How refrigerators work

Your question regarding a balloon filled with 40° gas in a room at 30° air, I believe has the wrong answer. The rate of heat transfer is proportional to the difference in temperature. Thus as long as the gases are kept from mixing, they will only approach and never reach the same temperature. Similarly, the moment your time interval begins, there will be some change in temperature in the balloon and some corresponding change in temperature in the room, depending on the comparative masses of gas in and out of the balloon. So of the answer alternatives provided, both 30 and 40 must therefore be wrong. 35 is the only possible correct answer. By using the term "a long time" without specifying whether long means 12 microseconds which is long compared to 3 nanoseconds, or 14 million years which is long compared to 3 days. the term long time is insufficiently defined to arrive at a more likely answer. Thus, the only correct answer should be 35°.

Easy Math Editor

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Comments

Hi Thomas, sorry I didn't see this at the time. I just happened upon it after seeing your wind-propelled land speeder question.

The rate of heat transfer is proportional to the difference in temperature. Thus as long as the gases are kept from mixing, they will only approach and never reach the same temperature.

You're right about this. Barring the consideration of fluctuations etc., the two will only asymptotically approach a shared limit though in practice, things are quantized and they will surely come to fluctuate about some new equilibria. Anyways, the question asks for the approximate temperature after a long time. I disagree that $\SI{35}{\celsius}$ is the right/only right answer, since the relative mass of the air in a balloon to the air in a room is small. The balanced should be tilted heavily to the room temperature.

Josh Silverman Staff - 2 years, 8 months ago

Josh,
I understand your point which certainly has validity but not knowing the mass of gas in the room nor the mass of gas in the balloon, I don't think it fair to assume that there is more mass outside the balloon than inside. It wouldn't be the first time that a trap was set for the unwary assumers.

How come you have not returned to the upwind vehicle question/issue? You said "tomorrow" many yesterdays ago.

Thomas Lippman - 2 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$