If the molecular mass of a gas increases by a factor of 4 at a constant temperature, what will its rms speed be?

Hello!

The absolute temperature (from the absolute zero) of a gas is directly proportional to the mean kinetic energy of its molecules. This energy is equal to `(M v_(rms)^2)/2,` where `M` is the molar mass of a gas (the mass of a mole of a gas). The molar mass is directly proportional to the molecule's mass, because each mole of a substance contains the same number of molecules.

The exact equation is  `v_(rms) = sqrt((3 R T)/M),` where `R` is the ideal gas constant which doesn't depend on gas properties.

Therefore if the molecule's mass increases by a factor of `4,` then the root-mean-square will decrease by the factor of `sqrt(4) = 2.`

That said, the only cause of such a change of a mass is a chemical reaction, but in that case the temperature will likely be changed too.

Do you approve of Vera's prank on Nuttel, who has a nerve problem, in "The Open Window" by Saki? Why or why not?

This is an interesting question. If Vera were my daughter and this event happened in my home, I certainly wouldn't approve of her frightening the wits out of a guest, especially a stranger who was there seeking hospitality and acquaintanceship. The fact that Framton Nuttel has some kind of nervous problem does not seem to enter into the equation. It would be just as wrong for Vera to play the same prank on a man who did not have a nerve problem. The author, Saki, chose to give Nuttel his neurosis in order to make his reaction to the three approaching hunters as headlong and impetuous as possible.

Framton grabbed wildly at his stick and hat; the hall door, the gravel drive, and the front gate were dimly noted stages in his headlong retreat. A cyclist coming along the road had to run into the hedge to avoid imminent collision.

And Vera had no way of knowing about Framton's nerve problem. He refrained from saying anything about it to her because of her tender years, but he told her Aunt Sappleton all about it when she arrived to take over as hostess. Would Vera have told Framton her ghost story if she had known he had a nerve problem? If so, I would strongly disapprove. If not, I would still disapprove but not as strongly. 

I can't help thinking that this is a story and that Vera's ghost story is a story within a story. That seems to make her prank less serious. It never really happened.

What life lessons are we taught in the poem "If"?

There are several life lessons taught in Rudyard Kipling's famous poem "If." For, this poem, addressed to Kipling's son, is a paean to the stoicism characteristic of the British of the Victorian Age, and to uprightness.

In this first stanza, Kipling initially stresses that one must "keep" one's head; that is, remain rational while others are becoming irrational and placing blame upon others rather than accepting responsibility:

If you can keep you head when all about you
Are losing theirs and blaming it on you...

Kipling also stresses self-discipline: "trust yourself when all men doubt you." "..wait and not be tired by waiting...."
And, he emphasizes manly rectitude: " Or being lied about, don't deal in lies."

Kipling emphasizes that it is important to dream and have an imagination, but control of one's imagination is necessary, as well, for one must be realistic:

If you can dream--and not make dreams your master...

One must also be strong and willing to take risks and lose, then turn and start again after watching the

...things you gave your life to, broken, and bend down to pick them up and "build'em up with worn-out tools.

In this stanza Kipling emphasizes fortitude and the ability to begin anew when necessary. A man must be able to suffer losses and start over:

If you can force your heart and nerve and sinew
To serve your turn long after they are gone,
And so hold on when there is nothing in you
Except the Will which says to them: "Hold on!"

This stanza emphasizes and extols the virtues of moral uprightness.  Kipling praises the virtue of humility--"the common touch"--and making the most of time--

...fill the unforgiving minute...with sixty seconds worth of distance won,

Then, he can conquer anything and be a true man.

Which living situation or family does Huck like best and where does he feel most a part of a family and why in The Adventures of Huckleberry Finn?

Huck Finn feels most comfortable and loved with Jim on the raft; therefore, Jim is more like family to him than anyone else.

Unlike all his other living situations, Huck feels both physically and emotionally protected by Jim. In addition, Jim uses terms of endearment for Huck, calling Huck "honey," and he cries with elation when Huck returns to him after he thought Huck was lost or possibly dead.

After Huck runs away and discovers Jim, they travel together. In Chapter 9, they explore an island near the cavern where they have been hiding after running way. One night, a frame house floats past them, and the two paddle out to it, thinking it may have something they can use. Inside, they discover a dead man who has been shot in the back; Jim quickly covers the man's head because he realizes he is Huck's father, and he does not want to traumatize the boy.

When Jim and Huck are separated in Chapter 15 after Huck is unable to tie up the raft when he lands on shore, he is worried and tries to find Jim. Huck eventually becomes exhausted, however, and falls asleep. When he awakens, Huck chases after "specks" in a canoe until he finally discovers the raft. This raft has been somewhat damaged and Jim has his head down between his knees as he sleeps with his one arm hanging over the steering oar. Unable to resist playing a trick on Jim, Huck makes him think he has merely dreamed that Huck left the raft. 

Finally, when Huck points to the debris on the raft and the broken oar, Jim realizes he has been tricked and is hurt by Huck's deception. Much like a father, he gives expression to his love for the boy first, but then reprimands him.

When I got all wore out wid work, en wid de callin' for you, en went to sleep, my heart wuz mos' broke bekase you wuz los', en I didn' k'yer no mo' what become er me en de raf'. En when I wake up en fine you back agin', all safe en soun', de tears come en I could a got down on my knees en kiss' yo' foot I's so thankful.

