19

Ice can be denser than water for certain values of $P,T$. Look at these two pictures taken from here: The darker areas in the second picture denotes areas of greater density. So you can clearly see that when pressure is increased, ice becomes denser than water along the coexistence line. For example at $T=400$ K ice VII is clearly denser than water ...


14

The most immediate answer would seem to be that a great variety of different crystal phases can exist because their long-range order makes it possible to classify them based on the different symmetries of their lattice structure. Since the liquid (or amorphous solid) phase only has short-range order and the gaseous phase doesn't even have that, it seems ...


14

I will try to answer these questions from different views. Macroscopic view The "quantitative" rather than qualitative difference in a liquid-gas phase transition is due to the fact that the molecules arrangement does not change so much (there is no qualitative difference) but the value of the compressibility changes a lot (quantitative difference). This ...


12

Why is the efficiency of human cells less than efficiency of an Otto engine? It's not. You are comparing two very different things. The low value of 18 to 26% efficiency you found for the human body is the energy produced by an exercising human compared to the energy consumed by that person. The high value of 56 to 61% efficiency is for an ideal Otto cycle ...


11

This answer was meant as a comment to @WetSavannahanimal aka Rad Vance but it is rather long and I hit the character limit. The reason for the opaque center should be due to the manner in which the water volume is freezing. Presumably the solution is not mixed and the outside freezes first forming a crystalline (ice) wall through which the gas cannot escape....


10

The bottom line is that hot water loses heat at high temperature, giving a small negative entropy change while the cold water gain heat at low temperature resulting in a high entropy change. The net entropy change is positive. We can explicitly see this: At any instant, the infinitesimal change in the entropy of the system is $$dS=\frac{dQ_H}{T_H}+\frac{...


10

You are mistaken. You seem to be assuming that there is some kind of inertia in the process of heat transfer, as in water sloshing about in a tank. There is no such inertia here, so there is no oscillation. You write: Since heat has been transferred from A to B, unless I'm mistaken this will place B momentarily at a higher temperature than A. Yes, you ...


10

You have to be careful to distinguish between microstates and macrostates. Thermodynamic equilibrium is a macrostate which consists of a mixture of all possible microstates of energy $E$ weighted by a Boltzmann weight $e^{- \beta E} / Z$. A state in macroscopic thermal equilibrium can be thought of as "moving through phase space" ergodically (i.e. the ...


9

For a pure substance that can exist in the solid, liquid, and vapor states (i.e., wood is not in this category), let's assume that a closed container is half full of liquid and half full of vapor. As the temperature rises, the liquid expands and the liquid density falls. Also, as the temperature rises, the pressure in the container rises due to the vapor ...


8

The short answer: Cloudy ice is caused by gases (mainly nitrogen and oxygen) dissolved in the water that come out of solution when the water freezes. The small bubbles trapped in the ice cause the white appearance. Boiling the water removes the air dissolved in it, producing clear ice as a result. Assuming that other impurities don't produce the same cloudy ...


7

The many worlds interpretation has a lot of problems, but this isn't one of them. You're imagining "creating alternate universes" as some energetic event, like a mini Big Bang, but what really happens is a smooth splitting of the wavefunction. For example, suppose we have a spin in a superposition of up and down states, $$\frac{1}{\sqrt{2}} (| \uparrow \...


6

From a strictly by-the-formulas point of view, entropy change is heat transfer divided by the temperature over which the heat transfer occurs. The heat transfer is clearly the same for both volumes but positive for the cold volume and negative for the hot volume (heat flowed out of the hot volume and into the cold volume) but the average temperature over ...


6

To get the entropy change for a system experiencing an irreversible process, the first step is to forget entirely about the actual irreversible process and, instead, devise a reversible process that takes the system between the same initial and final equilibrium states. That is what is meant by $dq_{rev}/T$. The reversible process that you devise does not ...


6

There are two definitions of entropy, which physicists believe to be the same (modulo the dimensional Boltzman scaling constant) and a postulate of their sameness has so far yielded agreement between what is theoretically foretold and what is experimentally observed. There are theoretical grounds, namely most of the subject of statistical mechanics, for our ...


