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平成２８年度大学院工学府修士課程物質科学工学専攻群入学試験

機能物質化学系科目試験問題

（１０枚の１０枚目）

分 析 化 学 受験番号

４．クロマトグラフィーに関する以下の問に答えよ。（１８点） （１）分配係数 K と容量比（分配比）k’の定義を式で示せ。ただし、固定相と移動相の体積を VS、VM、それらの

中における試料の濃度を CS、CMとせよ。 （２）試料全体のうち移動相に存在する試料の割合を求めよ。 （３）試料がカラムから溶出する時間（保持時間）tRを求めよ。ただし、カラムの長さを L、移動相の線速度を u

とせよ。 （４）理論段高さ Hと移動相の線速度 uの関係を示す van Deemter式を記述し、Hと uの関係を図示せよ。最小の

Hを得るためには具体的にどのような工夫が必要か、この式に用いたパラメーターを参照しつつ解答せよ。 （５）クロマトグラフ分析は、必ずしも Hが最小のところで行われるとは限らない。その理由を述べよ。 解答欄 （１）

（２）

（３）

（４）

（５）

５． 核磁気共鳴に関する以下の問に答えよ。（１５点） 下記の用語について 60字程度で説明せよ。（１）反磁性しゃへい（２）化学シフト（３）スピン－スピン相互作

用 解答欄

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Almost a year after Elon Musk, chief executive of Tesla Motors (TSLA) and SpaceX, first floated the idea of a superfast mode of transportation, he has finally revealed (a) the details: a solar-powered, city-to-city elevated transit system that could take passengers and cars from Los Angeles to San Francisco in 30 minutes. In typical Musk fashion, the Hyperloop, as he calls it, immediately poses (b) a challenge to the status quo—in this case, California’s $70 billion high-speed train that has been knocked by Musk and others as too expensive, too slow, and too impractical. In Musk’s vision, the Hyperloop would transport people via aluminum pods enclosed inside of steel tubes. He describes the design as looking like a shotgun with the tubes running side by side for most of the journey and closing the loop at either end. These tubes would be mounted on columns 50 to 100 yards apart, and the pods inside would travel up to 800 miles per hour. Some of this Musk has hinted at before; he now adds that pods could ferry cars as well as people. “You just drive on, and the pod departs,” Musk told Bloomberg Businessweek in his first interview about the Hyperloop. Musk published a blog post detailing the Hyperloop on Monday. He also held a press call to go over the details. Musk has built his entrepreneurial career attacking businesses he deems inefficient or uninspiring. He co-founded PayPal in a bid to shake up the banking industry, then used the fortune (c) he made selling the startup to eBay (EBAY) to fund equally ambitious efforts in transportation. Tesla Motors, for example, has created the highest-performing, highest-rated all-electric car and a complementary network of charging stations scattered around North America. Meanwhile, SpaceX competes against entire nations in the market to send up satellites and resupply the International Space Station. In the case of the Hyperloop, Musk started focusing on public transportation after he grew disenchanted with the plans for California’s high-speed rail system. Construction on the highly political, $70 billion project is meant to begin in earnest (d) this year, with plans to link cities from San Diego to Sacramento by 2029. “You have to look at what they say it will cost vs. the actual final costs, and I think it’s safe to say you’re talking about a $100 billion-plus train,” Musk says, adding that the train is too slow and a horrendous (e) land rights mess. Musk thinks the Hyperloop would avoid many of the land issues because it’s elevated. The tubes would, for the most part, follow I-5, the dreary but direct freeway between L.A. and San Francisco. Farmers would not have swaths of their land blocked by train tracks but could instead access their land between the columns. Musk figures the Hyperloop could be built for $6 billion with people-only pods, or $10 billion for the larger pods capable of holding people and cars. All together, his alternative would be four times as fast as California’s proposed train, at one-10th the cost. Tickets, Musk says, would be “much cheaper” than a plane ride. As for safety? Musk has heard of it. “There’s an emergency brake,” he says. “Generally, though, the safe distance between the pods would be about 5 miles, so you could have about 70 pods between Los Angeles and San Francisco that leave every 30 seconds. It’s like getting a ride on Space Mountain at Disneyland.” Musk imagines that riding on the Hyperloop would be quite pleasant. “It would have less lateral acceleration—which is what tends to make people feel motion sick—than a subway ride, as the pod banks against the tube like an airplane,” he says. “Unlike an airplane, it is not subject to turbulence, so there are no sudden movements. It would feel supersmooth.” The Hyperloop was designed to link cities less than 1,000 miles apart that have high amounts of traffic between them, Musk says. Under 1,000 miles, the Hyperloop could have a nice edge over planes, which need a lot of time to take off and land. “It makes sense for things

