Consider the following situation. A block slides on a rough surface. We have already given it an initial velocity. I consider my system to include only the block. Due to friction, the table performs work on the block, thereby reducing its kinetic energy. On the other hand, the block performs no work on the table, since the table surface does not get displaced at all. So, isn't it incorrect to say that work done on the system is the negative of the work done by the system?  If the work done by a system is not always the negative of the work done by the system, then how can both versions of the first law of thermodynamics hold true? The first law of thermodynamics in the physics point of view is: $\Delta U=Q-W,$ and in the chemistry perspective is: $\Delta U=Q+W.$  Both of these seem to be correct, as in the first case we are considering the work done by the system on the surroundings, and in the second case we are considering the work done on the system by external forces. But, if the work done by a system is not equal to the negative of the work done on it, then I have a feeling that the chemistry definition might be a better one. Please clarify.  Kindly note that I am already aware of the different conventions  used in physics and chemistry, and I completely understand their intended meanings. My question is not really related to thermodynamics, but something more fundamental. I have just taken the first law of thermodynamics as an example.
What is the sign of the  done on the system and by the system?  My chemistry book says when work is done on the system, it is positive. When work is done by the system, it is negative.  My physics book says the opposite. It says that when work is done on the system, it is negative. When work is done by the system, it is positive.  Why do they differ?
Let $f$ be a holomorphic function in $H={\{z\in\mathbb{C}}:\Re(z)&gt;0\}$ such that it is continuous in $cl(H)$, $|f(z)|\leq1$ $\forall z\in \delta H$ and $\lim_{|z|\to\infty}f(z)=0 $. Prove that $|f(z)|\leq1$ $\forall z\in H$. I thought about taking the bounded set $H\cap D(0,R), R&gt;0$. This way we could use the maximum modulus principle to prove it but I do not really know how to relate it with the limit since I would need $|f(z)|\leq1$ $\forall z\in H\cap D(0,R)$, and I do not have it on $D(0,R)$. $A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$ I'm trying to prove that if $A\neq 0$ is a commutative ring and there is an injective $A$-module homomorphism $A^m\hookrightarrow A^n$ then $m\leq n$ must necessarily hold.    This is exercise 2.11 from Atiyah and MacDonald's Introduction to Commutative Algebra, but unfortunately all the solutions available online are either very sparse with regard to this question or seem to use (to my surprise) a generalized version of Cramer's rule. Is there perhaps some other "cleaner" approach to solving this problem? Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$ I need to show that $$\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$$  I know that $\displaystyle \binom{n}{k}\binom{k}{i}$ is counting the number of ways to pick $k$ elements from $n$ and then $i$ elements from those $k$, so $\displaystyle \sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i}$ is counting the number of ways to do that $\forall k$.  I know that $\displaystyle \binom{n}{i} = \binom{n}{n-i}$ and that $2^{n-i}$ is the number of elements in the power set for $[n]\setminus[i]$.  How do I show that both sides are equivalent? I'm stumped on this one. Could anyone give me a pointer in the right direction? I am currently in need of using apt-get on a chroot directory. The setup is the following.  I have a chroot setup with schroot. This chroot environment needs to be stripped down as much as possible. Therefore I am planning to remove apt-get and commin from the chroot environment.  I know that Gentoo has the possibility to use portage on a different root directory. Is this possible to set a different root directory for apt.get to install software into my chroot directory?  Thanks in advance Is there a portable version of Chrome for Ubuntu? What does $\sum_{k=0}^\infty \frac{k}{2^k}$ converge to? This problem comes from another equation on another question (. I tried to split it in half but I found out that $$\sum_{k=0}^\infty \frac{k}{2^k}$$ can't be divided. Knowing that $$\sum_{k=0}^\infty x^k=\frac{1}{1-x}$$ I wrote that $$\sum_{k=0}^\infty \frac{k}{2^k}=\sum_{k=0}^\infty \left(\frac{\sqrt[k] k}{2}\right)^k=\frac{1}{1-\frac{\sqrt k}{2}}=\frac{2}{2-\sqrt[k] k}$$ But that's not what I wanted. Could anyone help me? Why "think bright" is used with adjective instead of adverb (think brightly)? I find "think bright" is much more common usage, but why? In my opinion, "Think" is a verb, so it is reasonable to use adverb to describe it.  Examples:      THINK BRIGHT!      