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27

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 ...


8

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 ...


4

Before mixing the average kinetic energy of the molecules which make up the tea is greater than the average kinetic energy of the molecules which make up the milk. This is restatement of the fact that the tea is hotter than the milk as the temperature of a substance depends on the average kinetic energy of the molecules which make up the substance. When you ...


4

The question doesn't say exactly what is meant by darkest, but it seems reasonable to interpret the brightness as the intensity of radiation from the object. In that case the relevant equation is the Stefan-Boltzmann law: $$ J = \varepsilon\sigma T^4 $$ where $\sigma$ is the Stefan-Boltzmann constant and $\varepsilon$ is the emissivity. The emissivity of a ...


3

P-V work is not the only kind of work that can be done on the contents of your system. In the case of your fan example, the fan is doing work on the gas within the container by exerting force on it through a displacement (of the fan blade). The kinetic energy imparted to the gas by the fan is then converted to internal energy by viscous dissipation (a ...


3

In statistical mechanics, the most important behavior of a system (and the starting point for any more detailed analysis) is the bulk behavior in the limit where its size is macroscopic (i.e. $N\sim 10^{23}$). Statistical mechanical predictions of macroscopic thermodynamic properties (like total energy and entropy) can be decomposed into distinct sectors ...


3

The heat death of the universe is the idea you are describing (this idea is also known as the Big Freeze). The problem with this idea is for it to work the cosmological constant has to be zero...and it isn't zero. It's very tiny, but it isn't zero. The other problem with your idea is the belief that because it all "freezes", so to speak, it'll all collapse ...


3

The Maxwell-Boltzmann distribution and the Boltzmann distributions are probability distributions, i.e. functions $\rho(\vec x,\vec v)$ of velocity and position of a particle, that say what is the probability density that the velocity and position belong to the small cube around the given value of them. The Boltzmann distribution is the more general one, $\...


3

Yes. An equivalent way of saying this is that if an ice cube (or iceberg...) melts, the water level remains unchanged. (I.e.: the melted iceberg exactly fits in the 'hole' it creates underwater.) To see this, think of what is holding the ice up: it's buoyancy, which is the upward force due to the pressure of the surrounding water. This force is directly ...


2

This is a really deep question. My explanation will maybe be not so rigorous, but I hope it can help shed some light. Let's start by saying that reversible work is indeed path-dependent, so it is not a state function. Consider for example the two reversible transformations $A$ and $B$ in the picture: They both are composed by an isobaric and an ...


2

Otto cycle consists of two isochoric and two isentropic processes. If $T_4$ approaches to $T_1$, then $T_3$ will approach to $T_2$, because for Otto cycle, line $3\to 4$ in $T-s$ diagram must always be vertically. Thus, although the numerator of the Otto efficiency approaches to zero, but the fraction doesn't approach to zero, because the denominator ...


2

Water evaporates if it has a higher temperature and or if the humidity of the air isn't at 100%. This is a nonlinear process as the vapour pressure of water is nonlinear with temperature and the rate of evaporation is linear with partial pressure difference (the partial pressure in the water is equal to the vapour pressure). The evaporation reduces the ...


2

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 ...


2

I think there may be some confusion as to terminology: compressibility is defined as $$ -\frac 1V \frac{\partial V}{\partial p}$$ where something like temperature or entropy is held constant, whereas the compressibility factor is defined as a certain ratio. (ref: https://en.wikipedia.org/wiki/Compressibility) In the ideal gas, particles do not interact ...


2

The starting point for the development of this equation is an energy balance on a fixed control volume of fluid: $$\int{\frac{\partial E}{\partial t}dV}=-\int{E(\vec{v}\cdot \vec{n})dA}+\int{(\vec{v}\cdot \vec{\sigma} \cdot \vec{n})dA}-\int{\vec{q}\cdot\vec{n}}dA$$ where dV is differential volume, dA is differential surface of the control volume, and $\vec{n}...


