thermodynamics

I have this diagram: And I have done these calculations: $$R_x=-20sin(30)+30cos(35)+80cos(45)=71.14 \; lb$$ $$R_y=20cos(30)+30sin(35)-80sin(45)=-22.04 \; lb$$ The magnitude of this resultant force is then: $$|R|=\sqrt{71.14^2+(-22.04)^2}=74.48 \; lb$$ Here's the part I need help with. I can get a theta angle for where the resultant force's angle is, but I want to figure out how one would get this…

In an assignment, we were asked to find the critical temperature of a collection of Rubidium-87 atoms. The answer used an expression derived for spin-zero bosons in Schroeder's Thermal Physics (which I have also found elsewhere online): $$ k_B T_c = 0.527 \left( \frac{h^2}{2\pi m} \right) \left(\frac{N}{V}\right)^{2/3} $$ Schroeder uses the expression $g(\epsilon)$ to denote the density of states…

Temperature estimation can now be performed with greater precision by exploiting the subtle signals preceding a system’s transition to a new state rather than relying on established equilibrium measurements. This work demonstrates enhanced sensitivity using driven, dissipative Kerr cavities near critical points, offering improved accuracy over previous methods limited to fixed conditions or narro…

I recently stumbled upon the Goodwin oscillator and after some prodding in python it seems like it can indeed generate a limit cycle. Online there is a lot of talk about it actually obtaining a limit cycle, but I am looking for a concise explanation of how it can possess one analytically.

A large and growing class of results establishes that some system breaks down in finite time when a force is supplied to it from outside. Such results are stated for a system on a fixed background, and they are read, in transit, as statements about the thing the system models. This paper gives a criterion for when that reading is licensed. We define an interaction domain by mutual information aga…

Nature, Published online: 09 September 2026; doi:10.1038/s41586-026-11025-1 A generative committor-guided path-sampling framework reconstructs rare biomolecular transition pathways and reveals the underlying thermodynamics and kinetics without using predefined collective variables or brute-force sampling, at an acceptable computational cost.

Physics employs several exact notions called time: an evolution parameter in classical and quantum mechanics, proper time in relativity, and a statistically selected orientation in thermodynamics. This paper asks what makes any ordering physically temporal rather than a numbering imposed from outside. The Grammar of Time begins with composable continuations, a future-sufficient carrier, and indep…

I want to have a bit of basic knowledge of statistical mechanics, which I will later use to understand something else in relation to density of states. I've been following Tong's notes Statistical Physics - Cambridge University All was good except the following bit from the very first chapter, section second law At this point, we turn again to our fundamental assumption — all states are equally l…

A new theoretical approach helps connect quantum physics with classical thermodynamics by clarifying what counts as heat and useful work in tiny quantum machines. When a machine is reduced to a single atom and particles of light, even basic concepts such as heat and useful work become difficult to define. This problem sits at the [...]

Nature, Published online: 08 September 2026; doi:10.1038/d41586-026-02722-y A physics pioneer who provided a new way to describe temperature, and the value of studying fossilized tracks in this week’s pick from the Nature archive.

In two weeks, I am giving two lectures about degenerate Fermi gases in a third-year undergraduate course on statistical mechanics. The textbook is the beautiful book by Schroeder. I want to highlight a few things that are amazing about the Fermi energy. 1. It is given by an incredibly simple expression. E F = ℏ 2 2 m (3π 2 n ) 2/3 2. Besides fundamental constants, it is only determined by the num…

Read our manuscript In the theory of partial differential equations (PDEs), an important problem is analyzing whether there is loss of regularity in finite time, even when there is smooth initial data. This is known as singularity formation, or blowups. A famous one is whether fluid dynamics represented by Navier-Stokes equations experiences such blowups, and […]

I am trying to work out how I would find the rate of heat transfer through two pipes made of the same material that are joined at their ends but which have different cross-sectional areas and lengths. One end of the combination is held at $T_1$ and the other at $T_3$ but I don't know the intermediate temperature $T_2$ where the two pipes are joined which is a problem since the thermal conductivit…

Some interesting science results recently, but I wanted to talk about one a little off the beaten path.  Most people have some exposure to the concept of thermal expansion , the idea that solids tend to increase in size as temperature is increased.  This is why people suggest running a stuck (metal) lid on a glass jar under hot water to make it easier to open - the idea is that the metal expands …

I am struggling with trying to solve the following problem, attempting just (a) and the first part of (b) for this exercise: During a reversible adiabatic volume change of an ideal gas, $PV^{\gamma}$ remains constant, where $\gamma$ is the ration of the heat capacity at constant volume to that at constant pressure. i.e. $\gamma = C_P/C_V$ . One mole of an ideal gas, initially at $300^{\circ}K$ a…