6

Gases in containers at high pressures have those pressures because there are more molecules in them than in the same container at atmospheric pressure, not because there is a difference between the molecular energies. At the same temperature, two containers with different numbers of molecules in them have the same probability distribution of energies. The ...


6

The temperature appearing the the Clausius inequality is definitely the temperature of the "boundary interface (with the surroundings)", or simply the temperature of the sources. One of the best places I have seen this discussion is in Fermi's book, chapter 5, section 11. He is explicit about it. To see this you have to recapitulate the steps in obtaining ...


5

Nothing in the laws of thermodynamics forbids multiple liquid phases for a single substance. The only limit is the simultaneous coexistence of at most three phases (at triple points). Water has a solid-liquid-gas triple point and several soid-solid-liquid and solid-solid-solid triple points; see the phase diagram of water and ice. In addition, although not ...


4

For quasi-stationary processes you can take the time derivative, no problem. Apart from the "state equation", there is a "process equation", for example, for an adiabatic expansion $PV^{\gamma}=\rm{const}$ or so. It is also quasi-stationary. What you can loose in taking the time derivatives are quick processes like sound or shock wave propagation and their ...


4

In particular I would like to know: if I have any reversible cycle followed by a gas, then the thermal efficiency of that cycle will be $$\eta=1-\frac{T_{\mathrm{min}}}{T_{\mathrm{max}}}.$$ As noticed by Wolphram jonny, the sentence above is not true. The Carnot theorem states that any reversible engine operating between two reservoirs has the maximum ...


4

This phenomenon you are describing is called the Mpemba effect after a Tanzanian student, Erasto Mpemba, who in 1963 noticed the temperature of ice cream affected how quickly it mix freezed, though the effect had been observed much earlier (the earliest known observation of this was by Aristotle in 4 B.C, though Aristotle probably didn't use ice cream). ...


4

For reference, the diagram is below. First, I'm just going to give a quick explanation of entropy. Before Boltzmann, people knew about entropy, they just didn't explain it correctly; namely, they thought of it as a measure of the uselessness of arrangements of gas. As an example, they thought that if you had a box, and all of the gas molecules in the box ...


4

Real world assumptions: No temperature gradients over the cross-section of the pipe. Plug flow (turbulent flow). Water heat capacity $c_p$ and density $\rho$ are temperature invariant. Consider an infinitesimal mass element $dm$ at temperature $T(x)$ travelling down the pipe at speed $v$. We apply Newton's law of cooling to it: $$\frac{dQ}{dt}=hdA\big(...


4

The Earth+windmill system has conserved angular momentum. When the windmill starts spinning the angular momentum of Earth must change in response. However this change is marginal. Furthermore the windmill system will stop spinning when the wind dies down and this will restore the original angular momentum of Earth (when I say Earth I mean everything inside ...


4

$1$ litre of water will remain almost $1$ litre as long as it is in the liquid state, no matter what the temperature is. The following formula gives you an order of magnitude estimate of the expansion: $$\Delta V=V_0\ \Delta T \ \beta$$ where $\beta$ is the coefficient of thermal expansion and $V_0$ is the initial volume. For water, $\beta \approx 10^{-...


4

It can't fall slower as the first cosmical speed (7.8 km/s), which is still very high. Although it would cause much smaller destruction as it would hit directly with the mean speed of the meteors (10-70km/s). The lower angle of the hit doesn't play a significant role, because considering its mass, the interaction with the atmosphere will be probably ...


3

Entropy is a tricky concept at first but with some rigorous thought it becomes more and more intuitive. When you mix hot and cold water they become inseparable in a closed system (closed to energy....we can still change the volume). Imagine putting a label on every single water molecule of the cold water and then picking them all out after you mix them with ...


3

Mixing the water at different temperatures is an irreversible process, in that once you mix them, you get an average temperature for the system and you can't undo the process, without doing work on the system. Entropy Postulate: If an irreversible process occurs in a closed system, the entropy S of the system always increase. This is because before you ...



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