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February 23

Identity involving partial derivatives

Ho, I want to check,

Given this relation: $dF=-SdT-PdV+\mu dN$ ,

is it true that ${\bigg (}{\frac {\partial S}{\partial V}}{\bigg )}_{T,N}={\bigg (}{\frac {\partial P}{\partial T}}{\bigg )}_{V,N}$ ?

I believe the answer is Yes and here is my reasoning:

The relation shows that $S=-{\frac {\partial F}{\partial T}}$ and $P=-{\frac {\partial F}{\partial V}}$ ,

so ${\bigg (}{\partial S \over {\partial V}}{\bigg )}_{T,N}{\stackrel {?}{=}}{\frac {\partial S}{\partial V}}=-{\frac {\partial ^{2}F}{\partial V\partial T}}{\stackrel {?}{=}}-{\frac {\partial ^{2}F}{\partial T\partial V}}={\partial P \over {\partial T}}{\stackrel {?}{=}}{\bigg (}{\partial P \over {\partial T}}{\bigg )}_{V,N}$

I have denoted with question marks steps in the reasoning that I am not sure are justified.

150.203.115.98 (talk) 02:11, 23 February 2013 (UTC)[reply]

Try Wikipedia:Reference desk/Mathematics instead. --Jayron32 02:21, 23 February 2013 (UTC)[reply]

The mathematics desk might be more relevant, but this is a thermodynamics question, so it's not out of place here.

To the OP: yes, that's true. In fact, it's one of the Maxwell relations. Your biggest source of confusion is that when taking partial derivatives, you should always specify what parameters you're holding constant. The relations you're using should actually be

S=-({\frac {\partial F}{\partial T}})_{V}

and

P=-({\frac {\partial F}{\partial V}})_{T}

, where V and T are the quantities being held constant. If you differentiate the first equation with respect to V while holding T constant, and the second equation with respect to T while holding V constant, you'll get the same expression on the right-hand side. You're allowed to arbitrarily exchange variables in a partial second derivative because of symmetry of second derivatives, specifically Clairaut's theorem. --140.180.254.250 (talk) 03:25, 23 February 2013 (UTC)[reply]

Clairaut's theorem requires that the second partial derivatives be continuous. Is this always true, physically? Or, do we assume/approximate that it is true? Or, is the statement to prove true even if the second partial derivatives are not continuous?

So the true line of reasoning is

{\bigg (}{\partial S \over {\partial V}}{\bigg )}_{T,N}=-\left({\frac {\partial ^{2}F}{\partial V\partial T}}\right)_{N}=-\left({\frac {\partial ^{2}F}{\partial T\partial V}}\right)_{N}={\bigg (}{\partial P \over {\partial T}}{\bigg )}_{V,N}

Using the equations you gave (but also holding N constant)

150.203.115.98 (talk) 05:58, 23 February 2013 (UTC)[reply]

The second derivatives of the potential are not always continues, of course. They are not in any second order phase transition, where Ehrenfest equations hold instead. Ruslik_Zero 19:03, 23 February 2013 (UTC)[reply]

What's a partial derivative? μηδείς (talk) 02:16, 24 February 2013 (UTC)[reply]

Non-calculus proof of E=mc^2

See [1], this non-calculus proof of E=mc^2. We know, F=m*a (where m is mass and a is acceleration) and it is given in the second equation of the linked article that F=m*c. How can this be possible? Since the SI unit of 'a' is m/s^2 while the SI unit of 'c'is m/s. According to me, this proof is wrong. I read the Wikipedia article Mass-energy equivalence, but the proof of E=mc^2 was very tough for me. Is there any other non-calculus (and other than dimensional analysis) proof of this equation? Thanks in advance. 106.216.105.77 (talk) 13:55, 23 February 2013 (UTC)[reply]

