I am having trouble understanding why a division is made between heat and work. The units for energy is $\text{kg} \, \text{m}^2 \, \text{s}^{-2}$. The only way to obtain this unit is if you exert a force over a distance - that is, if you do work. In other words, the only way to change the energy of something is if you do work on it. However, in thermodynamics, we are taught that there are two ways of changing the energy of a system: (1) heat transfer and (2) work. This got me thinking about how something other than work can change the energy of a system. But, given that heat transfer is just a transfer of energy through collisions at the microscopic scale, can we go as far as to say that heat is just work done at a microscopic level?
Although work and heat do the same thing (increase or decrease the internal energy of the system), There is still a fundamental difference between them. For example, The way in which entropy is defined is a very good way to differentiate between work and heat. But, why is there such a distinction between the two things? Is it the limitation of Newtonian mechanics that it never accounted for something like heat which could also change the energy of the system? Is the word "Thermodynamical work" or "Hidden work" suitable for heat?
I'm using a Samsung I9000 and I have some annoying apps that came pre installed by the phone vendor, like a music store, a custom web browser and other memory leaking apps.  Those crappy apps can't be uninstalled neither by Manage applications tool, nor by editing the apps tiles in the front menu.  I guess I have to be a root user or something to get rid of those apps, but I don't know how. Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism? Let $V$ and $W$ be vector spaces (say over the reals). There is a linear injection $V^* \otimes W^* \to (V \otimes W)^*$ which sends $\sum_i f_i \otimes g_i \in V^* \otimes W^*$ to the unique functional in $(V \otimes W)^*$ sending $v \otimes w \mapsto \sum_i f_i(v) \cdot g_i(w)$ for all $(v,w) \in V \times W$. In the finite dimensional case it is easy to see this is an isomorphism by comparing dimensions on both sides. I'm aware that this is not an isomorphism in the infinite-dimensional case (see Relation with the dual space in the  on tensor products) but I must admit that I'm not sure why. Cardinal arithmetic does not seem help here and, even if it did, I would be much happier to see an explicit example of a functional in $(V \otimes W)^*$ outside the range of this map. I'm having trouble cooking one up myself.  Added: Let me elaborate on my comment about cardinal arithmetic. Suppose that $X$ and $Y$ are infinite dimensional vector spaces over a field $k$. I'm confident that $\dim (X \otimes Y) = \dim X \cdot \dim Y$ holds. It is clear that $|X^*| = |k|^{\dim X}$ since we may identify a functional on $X$ with a function from a basis for $X$ to $k$. Also I think I've convinced myself that if $\dim X \geq |k|$ then in fact $|X| = \dim X$ ie. the cardinality and dimension of a vector space agree when the dimension is larger than the cardinality of the ground field. Consequently, assuming say that $|k| \leq \dim X \leq \dim Y$ it seems we have $$ \dim(X \otimes Y)^* = |k|^{ \dim X \cdot \dim Y} = |k|^{ \dim Y} = \dim Y^* = \dim X^* \cdot \dim Y^* = \dim (X^* \otimes Y^*)$$  which implies that in fact $(X \otimes Y)^*$ and $X^* \otimes Y^*$ are isomorphic but, rather frustratingly, the obvious map does not do the job. Did I make a mistake here? If not, is it generally true (ie without making assumptions about $|k|$) that there exists some isomorphism $(X \otimes Y)^* \to X^* \otimes Y^*$? How can I detect inside a TeX file which engine (pdftex/xetex/luatex) is used to compile the file? Is there a LaTeX package that provides this functionality? Rounded corner shape with rounded sides I usually prefer to fix a Linux system than to reinstall from scratch. My computers have seen many distribution upgrades and a list of PPAs or third-party repositories. APT usually makes sure that everything works in the end. However, the fact that the package manager thinks that all required packages are 'installed' does not guarantee that all the files are present on the file system.  Such a such situation may occur if you have to work-around dependency problems with dpkg --force-*. One could also reproduce such a situation by deleting a file from /usr as root.  Is there a simple way to verify whether all files belonging to an installed package are present?  If a such a problem package is found, aptitude reinstall fixes the problem. So, for example, when I type man ls I see LS(1). But if I type man apachectl I see APACHECTL(8) and if I type man cd I end up with cd(n).  I'm wondering what the significance of the numbers in the parentheses are, if they have any. is it possible to skip immediately preceding time points? So that, if, for example, you are using model order 2, that is, two time points, but not the two immediately previous time points, but rather, say for example, skipping 2 points, and then using those two points.  