Volume of Air, Fridge Questions

[holly]

Allrighty, I can't figure out the following questions from my Chapter Review, and I can't find any similar problems in the book or workbook.

Q. A volume of air has a temperature of 0 degrees C. An equal volume of air that is twice as hot has a temperature of: a)0 degrees C, b) 273 degrees C, c) 2 degrees C, d) 100 degrees C, or e) none of these.

I thought it would be 2 degrees C, but the answer supposedly is (b) 273 degrees C. Now, how did they get that? I tried to convert 64 degrees F back into C, but the answer wasn't one of the choices. Then I thought perhaps it has something to do with Kelvins. Isn't 273 degrees C the same as 1 Kelvin? And so it would be twice that, right? Also not one of the choices. 273 degrees sure sounds like a lot of hot air to me.

This is also a puzzler:
Q. If you run a refrigerator in a closed room with the fridge door open, the room temp will a) increase, b) decrease, c) remain the same. I think it would cool the whole room, because lots of cold air comes out whenever my son hangs the door open for a half-hour pawing through the contents and drinking from the milk carton.

Posting homework questions at 11:30 pm on a Friday night, how pathetic. And I'm knee-deep in sugar, making Panorama Eggs for the poor for Easter. So please help my sticky situation. I can hardly concentrate on physics with my kitchen strewn full of sugar. Thanking you in advance.

 

[cookiemonster]

1) Kelvin! 0 degrees C = 273 Kelvin. Kelvin is the absolute scale of temperature. And the conversion between the two is

Kelvin Temp = Celsius Temp + 273

2) The temperature of the outside room would decrease and the temperature of the inside of the fridge would increase (to room temperature, in fact...).

cookiemonster

 

[Doc Al]

No way to air condition!

Originally posted by holly
This is also a puzzler:
Q. If you run a refrigerator in a closed room with the fridge door open, the room temp will a) increase, b) decrease, c) remain the same. I think it would cool the whole room, because lots of cold air comes out whenever my son hangs the door open for a half-hour pawing through the contents and drinking from the milk carton.

This is a bit of a trick question. Obviously when you open the refrigerator, some cold air escapes--for a while. But realize that the refrigerator creates more heat than it removes. Operating in normal closed-door fashion, the net effect is to warm up the room. (Any heat removed from inside is sent outside along with the additional energy that it takes to run the refrigerator.) Keep the door open and it will have to work that much harder trying to cool things down--thus dumping even more heat into the room. Bottom line: don't try to use the refrigerator as a room air conditioner.

 

[cookiemonster]

Of course, then you have to consider the case where the hot air is removed from the room (to outside, perhaps...).

I'd forgotten to consider that the fridge generates heat, too. Good catch. But it's still a poorly designed question.

cookiemonster

 

[holly]

Thank you, thank you for answering.

But I don't understand the Kelvin business. If the volume of air is TWICE as hot, then why isn't the answer 273+273? We have to do twicet the temp, the question says so! Because twice 0 is 0, you can't do that, can you, in math? Something about you can't double zero? So you have to double the Kelvins? Where does the air being twice as hot come in? I'm turned around.

I follow the fridge reasoning of Doc Al's reply. Ooo, I understand something! Let me mark it on my calendar!

****Doc Al, will you EVER reveal what your avatar is? Admit it, you don't know either. Maybe you drew it when you weren't feeling well.****

****Cookiemonster, will you EVER get an avatar? I love it, he has the brain of Einstein and he can't figure out how to get an avatar.***

 

[Doc Al]

Originally posted by holly
But I don't understand the Kelvin business. If the volume of air is TWICE as hot, then why isn't the answer 273+273? We have to do twicet the temp, the question says so! Because twice 0 is 0, you can't do that, can you, in math? Something about you can't double zero? So you have to double the Kelvins? Where does the air being twice as hot come in? I'm turned around.

Only when measured on the Kelvin scale is temperature proportional to thermal energy. So the answer is 273 + 273! On the Kelvin scale. But you have to convert back to the Celsius scale.

The reason why is that only the Kelvin scale has its zero at the absolute energy minimum. Celsius has an arbitrary zero that is nowhere near absolute zero. That's why you get silly answers like 1 degree C is infinitely hotter that 0 degree C, if you don't realize that that reasoning only works on the Kelvin scale.

I follow the fridge reasoning of Doc Al's reply. Ooo, I understand something! Let me mark it on my calendar!

Yay!

****Doc Al, will you EVER reveal what your avatar is? Admit it, you don't know either. Maybe you drew it when you weren't feeling well.****

Bah!

****Cookiemonster, will you EVER get an avatar? I love it, he has the brain of Einstein and he can't figure out how to get an avatar.***

I think you should draw something fitting for the cookiemonster. Something that captures his essence. Get to work!

 

[cookiemonster]

If I have the brain of Einstein, I needn't concern myself with such trivial matters as avatars!