On the linked page, m in the second equation seems to represent the mass gained per unit time and so has units of kg/s rather than kg (so the units come out as kg m/s² on both sides). Similarly in the first equation E is energy gained per unit time and so has units of J/s (i.e. W) rather than simply J. Since the argument compares rate-of-change of energy with rate-of-change of mass, it is calculus (sort of) - but writing e.g. the rate-of-change of energy as E rather than dE / dt disguises this. --catslash (talk) 14:27, 23 February 2013 (UTC)[reply]

It's an elegant argument, but not mathematically stringent. It avoids a proper calculation of the limit, and simply assumes that speed is constant (which is not, strictly true). But it does provide a nice physical insight. --Stephan Schulz (talk) 14:50, 24 February 2013 (UTC)[reply]

Coal Fired Boilers - Briquettes

Hi

I was asked to get info on making briquettes with company waste such as coal dust mixed with saw dust or wood chips.

My question is, can the two substances be mixed together and processed together to make briquettes for coal fired boilers? If so what is the mix ratio to make it a cost saving and green project? Where can I get good drawings or advice?

Currently, the company is under pressure to reduce costs. All the coal dust and wood chips go a dump site and I don't agree with it.

This is items which can be recycled and will give cost savings on the long run.

Any solutions?

Regards

Gert de Ridder (Email address & phone nummer removed) — Preceding unsigned comment added by 105.226.163.32 (talk) 15:40, 23 February 2013 (UTC)[reply]

I have removed your personal details for security - Cucumber Mike (talk) 15:59, 23 February 2013 (UTC)[reply]

My understanding is that those things don't generate as much energy per unit volume as coal does, so I think you will need to find out how flexible your boilers are. This comes down more to what the boilers can handle than to what you can do with the waste. Looie496 (talk) 16:11, 23 February 2013 (UTC)[reply]

Note that the mass of the briquettes, and how well compressed they are, will determine how fast they burn, with low mass, uncompressed ones burning faster. So, if the mass of each is low enough, and/or they are uncompressed enough, they should provide sufficient heat. However, they won't last as long. You could just experiment with different sized briquettes to find the right form. How do you intend to compress them ? I wonder if a trash compactor would work. You might need to add some type of flammable binder. StuRat (talk) 16:59, 23 February 2013 (UTC)[reply]

Reusing industrial scrap wood for briquettes goes back at least to Henry Ford and the Model T (Kingsford (charcoal)). It is a well-understood process that should be well documented. Rmhermen (talk) 17:23, 23 February 2013 (UTC)[reply]

Also note that, while coal dust can be burned directly, you need special equipment to do so. Trying to burn it in a regular coal furnace may result in an explosion. (I know you're not planning on doing this, but feel the warning is needed, just in case.) Therefore, you should store the coal dust in a sealed container, far from an ignition source, prior to compacting it into briquettes. StuRat (talk) 17:43, 23 February 2013 (UTC)[reply]

First Gert. Where are you located on this huge planet? Some governments give grants to instal equipment to make use of what otherwise is waste – so knowing you location would help. Second, what ~~cheapskate~~ company are you working for that doesn’t want to contract a consultant? To economically utilize waste as fuel, inevitable require some outlay in equipment. To make sure that this this expense is economically recoverable and viable, a good costing exercise is required -hence need for a qualified consultant (vis Wikipedia). It is better to use tried and tested technology, than to follow what you and your employer can glean from Wikipedia (although having said that, please pay me... ASPRO US$1000 for this consultation as it will save your company thousands more dollars further down the line) . For an example, this company builds bespoke waste processing plants [1]--Aspro (talk) 18:28, 23 February 2013 (UTC)[reply]

For a small project like this, the consulting fee may not be recovered for years. (And if they don't have to pay Gert overtime, then working on this project won't cost them any extra, as opposed to the consultant.) StuRat (talk) 19:01, 23 February 2013 (UTC)[reply]