:https://www.jumpstartfund.com/

like L.A. to San Francisco, New York to D.C., New York to Boston,” Musk says. “Over 1,000 miles, the tube cost starts to become prohibitive (f), and you don’t want tubes every which way. You don’t want to live in Tube Land.” Right? In the months since Musk first mentioned the Hyperloop, there has been plenty of speculation. Critics (g), dealing with limited information, have contended that the specifications laid out by Musk would be nearly impossible to achieve. Such a long, pressurized tube would require an immense amount of energy while also producing tons of air friction and heat. Now Musk argues that the Hyperloop represents a type of middle ground that other people have yet to consider. Instead of being a complete vacuum or running at normal conditions, the Hyperloop tubes would be under low pressure. “I think a lot of people tended to gravitate (h) to one idea or the other as opposed to thinking about lower pressure,” Musk says. “I have never seen that idea anywhere.” Inside the tubes, the pods would be mounted on thin skis made out of inconel, a trusted alloy of SpaceX that can withstand high pressure and heat. Air gets pumped through little holes in the skis to make an air cushion, Musk says. The front of the pod would have a pair of air jet inlets—sort of like the Concorde. An electric turbo compressor would compress the air from the nose and route it to the skis and to the cabin. Magnets on the skis, plus an electromagnetic pulse, would give the pod its initial thrust; reboosting motors along the route would keep the pod moving. And: no sonic boom. With warm air inside the tubes and high tailwinds, the pods could travel at high speeds without crossing the sound barrier. “The pod can go just below the speed of sound relative to the air,” Musk says. So, science, or science fiction? About a dozen people at Tesla and SpaceX have helped Musk with the design and checked the physics behind the Hyperloop. I briefed Martin Simon, a professor of physics at UCLA, on some of the Hyperloop details, and he declared it feasible from a technological standpoint: “It does sound like it’s all done with known technology. It’s not like he’s counting on something brand new to be invented.” Simon points out that the acceleration methods proposed by Musk are used at amusement parks to get a roller coaster going. Other companies have looked at these techniques for passenger and freight vehicles. What sets the Hyperloop apart, though, is the use of the air cushion to levitate (i) the pods. “He has separated the air cushion and the linear induction drive, and that seems new,” Simon says, adding, “It would be cool if they had transparent tubes.” The critics of California’s high-speed rail may be dismayed (j) to learn that Musk does not plan to commercialize the Hyperloop technology for the time being. He’s posting the plans and asking for feedback and contemplating building a prototype. “I’m just putting this out there as an open source design,” he says. “There are sure to be suggestions out there for making this better, correcting any mistakes, and refining the design.” Musk maintains that he has too much on his plate to deal with bringing the Hyperloop to fruition. “I wish I had not mentioned it,” he says. “I still have to run SpaceX and Tesla, and it’s fucking hard.”

Musk says he would support another person or organization that wanted to make the Hyperloop a reality. It is a question

of finding the right person and team to get behind it,” Musk says. “Creating a prototype is not that expensive.” But if no one advances or acts on Musk’s ideas, he may come back to the Hyperloop in a few years’ time and pursue it as part of Tesla. “Down the road, I might fund or advise on a Hyperloop project, but right now I can’t take my eye off the ball at either SpaceX or Tesla.”

Bloomberg Business

(a) reveal ( ) (b) pose ( )

(c) fortune ( ) (d) in earnest ( )

(e) horrendous ( ) (f) prohibitive ( )

(g) critic ( ) (h) gravitate ( )

(i) levitate ( ) (j) dismay ( )

Musk has built his entrepreneurial career ~

Hyperloop