The following question is from Mad About Physics by Christopher P. Jargodzki and Franklin Potter. This book is filled with Q&A posers, and are interesting and informative. But there is one that I just don’t get. I took two semesters of general physics but it was classical mechanics; this involves heat radiation.
I don’t see how the energy radiated off has anything whatsoever to do with what the object can “see.” I would have thought that the answer to that had more to do with meteorology (cloud cover acts like a blanket, raising humidity) than radiation. (Since the problem states that the temperature is the same, heat loss through convection is not an issue.)
What determines the rate at which a body radiates heat?
The clouds also radiate heat back towards the Earth, which is then absorbed by the car. Since the warmer clouds radiate more heat than the clear night sky, the car can’t cool off as fast. It’s also why burgers stay warm under an infrared heat lamp–the lamp radiates heat back to the burger faster than the burger can radiate it away into the surrounding air.
Seems to me we had a thread on this where someone took their IR pyrometer outside on clear and cloudy nights and reported on the temperature of the sky. Was that you Q.E.D?
Now that makes sense. Although their answer did discuss the temperature of the sky, they left out that crucial link of whatever is overhead radiating heat back down, and I didn’t make the connection without being hit over the head.
The clouds intercept the heat that would normally radiate away into space and re-radiate some of it back to earth. For a really cold day during winter find one after a cloudy day followed by a clear night. Not much heat is delivered to the ground during the cloudy day, and a lot of heat is radiated away during the clear night.
I’ll have to find a link, but from time to time I hear reference to creating a refridgerator in, say, the desert using a tube pointed at the night sky, it was something along the lines of what you were saying.
Really, it’s nothing much to do with where the radiated heat from the car ends up; that energy was leaving anyway; it’s all about how much heat is radiated toward the car from the environment, including the clouds.
Clouds don’t stop heat being radiated away from the car, they just replace it; even when equilibrium is reached, there’s still heat radiating away from the car, it’s just equal to the incoming amount of heat.
So the question in the OP is designed to be misleading, and a simpler version would be, which get cold faster, a car on a cludy night or a car on a clear night? Living in a place that’s cold for several months out of the year, the answer’s instinctual and you get to know it in kindergarten – if it’s clear out, it’s going to be cold. If it’s cloudy, it’s going to be a nice day. Although… that rule’s been not true this year. It’s probably only been cold three or four days this winter (where winter includes late fall in our non-specific way of indicating it).
Not quite. The question is in the typical physicist tradition of carefully specifying the conditions. Specifying that the air temperature vs. clock time is the same on both nights shows that the clear night isn’t “colder” according to one method of measuring it. So the question gets you to think about the different measurements of temperature and what they mean.
Your point is of course entirely correct, that clear nights feel colder and tend to be actually colder, since the air, buildings, rocks etc. will all radiate their heat away to the sky and cool down faster.
But it is possible that the air on a clear night can be as warm or warmer than the air on a cloudy night, and despite this an object such as a car can come to a lower equilibrium temperature on the clear night. It can even come to a significantly lower temperature than the air around it.
These physics notes (a Word document) have a worked example towards the end indicating that under the right conditions, you should be able to get water to radiatively cool to ice even if the air temperature is as warm as 60[sup]o[/sup] F.
Just another thought - I’m not sure how big this effect is with respect to people. That is, if you have two nights where the air stays at 60[sup]o[/sup] F all night (say, it’s blowing past hills that keep it warm) but one night is cloudy and the other is clear, do you have to wrap up more on the clear night? I suspect not, since we generate heat internally and lose most of it by convection, but I don’t have any real data.
One thing can mess up the stated problem. The car can’t be close to a large body of water. Even if fog isn’t produced, more times than not the vehicle will have dew covering it on a clear or cloudy night. Maybe as much doesn’t condense on the car in one situation, but when it runs down the the sides off from the top in both cases it doesn’t matter.
[QUOTE=matt]
But it is possible that the air on a clear night can be as warm or warmer than the air on a cloudy night, and despite this an object such as a car can come to a lower equilibrium temperature on the clear night. It can even come to a significantly lower temperature than the air around it.
[QUOTE]
And, presto, the moisture in the air condenses out on the colder car, or the grass, instead of forming a mist in the air.