That is why I wanted to know where he was located. Some grants are available to pay a boffin to come in and say – don't shovel the coal-dust strait into the furnace as it will suffocate the fire bed. Mix it first with a little binder (say cellulose wall paper paste) and then throw the binded chunks in... Do you know how much little companies have to pay just for legal advice? Advice from popper recycling expert is cheap in comparison. If they think they can not afford to pay for that, then our poster should think seriously about working for another company that is still going to be in business this time next year. --Aspro (talk) 20:18, 23 February 2013 (UTC)[reply]

...and it will look great on his resume. --Guy Macon (talk) 19:19, 23 February 2013 (UTC)[reply]

No. it may look impressive on his résumé but at a job interview he may come across a just a lucky amateur – providing he even succeeds in fulfilling his current employers wishes.--Aspro (talk) 20:18, 23 February 2013 (UTC)[reply]

Selective Knockout

Hello. I want to demonstrate whether the heart is the only tissue that requires Mef2 for embryogenesis in mice. Do I knockout Mef2 in every tissue that expresses it except for the heart? If so, how can I go about that? Thanks in advance. --Mayfare (talk) 17:42, 23 February 2013 (UTC)[reply]

What approaches have you considered so far? You'll forgive me, but this sounds a bit like a homework problem.... TenOfAllTrades(talk) 19:05, 23 February 2013 (UTC)[reply]

Does sound a bit like homework - Let's stake out gene knockout, Mef2, promoter (genetics), enhancer (genetics) to begin with. Especially the Mef2 article because if you're knocking out all four you'll definitely be busy ... You may decide you find gene knockdown to be of interest. Wnt (talk) 20:18, 23 February 2013 (UTC)[reply]

Feeding of K-9 dogs

My friend told me that K-9 dogs (law enforcement dogs) are only fed once a day. And she said that this is done to keep them "hungry and fierce".

Is it true that K-9 dogs are only fed once a day? If so, is "keeping them hungry and fierce" really the reason? I don't see why you'd want that -- it doesn't sound like their job description.

Thanks. And I would be extra grateful if you cite to a source...

99.100.214.111 (talk) 22:35, 23 February 2013 (UTC)[reply]

The International Police K9 Conference doesn't say anything about the frequency of feeding, but it does say; "Working dogs use a lot of energy. To replace this, a large amount of high quality, nutritious dog food is required. These dogs should be offered all of the dog food they want, unless they begin to become overweight." So it doesn't seem to be recommended that they be kept hungry. However, The Glendale Police K-9 Unit says; "They normally eat once a day at the end of our shift. Feeding them before work will cause them to be sleepy, just like after we eat a big meal." I'm not sure if this is universal practice. Alansplodge (talk) 00:17, 24 February 2013 (UTC)[reply]

No, being fierce is NOT part of a police dog's job decription. Many police dogs are drug or explosives detection dogs - for this what is wanted is a well fed happy dog that just wants to enjoy the "game" of detection and please its' master. For apprehension dogs, the last thing you want is a fierce dog - want you want is a fit dog that obeys commands absolutely. The idea is to bring down and restrain the villain, not damage him. Police dogs are generally the larger and more intelligent breeds e.g., german sheperd. These large breeds only need a meal once a day, whether they are in police service or are just pets. This does not preclude giving them small treats now and then, which when done sparingly and at the right moments, gives you a better dog. Small breeds may need meals twice a day. See http://www.purina.co.uk/content/your-dog/feeding-your-dog/the-right-food-for-your-dog/feeding-your-adult-dog. Wickwack 121.215.50.17 (talk) 02:18, 24 February 2013 (UTC)[reply]

A childhood friend's father was a London police dog handler. The dog had a huge kennel in their back garden, which we used to play in along with the dog. I'm sure it could have easily taken off one of our arms or legs, but she was a model of tolerance. Alansplodge (talk) 09:29, 24 February 2013 (UTC)[reply]

That could be misleading though. One of the built-in virtues of large dogs is that they instinctively understand that children are human puppies. My own experience of large dogs is that they'll tolerate a lot of horseplay and rough handling from children that they will not tolerate from adults. They treat people they know differently to people they don't know too. Wickwack 60.228.244.46 (talk) 11:05, 24 February 2013 (UTC)[reply]