... or something like that?

cookiemonster

 

[holly]

cookiemonster, even Einstein would need an avatar, maybe a Death's Head with fluffy hair. Perhaps Doc Al will let you use his "avatar." You could use the negative of it, and then we'd have two that make no sense. I was wrong about it being a peach: it's clearly a pathetic rendering of the Pringle's Potato-Chip man, as drawn by someone who doesn't get enough fresh air and sunshine, shall we say.

Wah! Wah! I can't understand the volume of air part yet! From what I have been able to see, to get Celsius to turn into Kelvins, I have to use C = K - 273, is that correct? So, in this case, 546 - 273, giving 273. Now, that just seems crazy. Didn't we start with 273? Just going in a circle...

There is another problem, this one's little brother, I guess:
Q. Consider a piece of metal at 5 degrees C. If it is heated until it has twice the thermal energy, its temperature will be: blah blah blah...one of the answers is 278 degrees C, so I am guessing that's the one, since the first problem's answer was 273, and this one was 5 degrees hotter to start with. But this leads me back to the confusion about the first question, with the 0 degrees C starting temp. I am confused about how I am getting the Kelvins. It doesn't seem right that with zero C, I went to 546 Kelvins, yet 5 C is five times that, but the answer is only five MORE. Can I always just add the number I start with to 273?? That would be great.

Thanking you...

 

[cookiemonster]

Heh, I've learned that Celsius is bad. And Fahrenheit is bad. And Kelvin is good.

So my advice, forget about Celsius. Let's rewrite the questions without it.

Q. Consider a piece of metal at 278 K. If it is heated until it has twice the thermal energy, its temperature will be:

Okay. 278*2 = I can't add and I'm not going to try.

Problem solved. We're done thinking. All we do now is find an answer that matches in some form, which involves mindlessly subtracting 273 to get the celsius temperature, but we're not going to let subtracting confuse us, because we've stopped thinking!

Now let's try the next one.

Q. A volume of air has a temperature of 273 K. An equal volume of air that is twice as hot has a temperature of: a)273 K, b) 546 K, c) 275 K, d) 373K, or e) none of these.

273*2 = 546. Problem solved!

Easier, right?

cookiemonster

 

[holly]

cookiemonster, I think your avatar ought to be a big ol' brain with two fangs coming off the frontal lobes.

Are you being cruel to me? Because I can rarely tell. You need to tell me outright: You Are Being Mocked! Then I will be suitably ashamed.

I followed the new way of doing the question perfectly! The AIR question. Where it was zero degrees and then became substantially hotter for some reason. The first question. Yes, why were we dealing with Celsius anyway? Where's the sense in that? I like your new way very much.

BUT, for the next problem, we are talking of a piece of METAL. This is the same piece of metal we threw overboard from a raft about two weeks ago, so it may be haunted and have an evil air about it. It is starting at 5 degrees C. Can I throw the degrees away and go to Kelvins now? 273 x 5, is this correct, to rid it of Celsius degrees? Now it is 1365 Kelvins. But it becomes twice as hot, making it 2730 now. But we have the answers in Celsius. So, I take 2730 and subtract 273, and giving me 2460, in C. That is not one of the choices.

Physics is obviously some sort of weed-out subject, and I am a weed.

(edited atrocious spelling)

 

[Doc Al]

Originally posted by holly
It is starting at 5 degrees C. Can I throw the degrees away and go to Kelvins now? 273 x 5, is this correct, to rid it of Celsius degrees?

No. Yes, go to Kelvin, but you must convert properly. To convert a temp from C to K, add 273. That means X degrees C = X+273 degrees K. (To convert back, do the reverse: Y degrees K = Y-273 degrees C.)

For any of these "X times hotter" kind of problems, follow these steps:
(1) Convert to Kelvin (if needed)
(2) Do your multiplying or whatever
(3) Convert back to Celsius (if needed)

So: Temp of metal = 5C.
(1) Convert to K: Temp = 273+5 = 278K.
(2) Multiply: New Temp (twice as hot) = 278x2=556K.
(3) Convert back to Celsius: New Temp = 556-273= 283C.

 

[holly]

Thank you very much. I greatly appreciate the walk-thru. I thought it was 273 Kelvins PER Celcius degree, sorry. I see what cookiemonster and you are saying now, and I have copied down that 3-step method, so that will take care of a bunch of "getting hotter" problems.

Thank you guys again. Now on the test, no matter what numbers he's going to put in, I'm going to be able to figure it out!

Now if I could just figure out what that avatar is supposed to be...

 

[cookiemonster]

I was getting a little worried about you, holly, when you first multiplied by 273 to get Kelvin and then subtracted to get back to Celsius, all in the same problem... But you got it now, so that's good.

Hey, the little title thing below my name is different now, so you can be happy about something else.

cookiemonster

 

[holly]

cookiemonster! Where did you get the little "i like cookies" slogan? That's great! That's almost as good as having an avatar! I almost fell out of the chair when I saw it. I'm SO glad you have a slogan. I get so worried about you physics types...!