How does the second law of thermodynamics disprove all  machines?
Fermi in his lecture asserts:     The second law of thermodynamics rules out the possibility of constructing a perpetuum mobile of the second kind.   So, this means there can be no machine which just transforms all the heat energy gained by cooling surrounding bodies into mechanical work.  But how does actually the Second Law prohibit this?   The hot reservoir provides heat energy to the system. Does it cause a decrease in entropy of the universe(system + hot reservoir)? How? In order to receive heat wouldn't the system have to be cooler than the reservoir? If so, then entropy increases as the heat energy gets expelled from the reservoir at a higher temperature than the temperature the system receives the heat energy. Is it so?  I'm not getting how the Second Law nullifies the existence of this machine. Could anyone please explain how the Law prohibits the perpetual machine of the second kind?
Best way to track onchange as-you-type in input type="text"? In my experience, input type="text" onchange event usually occurs only after you leave (blur) the control.  Is there a way to force browser to trigger onchange every time textfield content changes? If not, what is the most elegant way to track this “manually”?  Using onkey* events is not reliable, since you can right-click the field and choose Paste, and this will change the field without any keyboard input.  Is setTimeout the only way?.. Ugly :-) Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices? Let $\mathcal E=\{A \in \mathcal M_n(\mathbb R): A \text{ is of companion form} \}$. That is, $A$ has the following form \begin{align*} A=\begin{pmatrix}  0 &amp; \cdots &amp; 0&amp; -a_{0} \\  1 &amp; \cdots &amp; 0 &amp; -a_{1}\\ \vdots &amp;\ddots &amp; \vdots &amp;\vdots \\ 0 &amp;\cdots &amp; 1 &amp; -a_{n-1} \end{pmatrix}. \end{align*} Let $\mathcal D = \{A \in \mathcal M_n(\mathbb R): A \text{ is diagonalizable in $\mathcal M_n(\mathbb C)$}\}$. We know $\mathcal D$ is dense in $\mathcal M_n(\mathbb R)$. I am wondering whether $\mathcal E \cap \mathcal D$ is dense in $\mathcal E$. The set $\mathcal E$ is closed. It is not clear to me whether this statement is true. Accidentally hit "toggle full screen", How do I exit? I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program. Let $X$ and $Y$ be topological spaces. A function $f: X \rightarrow Y$ is defined as continuous if for each open set $U \subset Y$, $f^{-1}(U)$ is open in $X$. This definition makes sense to me when $X$ and $Y$ are metric spaces- it is equivalent to the usual $\epsilon-\delta$ definition. But why is this a good definition when $X$ and $Y$ are not metric spaces?  How should we think about this definition intuitively? Word for people who don't make their deadline I recently installed the apache2 package using the Software Centre, I want to create an alias apacheres which will replace the more cumbersome command /etc/init.d/apache2 restart.  I opened the .bashrc file in my home directory, and it contains the following lines:  # Alias definitions. # You may want to put all your additions into a separate file like # ~/.bash_aliases, instead of adding them here directly. # See /usr/share/doc/bash-doc/examples in the bash-doc package.  if [ -f ~/.bash_aliases ]; then     . ~/.bash_aliases fi   So I created a .bash_aliases file in my home directory, and added only this line:  alias apacheres ='/etc/init.d/apache2 restart'  When I started my terminal, I get this error message:  bash: alias: apacheres: not found bash: alias: =/etc/init.d/apache2 restart: not found   The shell has obviously read the file, otherwise it wouldn't know of its existence. I have checked the directory path and I can find the file apache2 there. What do I need to do to make this alias work? How do I get Pokémon Go to detect my phone's orientation? When initiating a battle it starts off in AR mode, but then warns me saying my phone's orientation is not detected. I am then forced to turn off AR mode. Has anybody experienced this? If so, what are the solutions?    Per comments, I am unsure this is a permissions issue. I have everything turned on. I have meticulously read through similar questions, answers and their comments but I still do not understand how the deletion is done. From what I understand I email the customer service and then they do what exactly?     1) They disable my account so that I can no longer use it?      2) They reassign all of my questions and answers to some other   account? To which one?      3) They delete all my questions and answers so that they go away from   public view?   What is the flexibility (if it exists) of the deletion procedure? Is it possible to erase the traces of my former association with the site. Can I request any of the following be done?     4) All of my questions and answers be deleted from public view?      5) Some of my questions and answers be deleted? If yes what criteria?      6) Can I have all of my contributions be assigned to some other   account which runs as sort of a "collective account" and already has   tons of content so that it doesn't happen like my contributions just   move to some other url but still stay grouped under that location and   therefore that location can be discovered as representing my account?      7) Can I have my contributions dispersed through several "collective   accounts?      8) Can my current public name be removed from any comments to my posts   so that my posts cannot be identified later as once belonging to me?   Please be polite with me. I wouldn't have asked if I have found the answer in the other questions. The other questions are also old and it is not clear what the situation is as per 05/2012.  