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There is actually a very simple derivation of the Second Law in classical thermodynamics for an ideal gas, assuming only classical mechanics and the First Law. Here is a brief sketch -- whether this constitutes a "proof" depends largely on taste, the level of rigor desired, and how comfortable you are with thermo-style derivations.
The Second Law of Thermodynamics is an approximation, it has statistical or probabilistic validity. Statistical Mechanics corrects the plain flat out version of it that says entropy never decreases to the following.
The second law of thermodynamics and the associated concept of entropy have been sources of confusion for thermodynamics students for centuries. The objective of the present development is to clear up much of this confusion.
The second law of thermodynamics proposed by Clausius, Kelvin, Carnot ..etc in its original form as T dS> dQ for irreversible process and Tds =dQ only for reversible thermodynamics process. The thermal efficiency of any cycle is defined as the work done or performed by the working gas (WD) divided by the inputs of heat Q. Applying the second ...
The second law of thermodynamics says that entropy can only increase, so if the early universe had been in a state of maximum entropy, then the cosmos would have experienced its heat death immediately after being born. This contradicts the observation that the present universe contains burning stars, heat engines, and life.
2nd law in term of entropy: The second law of thermodynamics can be stated in terms of entropy. If a reversible process occurs,there is no net change in entropy. In an irreversible process, entropy always increases, so the change in entropy is positive. The total entropy of the universe is continually increasing
I think that the second law of thermodynamics is a direct consequence of the symmetry of spacetime. Imagine you have two identical cubes of metal A and B with one common side, the first one warmer than the other. If you wait long enough, A and B will end up being at the same temperature. The same phenomenon would occur if B were warmer than A.
The second law of thermodynamics states that all energy sources spontaneously go from a "more concentrated" state to a "less concentrated" state (e.g., hot objects always spontaneously cool down to ambient conditions, but cold objects never spontaneously heat up above ambient conditions).
A certain volume of space with a uniform distribution of particles has maximum entropy. However, the action of gravity would condense these particles, decreasing the entropy of the system, which would violate the second law of thermodynamics. My question is simply: what am I missing here? What is the solution to this contradiction?
Background. Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as foll