It's actually not abnormal to feed a dog once a day. We had a labrador cross that lived to almost 15 and we only ever fed her once a day, and she was never "hungry and fierce". Vespine (talk) 21:59, 24 February 2013 (UTC)[reply]

Also, stating that a dog is only fed "once a day" is a touch misleading. Does that mean they only got a handful of kibble or a huge bowl of chopped steak? It's not unusual to only put food down for a pet once, and let them eat throughout the day as they're hungry. — The Hand That Feeds You:^Bite 23:48, 27 February 2013 (UTC)[reply]

Not very misleading. Most dogs eat everything they are given right away. Most dogs have a routine where they sleep or are more or less inactive for much of the day, but they can turn on vigorous activity at any time - that's why they need to eat only once per day. If your dog cannot eat all the food you've given him in one session, you'll end up with a fat or obese dog. You see a lot of obese dogs these days, though, just like you see a lot of obese humans. I think a lot of people don't realise their dog is obese though, as they don't realise that, while for a human the waist measurement should be only a little but smaller than the chest measurement, for a dog it should be very much less. And a medium sized or large dog that cannot out run a fit human is very unfit dog. Wickwack 124.182.57.146 (talk) 00:31, 28 February 2013 (UTC)[reply]

Is it possible that a supertanker or a cruise ship that is made of all woods, treenails and tar, can float for a long time?

Let's suppose people build a supertanker or a cruise ship that is made of all woods and tar? Can it float on water for a long time? Why can the ship float and why can't it float? 173.32.116.184 (talk) 23:35, 23 February 2013 (UTC)[reply]

The Influence of Iron in Ship Construction: 1660 to 1830 says that the bigger wooden ships were subject to flexing and twisting of the hull, causing the wooden joints to open. Early in the 19th century, iron bracing was being fitted to large wooden warships in order to stiffen them. The introduction of steam propulsion required an even more rigid hull. So when the technology to make an iron ship became available, HMS Warrior (1860) was the result. The biggest wooden ships were tiny compared to modern steel vessels; HMS Victory is 70 metres long, RMS Queen Mary 2 is 345 metres and the TI class supertanker is 380 metres. Alansplodge (talk) 23:56, 23 February 2013 (UTC)[reply]

To add a couple of specific examples - the oldest wooden ship still afloat is the USS Constitution (215 years), although she's undergone a great deal of maintenance in that time. The largest wooden ship ever was the Baron of Renfrew, which lasted for three months. The largest working wooden ship was the Great Republic, which lasted for 19 years. Tevildo (talk) 00:19, 24 February 2013 (UTC)[reply]

Good examples - Baron of Renfrew was 93 metres long and that was too much. Alansplodge (talk)

If you make an unballasted wooden ship (oddly, we don't appear to have an article on the general use of ballast in ships), it'll float no matter how much water it takes on (assuming it isn't carrying much cargo), but an unballasted ship also tends to be topheavy and at risk of capsizing. --Carnildo (talk) 05:39, 24 February 2013 (UTC)[reply]

In that case, it's also called a raft ;-) --Stephan Schulz (talk) 15:20, 24 February 2013 (UTC)[reply]

Rafts aren't the only example of unballasted ships -- one theory for the lack of trireme wrecks in the Mediterranean is that they were unballasted and so didn't sink when rammed; rather, they stayed afloat but unusable and were either salvaged or broken up. --Carnildo (talk) 01:43, 27 February 2013 (UTC)[reply]

If you can make a wooden ship that's 70 meters long - then you can make a ship that's 140 meters long by connecting those two smaller ships through some kind of universal joint that allows them to flex without breaking. Given that, I don't see why you couldn't produce a vessel of almost any size by joining them together. The problem is with propulsion and such. A wooden ship of that type would be hard to propel and to steer...to say the very least! SteveBaker (talk) 21:12, 25 February 2013 (UTC)[reply]