2

For a general closed systems containing only a single chemical species, you have, if you express $U$ as a function of its natural variables $\{S,V,N\}$ $$U=U(S,V,N)=TS-PV+\mu N$$ from which we obtain $$d U = \frac{\partial U}{\partial S} dS + \frac{\partial U}{\partial V} dV + \frac{\partial U}{\partial N}dN=T dS - P dV + \mu dN$$ $U$ is a function of $\{...


1

Thermodynamics was developed largely with gases in mind. In this case work can be done on the gas, the $p\Delta V$ term. But there is also the internal energy U to consider, so when one wants to compare experiments done on the same substance under different conditions it is useful to define a new quantity, which is the enthalpy, as the internal energy plus ...


1

In physics one of the most fundamental concepts is the conservation of energy and in thermodynamics we systematize, in an ideal manner how to account for the energy and changes in energy in systems. The units of enthalpy are energy units such as Joules. And for a homogeneous system, the enthalpy is the sum of the system internal energy and the pressure ...


1

Ok, let's take the 1st law (in any reference frame) as $$\frac{D}{Dt}E_t(V) = P + Q $$ where $V$ is a part of the body, $P$ is the work rate by mechanical processes and $Q$ is the change of heat content. They will hopefully become more clear when I say how they can be calculated: $$P= \int_V dV \rho \vec{v} \vec{b} + \int_{\partial V} da \vec{v} \mathbf{T}\...


1

You are talking about two different cases. At first you say: We notice that our liquid is no longer as hot as before adding milk. And your meaning about "our liquid" is the tea. Then you say: The total thermal energy of the system (the cup) is conserved. And your meaning about "system" is tea + milk. The total thermal energy of tea and milk is ...


1

When you say that the system (ie the contents of the cup) is not as 'hot' as before, you are talking about temperature. However, the system was initially at two different temperatures (hot tea, cold milk). There is no obvious way of comparing the two initial temperatures with one final temperature. To decide if there has been a change in temperature, you ...


1

But for an ideal gas, internal energy is only a function of temperature and so internal energy remains constant here,no change in average kinetic energy of gas particles takes place, so where does the chaos come from to increase entropy of the system. 'Chaos' is not a very well defined term in context of statistical physics. It is not necessary to use it ...


1

You are correct that quantum mechanics is the basic framework of nature, but not everything in this basic level is quantized, in the sense of coming in a discrete spectrum. Even the spectrum of the hydrogen atom at very high n has such close spacing where it can be called a continuum. The first quantum level is bound atoms. The second level is bound ...


1

The compressibility factor was originally derived from empirical testing of gases to correct for the observed non-ideal behavior at more extreme pressures and temperatures. Although it cannot be derived from first principles in the kinetic theory of gases, the experimentally derived factors can be reconciled using Van Der Waal's equation that deals with the ...


1

Imagine a portion of the(liquid) water. It will be in equilibrium with the whole fluid. The buoyancy force $E_1$ over this portion matches its weight. Now freezes this same portion. The buoyancy force $E_2$ on the ice equals its weight. Since the weights are the same, the buoyancy forces are equal. This implies the volume of fluid dislocated in both ...


1

If you isolate the balloon from everything else then after filling it with gas the balloon will soon attain the temperature of the gas. Then the balloon and gas will be in thermal equilibrium and no more heating/cooling will take place. Upon colliding with balloon skin the atom is not always lose energy but half the time it will gain energy (if the two ...


1

Your balloon is not an isolated system, it can exchange heat with the environment as the "skin" material is not a perfect insulator. The expanding gas inside a balloon will cool as it expands, but the outside air will warm it up again after some time, the speed will depend on the balloon material and volume, but eventually the heat exchange between ...


1

Clausius' statement about heat not being able to flow spontaneously from a cold body to a warm body is sufficient to prove that no engine can have an efficiency greater than that of a perfectly reversible engine. But it's not enough to prove that the Carnot engine is the only reversible engine. For example, there could be a perfectly reversible engine where ...



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