13
Entropy on the Earth has decreased over time as more and more structures and patterns have been added.
The entropy of the earth has decreased over time due to the fact that it has cooled down significantly and not due to increased complexity of life or certain structures.
...the Earth as a system clearly has much lower entropy than it had in the past...
...
13
To differentiate itself from its surroundings, any living organism (no matter how simple) must decrease its entropy. Or, at least, it must ensure that its entropy increases more slowly than its surroundings. This takes energy, which creates heat. The organism must excrete this heat into its surroundings. And this means that the total entropy of the organism ...
7
An organism (or any self-replicating arrangement of matter) is a machine that concentrates environmental negentropy in itself while increasing total system entropy.
The false belief that evolution represents a movement from higher to lower entropy because more advanced life forms seem more "ordered" is common. Earth is indeed not a closed system. ...
5
It is a convention that we take the direction of increasing time as the direction of increasing entropy. We could reverse the convention. But in either case the thermodynamic arrow of time must align with the perceptual arrow of time because it is not possible to use an observed state in the present (a memory or other record) to infer the details of a state ...
4
There is some ambiguity in how entropy is defined in thermodynamics/stat. physics, as, e.g., discussed in this answer. To take the two most common definitions:
In thermodynamics entropy is defined phenomenologically as an extensive quantity that increases with time - so it is extensive by definition
In statistical physics entropy is defined as a logarithm ...
4
Let's say one particle can be in one of $\Omega_1$ states. Then two particles can be in $\Omega_2 = \Omega_1^2$ states (because particle 1 can be in one of $\Omega_1$ states, and particle 2 can be in one of $\Omega_1$ states). Carrying on this logic, $N$ particles can be in
\begin{equation}
\Omega_N = \Omega_1^N
\end{equation}
states. Since the entropy of ...
3
If I understand your question correctly, you are asking:
You define entropy as $S=\int\frac{\delta Q}{T}$.
Clearly, $T$ is an intensive quantity, as is $\frac{1}{T}$.
If $\delta Q$ is extensive, then so is $\frac{\delta Q}{T}$, since a product of an intensive and an extensive quantity is extensive.
So, if $\delta Q$ is extensive, then $\int\frac{\delta Q}{T}...
3
Generally, I think what these popular treatments are trying to get at is the Loschmidt paradox. Roughly, this asks the following question: why, if the underlying laws of physics are symmetric, is there any preferred direction of time at all? Why is one direction of time (the one we call the past) different from the other (the one we call the future)?
There ...
2
Your first equation is incorrect and your final conclusions are correct.
We have conservation of energy which is expressed
$$
dU = dQ + dW \tag{1}
$$
and by arguments involving Clausius' theorem one can arrive at
$$
dU = T dS - p dV. \tag{2}
$$
Both the above equations hold no matter how the changes are taking place. (1) can be interpreted as a statement ...
2
The problem is the relationship $\delta Q\leq TdS$. It should more properly read $$\int{\frac{dQ}{T_B}}\leq \Delta S$$where $T_B$ is the temperature at the boundary interface between the system and surroundings (through which dQ flows). For a reversible process, $T_B$ is equal to the system temperature T.
In all cases, between two closely neighboring ...
2
The third law of thermodynamics states, "The entropy of a system approaches a constant value as its temperature approaches absolute zero."
This constant entropy, $S_0$ must be independent of any other state variables, like pressure, volume, applied magnetic field, etc. No matter what the starting state, as $T\rightarrow 0$ the same $S\rightarrow ...
2
Actually, the final temperature is 49 C. If C is the heat capacity of the liquid water and $T_R$ is taken an absolute reference temperature for zero entropy for water, then the initial entropy of the 1 kg of water is $(1)(C)\ln{[(273+7)/T_R]}$, the initial entropy of the 2 kg of water is $(2)(C)\ln{[(273+70)/T_R]}$, and the final entropy of the 3 kg mixture ...
2
Yes, the statement by Brian Clegg is absolutely correct. This is in full accordance with the "Dissipative Structures Theory" established by the Nobel laureate Ilya Prigogine. We regard the so called self-organized system of Earth as a system in a Dissipative Far Equilibrium State indeed. Such a system which has passed non-linear far equilibrium ...
2
Does entropy change when work in done on the system?
Total entropy change equals entropy transferred plus entropy generated. Only heat transfers entropy. Reversible work itself does not transfer entropy. It is only the heat that may result from reversible work that transfers entropy. On the other hand, irreversible work does change (increase) entropy due to ...
2
You are not missing anything, what you said is correct.
Physical theories are time symmetric, e.g. Maxwell's equations.
There is one exception and that's cosmology, however that's more of a problem for our cosmological models and doesn't show that the arrow of time is not reversible.
See also this question Does time symmetry cause the matter/antimatter ...
2
The second law entropy statement refers to the entropy of an isolated system.
If a system can move reversibly between states of different entropy, then it is not an isolated system. But the combination of system with its environment might together be isolated. So then any entropy moving out of the system goes into the environment, and any entropy moving out ...
1
If you define the system consistently, the 2nd law always holds. If you define the system inconsistently, you can violate any law of physics you like.
Case 1: The system is always the refrigerator in isolation, before, during, and after the thought experiment. All the normal laws of physics apply, but nothing happens.
Case 2: The system is the refrigerator ...
1
There are two ways that the entropy of a closed system can change:
By heat flow across the boundary between the system and its surroundings at the boundary temperature $T_B$. This part of the entropy change is given by $\int{\frac{dQ}{T_B}}$, where the integral is carried out along the process path from initial state to final state. This contribution to ...
1
In classic thermodynamics, the existence of entropy, and that is is maximum at equilibrium, is a postulate. An axiom. This means that it is not "justified". There is no explanation of why. As you say, it is leap. Fortunately, the postulates are the only leaps. Everything else in the theory can be mathematically proven from those postulates.
The ...
1
If I'm not mistaken, Callen pulls a fast one and redefines some terms at the end of Chapter 1, so that all equilibrium states now have $d^2 S < 0$ (bolding mine):
By straightforward differentiation, we computer the extrema of the total entropy function, and then, on the basis of the sign of the second derivative, we classify these extrema as minima, ...
1
You can see from the definition of entropy
$$
S=k_B \log W
$$
that it is not energy: $W$ is the number of microstates, hence $\log W$ is just a pure (dimensionless) number, consequently dimension of entropy is equal to that of $k_B$ which is energy per temperature. Therefore entropy is neither energy nor temperature: it is a new independent concept.
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