The National University of Science and Technology MISIS   () What are the possible catch bonuses and how much experience do they reward? How do I migrate my Keychain's "Local Items" to a new Mac? After preforming a Mavericks-Mavericks migration using Migration Assistant, I have a "Local Items" Keychain on my new machine in which many (perhaps most) items are out of date (using old passwords), and some are missing altogether. While I have access to a copy of the entire contents of the ~/Library/Keychains/ directory from my old machine, which presumably contains all the information I'm missing, I see no way of importing that information into my new machine.  How can I import the "Local Items" from my old Keychain into the Keychain on my new machine? Assume you have some objects which have several fields they can be compared by:  public class Person {      private String firstName;     private String lastName;     private String age;      /* Constructors */      /* Methods */  }   So in this example, when you ask if:  a.compareTo(b) &gt; 0   you might be asking if a's last name comes before b's, or if a is older than b, etc...  What is the cleanest way to enable multiple comparison between these kinds of objects without adding unnecessary clutter or overhead?   java.lang.Comparable interface allows comparison by one field only Adding numerous compare methods (i.e. compareByFirstName(), compareByAge(), etc...) is cluttered in my opinion.   So what is the best way to go about this? Anyone ever seen a "wok adapter" for induction cooktops? In theory a cheap pressed steel wok would work on an , but the "contact patch" for a traditional round bottomed wok would be so small it would be ineffective.  Has anyone seen a steel or cast-iron "wok adapter" with a flat bottom and a concave "bowl" on top to sit the wok in, serving dual purposes of supporting the wok on the stovetop and transferring the induction heat to the wok?  Could anyone speculate if this would this even work? Or wouldn't you be able to get the wok hot enough? I have a nominal variable (different topics of conversation, coded as topic0=0 etc) and a number of scale variables (DV) such as the length of a conversation.   How can I derive correlations between the nominal and scale variables? I own a Nikon D40X and just the kit lens and I'm considering buying either a macro lens or some extension tubes.  I don't necessarily want to do true 1:1 macro, just some close ups of bugs, fungi and flowers. In Avengers: Endgame,       Thanos was able to stop and catch Mjolnir and Stormbreaker mid-air as both Captain America and Thor used/called them BEFORE he got the Infinity Stones.   Since this character is clearly not worthy and had no super powers at the time, how were they able to wield Thor's Mjolnir and Stormbreaker, when even the Hulk couldn't do it in The Avengers? Solving an Op-amp circuit The image of the circuit is shown below and it required to find \$V_0\$,  My first attempt at solving this problem is by changing the current source into a voltage source with 1-V and 2k\$\Omega\$ resistance. The fact that the inverting and non-inverting terminals aren't grounded make this problem look difficult.To the point which, I don't know how to proceed with this question or where to start. I would appreciate any help. Following some thought and another schematic from a hint suggested by Alfred, I produced a schematic representing our work.  And  my solution for the problem is below, Using node equation at nodes A and B we have, $$\frac{V_A-V_B}{1k}=-0.5 \text{mA}$$ $$\frac{V_B-(2+V_A)}{1k}=-0.5-x$$ where x is the current that is sent in the output of the op-amp. Using KCL, at the bottom node near the current source we see that the same current that goes through the op-amp also goes through the \$2\text{k}\Omega\$ resistor. Hence, we have, $$\frac{-V_A}{2k}=x$$ Replacing this in the second equation, $$\frac{V_B-(2+V_A)}{1k}=-0.5+\frac{V_A}{2k}$$ And and solving the equations yields \$V_A=-2 \text{-V}\$ and \$V_B=-1.5 \text{-V}\$ Who invented "dooblidoo"? The word  is used by several different youtube channels as a different word for the youtube description bar. I've seen it used by the  and by .  Who was first to use and invent the term? Is it possible to annotate equations (i.e. arrow signs/curly braces) to define each variable? I have quite a simple question. I was wondering if it was possible to do something like this in LaTeX:    But formatted a little more nicely.  It doesn't need to be arrows necessarily. Just some form of annotation marker. find . -name *.rb   doesn't work on my ubuntu  I have to do  find . -name "*.rb"   to get it to work.  Why is that? I have a Student object and have a pick list field  "Student Status" in this object. Status can be Full-Time OR Part Time. 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