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It is a matter of convention in a specific community, which typically arose by accident, like many other things. Just to give a few examples: writing the complex exponent $e^{\pm i\omega t}$ where to …

Translational modes typically have a continuous spectrum, so that their states with non-zero energy are populated at very low temperature. On the other hand, rotational and vibration modes have discre …

Matter is atoms and molecules, whereas heat is a change in energy (not even the energy itself) of these atoms and molecules. So they are not really the same thing. The Einstein's equation, $E=mc^2$, …

All texts on statistical physics/thermodynamics address this point, although not necessarily in terms of homogeneous functions, i.e., not necessarily in terms of equations - as it is often the case in … Remarks In practice, in many problems thermodynamics/stat phsyics is reduced to non-interacting Hamiltonians, for which the additivity of energy is exact. …

Process with no heat flow is generally referred to as an adiabatic process. Quasistatic processes might be adiabatic or not. In fact, neither isothermic, nor isobaric, nor isochoric processes are adia …

Syringe is usually modeled as cylinder with a piston - it is only one wall that moves, and there is usually a force applied to it, or a work done by they gas/liquid pushing against this wall, since th …

The other answer correctly mentioned that the primary cause is different number of atoms, and the molar heat capacities are approximately the same, as per Dulong-Petit law. However attributing this to …

The point of the statistical mechanics is pretty much to describe the state of a system of many particle in terms of macroscopic variables. The introductory chapters of statistical physics textbooks u …

It depends on the details of the problem (which are, admittedly, not always clearly stated). For example: Some problems with massive pistons deal with a static situation, where the mass of the piston …

The body A would definitely cool down (as per the second law of thermodynamics), whereas whether body B heats up or cools down depends on how many energy will leak into radiation (which is neglected inn … This is just a radiative reformulation of what is known as Maxwell demon (closely related to Brownian ratchet) - a clever device that is supposed to beat the laws of thermodynamics, but separating particles …

It is not actually the same system. The (sub-)system of interest is a part of a much bigger system. In many cases it is convenient to think of it as a collection of "identical" systems, i.e., the syst …

Entropy production Finally, in the context of non-equilibrium thermodynamics one does extend the definition of entropy to non-equilibrium states, speaking of the entropy production. … Minimum Principle in Non-equilibrium Thermodynamics …

The Fundamental thermodynamic identity is: $$ \text{d}U = T\text{d}S - p\text{d}V $$ Isentropic process means no entropy change, that is $\text{d}S=0$. Isochoric process means no volume change, that i …

What exactly is meant by "the single particle explores the states of each one of the particles in the larger system in thermal contact"? This is not a proof, but an assumption called ergodicity, o …

I think @hyportnex has already given a very good answer, but I would like to add a few clarifying comments: In the "talk" tab for Wikipedia Heat Engine article, someone is questioning whether an inte …