So, e.g., it would be y=x(t-3) + x(t-4). I can't seem to find a satisfactory answer to this anywhere on the web. While  poses a related question, I don't think it sufficiently answers mine...  During the opening chapters of Jedi Search, Luke addresses the new Senate on the need to find new Jedi talent, or Force sensitive individuals. During this proposal, he cites that the most fruitful leads of Jedi potential are in the descendants of Jedi Knights: as Force sensitivity is hereditary. The book even discusses the notion that Leia should be comparatively well attuned to the Force, due to her being the child of Anakin Skywalker.  I understand that the concept of the Jedi as a totally celibate and monastic order was something that was retconned into the lore after Episode II: Attack of the Clones, and that there are examples of entire nuclear Jedi families exist (such as Andur Sunrider and Plo Koon)...  But if Force-manipulative ability is passed down genetically (as a potentially mutative property of their genetic makeup), why would the Jedi order be so numerous if they practice Chastity?  Even if procreation is not expressly forbidden (as in the pre-retcon Expanded Universe): why would Jedi need special permission to produce more Jedi potential children?  How are more Jedi created, if not through procreation? Has their profusion been deliberately retarded, and if so why? is there another explanation for their (pre-empirical) plenitude? Is there a human home planet? Did all the humans in the Star Wars universe originate on a single planet some time in the distant past, or did they originate on different worlds and intermix into one species over millenia?  This is specifically about only humans, not humanoid aliens. I would prefer answers from the main canon or EU canon. Is this algebraic identity obvious? $\sum_{i=1}^n \prod_{j\neq i} {\lambda_j\over \lambda_j-\lambda_i}=1$ If $\lambda_1,\dots,\lambda_n$ are distinct positive real numbers, then  $$\sum_{i=1}^n \prod_{j\neq i} {\lambda_j\over \lambda_j-\lambda_i}=1.$$ This identity follows from a probability calculation that you can find at the  top of page 311 in the 10th edition of Introduction to Probability Models by Sheldon Ross.   Is there a slick or obvious explanation for this identity?   This  question is sort of similar to ; clearly algebra is not my strong suit! Sometimes, when fighting an enemy, your character will do a special move, with a third person view animation, instantly killing the enemy. But these types of moves seem to be random, sometimes being used on enemies with nearly full health, other times not having a finishing move at all during a whole fight.  What are the parameters determining when a finishing move is used? Show that if $n>2$, then $(n!)^2>n^n$. Show that if $n&gt;2$, then $(n!)^2&gt;n^n$.     My work: I tried to apply induction. So, at the induction step, I need to prove, $n^n&gt;(n+1)^{n-1}$ Here, I tried to use induction again without any luck. I also took log of both sides, but I did not get anything. Please help! d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$ /oracle/GR1/121/bin/sqlplus / as sysdba &lt;&lt;EOF &gt;&gt; $LOGFILE whenever sqlerror exit sql.sqlcode; set echo on; set serveroutput on; STARTUP; EXIT EOF   Already tried it with the path, but it hasn't worked. Windows 10 Asks me to Enter a Password I am using Windows 10 Pro x64 on my personal laptop on which I have a single user account with no password. For some reason however, Windows 10 has started asking me to enter a password whenever I boot up my machine. All I have to do is press the button without entering anything, and I log in, but I would much rather skip this step in favor of an automatic sign-in. Why has this started happening only now? What can I do to stop this behavior? Will hardware changes affect system? How do you access the matched groups in a JavaScript regular expression? In Trailhead we have the query to get the Contacts for the Account named "SFDC Computing", with an inner query.   SELECT Name, (SELECT LastName FROM Contacts) FROM Account WHERE Name = 'SFDC Computing'   It works fine for my purposes.  "Contacts" is the name of the relationship, per Trailhead. So, I went to Object Manager and examined the Account object's "Fields and Relationships". There is nothing named "Contacts"!   In general, how do I get the name of the relationship, for use in similar SOQL queries? input() error - NameError: name '...' is not defined I am using a premium legit version of Minecraft that I purchased. I can log into minecraft.net as well as mojang.com but I am unable to login to Minecraft the game through the minecraft.exe or the Technic launcher. The Minecraft servers are up and running fine. My internet connection is also fine. I double checked my credentials and even tried changing my password. I tried using both my username and my email. I tried all of this on two separate accounts that I own. I tried deleting my login, launcher, launcher.pack.lzma, and launcher_profiles.json and then reopening Minecraft. I tried re-downloading minecraft.exe.   Nothing has worked and I seem to have run out of options. I sent a help request to Mojang but in the meantime I was hoping that maybe you guys could offer some advice.