UPDATE (for those interested):  I asked the Stackoverflow team about the procedure. Apparently none of the points 2-8 I asked above are possible, only 1 will take place. The link to my user page from my contributions is going to be removed and replaced with non-clickable text of an anonymized user name like "user1234". Whether this number is the same as my current user_id is not clear. That's all the information I got.  I'm going now to rename myself to "Anonymous" then request the account deletion. Those interested in the procedure will witness the exact result on this page.  Farewell. Is the intersection of a closed set and a compact set always compact? Boot partition full, can't remove kernels How to disable all caches in safari 11? I have a Schengen visa valid from 19/07/2016 to 10/08/2016. But the duration of stay is 7 days only.  I want to stay for 6 days more, for a total of 14 days. And my flight includes travel from a Schengen state to another. Beamer: How to Disable `\pause` Temporarily How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? I've found in Wikipedia the formula for calculating an individual row in Pascal's Triangle: $$v_c = v_{c-1}\left(\frac{r-c}{c}\right).$$ where $r = \mathrm{row}+1$, $c$ is the column starting from $0$ on left and $v_0 = 1$.  Now, I've tried to do by hand and it works,  but I don't understand how to find this magic formula when I don't have access to Wikipedia...:) Why is this command deleting all entities? I'm trying to remove a specific, named, item if it is dropped on the floor. I have the following on my command block:  kill @e[type=Item] {Item:{tag:{display:{Name:"RedFlag"}}}   But it's removing all items, not just the one I want. What am I doing wrong?  I also tried  kill @e[type=Item] {Item:{id:"red_flower",Damage:2}}   But that didn't work either, it's still removing all items, even things that aren't red flowers! Specific derivatives have specific names. First order is often called tangency/velocity, second order is curvature/acceleration. I've also come across words like Jerk, Yank, Jounce, Jolt, Surge and Lurch for 3rd and 4th order derivatives. Is there a widely agreed list of names for these? How many orders have specific names?  In this case, I'm dealing with NURBs curves, so the "tangency" and "curvature" related words are to be preferred over "velocity" and "acceleration" words. Breaking an equation cluster that does not fit on the rest of page across two pages Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$ I am looking at the circuit diagram from   The gnucap description for it is given as C1 0 2 1UF R1 1 2 1K R2 0 2 1K Vin 0 1 AC 1 .OPTIONS PHASE=RADIANS .PRINT OP V(Vin) .OP 0.00 100.00 BY 10.00 BASIC .END  I can run the simulation on this using gnucap fine, see output. But is there a way to generate the schematic visually from just the textual description above using a simple command line tool? Foreword  This question was inspired by initial mistakes in . I wanted to explore the strange circle with $A&gt;\pi r^2$ and got lost into geometrical jungle.  A  is usually described by it's height $h$, radius of the base $a$ and radius of the sphere $r$. Besides we have a relation $a^2+(r-h)^2=r^2$ so the cap actually only has two degrees of freedom.  When considering a case of circle on a sphere (like the Earth), it's the surface of a spherical cap, but we can't see the height or other classic parameters of this spherical cap. Instead we encounter parameters like area $A$, perimeter $C$ and diameter $d$. I will try to write formulae for these: $$A=2\pi rh$$ $$C=2\pi a$$ $$d=2r\theta$$  Where $\theta$ is introduced with $\sin\theta=\frac{a}{r}$ or $\cos\theta=(1-\frac{h}{r})$.  As the cap only has two degrees of freedom, it should be a good problem with unique solution if only two values are known.  A-C Problem  The simple example: $A$ and $C$ are given. I show this only as example before the other tasks.  We can easily find $a=\frac{C}{2\pi}$ and then solve:  $$A=2\pi rh = 2\pi r (r-\sqrt{r^2-a^2})$$  to obtain  $$r=\frac{A}{2\sqrt{\pi(A-\pi a^2)}}$$  Parameters $a$ and $r$ are now known and it is straightforward to find $h$, $d$, $\theta$ and anything else.  C-d Problem  $C$ and $d$ are given.  First step once again is easy: $a=\frac{C}{2\pi}$. The knowing of $a$ suggests that we might prefer the $\theta$ definition with the sine. We obtain: $$d=2r\theta=2r\arcsin\frac{a}{r}$$  That's where I got stuck. Is there an easy way to solve this? Is there a hard way to solve this?  I tried solving numerically with Wolfram Mathematica and it went into complex numbers. When solving the geometrically equivalent $\sin\frac{d}{2r}=\frac{a}{r}$ I got some roots, but the search seemed very unstable and not finding the root closest to initial value. Besides it was finding a lot of different roots while I am pretty sure that there should only be one $r$ for each pair of $d$ and $a$. What would be the right formulation to solve this problem numerically?  A-d problem  $A$ and $d$ are given. This seems the hardest one. We obtain a system of equations:  $$A=2\pi r h$$ $$d=2r\arccos\left(1-\frac{h}{r}\right)$$  (The first equation suggested solving the problem in $h$ and $r$).  Is this system solvable analytically? Or numerically? My experiments with Wolfram Mathematica never converged.   Of course, I could express $h$ or $r$ from the first equation and leave only the second in one of these forms: $$d = 2r\arccos\left(1-\frac{A}{2\pi r^2}\right)$$ $$d = \frac{A}{\pi h}\arccos\left(1-\frac{2\pi h^2}{A}\right)$$  But I have no idea how to solve these either.