Jim then scolds Huck for deceiving someone who cares about him:

...how you could make a fool uv old Jim wid a lie. Dat truck dah is trash; en trash is what people is dat put dirt on de head er day fren's en makes 'em ashamed.

After experiencing the violence of the feuding Grangerfords and Shepherdsons in Chapter 18, Huck is relieved to be back on the raft with Jim:

I was powerful glad to get away from the feuds, and so was Jim to get away from the swamp. We said there warn't no home like a raft, after all. Other places do seem so cramped up and smothery, but a raft don't. You feel mighty free and easy and comfortable on a raft.

The hypocrisy of the King and the Duke and the self-righteousness of Dr. Robinson, who walks away from the Wilkinson girls after they refuse to listen to him about the two frauds, add to Huck's moral confusion. This confusion is only allayed when Huck is with Jim, whose honesty and openness has a profound effect on him.

After the King steals Jim and sells him, Huck becomes disgusted with society. Although he writes to Miss Watson informing her of Jim's capture, he tears up the letter. In doing so, he ends his moral dilemma over "stealing" her slave from her by deciding, "All right, then, I'll go to hell." Moreover, he decides Jim has all the qualities of a true and decent human being; further, he cannot deny the feelings he has for Jim. This causes Huck to follow his heart and act on behalf of Jim, who has been both a father-figure and a friend.

In the novel "The Dispossessed" Anarresti culture sought to eliminate hierarchies within its society. To this end, Odo provided no formal/legal...

The relationship between Takver and Shevek, while not expressly forbidden by the Annarean government, is highly controversial. While Le Guin explains that Odo originally set up a society with no legal form of marriage in order to prevent Annares from becoming a hierarchy like Urras, this policy becomes limiting to the young couple. Shevek and Takver feel a deep bond and desire to share their lives with each other. In this sense, the monogamous relationship between Takver and Shevek fits in with the larger theme of the story. A lack of formal contracts and institutions in which two people effectively belong to one another is only freeing for the Annareans who have no desire to enter into such contracts. By contrast, Takver and Shevek find Annarean society highly restrictive.

More tension is created when Shevek is sent away on a lengthy tour of labor. Takver is also sent away to continue her work on addressing the problem of starvation on Annares. Because marriage is not an officially recognized institution, the Annarean government has no obligation to keep the spouses together. The tension can be further resolved into a coherent theme when contrasted with the opposing tensions Shevek experiences on Urras. While the Urrasti government permits marriage, its social institutions create great pressure to conform in a different way. "The Dispossessed" uses these tensions to illustrate how even restrictions created from the purest motives will have a negative impact on someone.

When he was mayor of New York City, Michael Bloomberg proposed a ban on any "sweet drinks" more than 16 ounces. Although it was ruled illegal by...

Clearly, a ban on these drinks would intrude on personal freedom.  The issue is not whether it intrudes on personal freedom but whether it does so excessively.

Essentially every government law infringes on personal freedom in some way.  The speed limit intrudes on our freedom to drive whatever speed we want.  The ban on cocaine and heroin infringes on our freedom to do whatever we think will make us feel good.  The ban on sugary drinks would infringe on our right to eat and drink what we want.  However, while laws always infringe on our freedoms, we accept them because we think they do not intrude too much in comparison to the bad things that they prevent.

It is in this context that we have to think about the proposed NYC ban.  Does it do enough good to overcome the way in which it infringes on our freedom?  A ban would presumably help at least somewhat to reduce the problems associated with obesity in the city.  This would make people healthier and reduce the government’s need to spend on health care.  The question you have to answer for yourself, then, is whether that is enough of a benefit to justify telling people what they can and cannot drink.  One thing to think about as you consider this question: where do we draw the line?  Could the government ban us from eating large steaks (or all meat) because it thinks fat is unhealthy?  This is a matter of personal opinion.  What do you think?

As for what companies should do about this, I would say they should do two things.  First, they should advertise, telling people to fight for their right to eat and drink what they want.  Second, they should work to develop new drinks that would have less sugar. If they could do that, they would be covered in the event that such a ban does eventually end up happening.

Why does Blanche say, "Now it's time to bury someone I hate?" in Brighton Beach Memoirs?

Blanche says this after she has had a long fight with her sister, Kate. The fight is instigated in part because Blanche's date with Frank Murphy has been canceled, as Frank has had an accident. Kate feels that Blanche is too self-centered, and it is clear that Blanche's route out of her sister's house--marriage--seems nowhere in sight. Blanche resolves to move out of the house and find a job.

After she fights with Kate, Blanche begins to fight with Nora, her daughter. Nora tells Blanche she feels unloved, and Blanche responds that she is sorry, but "I am tired of apologizing. After a while it becomes your life's work and it doesn't bring any money into the house" (page 96). Blanche realizes that she has been a weak, apologetic person who has tried to make her way in life by depending on others. She has now resolved to be more independent and to find a job, feather than depending on her sister and her brother-in-law, Jack, who has just had a heart attack. Blanche says, "I've already buried someone I love. Now it's time to bury someone I hate" (page 96). By this, she means that she already buried her husband, and now she wants to bury her old, dependent self and be reborn (metaphorically) as a more independent and active person.