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Q & A: Lb of Water/Ice and Hot Air/Cold Air

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Most recent answer: 10/02/2013
so i know you answerd which weighs more, 1lb water or 1lb ice. i think you said same. but now when you take a ballon full of hot air it raises and cold air it sinks, does this mean on a scale the weight changes. so the warmer something the lighter. no?
- brian (age 23)
concord, ca

Well, the reason you're getting confused is that the question is misleading

A pound of ice and a pound of water have the same weight but your mind is conditioned to picture them and you know that ice and water have different densities. While a given pound of water and a pound of ice would have the same mass, the volume would be different. The water would have less volume, because water is more dense than ice (which is why ice forms at the top of a lake).

The situation with gases is a little different. When you heat a gas, you don't change its mass. (Wow, that rhymes. :)) The speed of the molecules bouncing on the balloon increases when you increase the temperature and so the density changes (because the volume changes). This change in density causes the balloon to rise, because the hot balloon is less dense than the air around it. Likewise, a cold balloon falls because it is more dense than the air around it.
(In other words, if you ’weigh’ the baloon, what you measure is not its total weight but the difference between its weight and the weight of the air it displaces. So that depends not just on weight but also on volume. When you weigh water or ice in the atmosphere, either one is so dense that the weight of the air they displace isn’t very important.)

I hope that this explains this common trick question and why it is so confusing to everyone.


(published on 10/22/2007)

Follow-Up #1: drag of hot and cold air

Based on your statement that cold air is more dense than hot air, does cold air move objects in the air easier
- Brendan

This actually depends on how fast the object is moving through the air and on its size and shape. For slow-moving objects, the way the air provides resistance to motion is via air molecules randomly bouncing of the object and gradually carrying away its momentum as they bounce off other air molecules. This effect is called viscous friction. The resistance an object moving in air is proportional to the air’s viscosity, if the object is moving slowly.  Even though the density of the air is less at higher temperature (at standard pressure) the viscosity of air increases a bit.  It turns out that the air density itself doesn't affect the viscosity. That's because if you increase the density of molecules you decrease how far they travel before bouncing off another, and those two effects cancel. However, the temperature matters directly because hotter molecules move faster and therefore carry momentum away faster. So the hotter air has more viscosity. 

 For liquids, viscosity usually goes down rapidly as temperature increases. It’s harder to push something through a cold liquid than a hot one because in typical liquids hydrogen bonding between molecules increases with colder temperatures. However, some liquids get more viscous as they warm up, because long-chain molecules in them unravel and start to get tangled up with each other. 

The viscous drag grows only linearly with the object's velocity through the fluid. For fast-moving objects a different type of drag becomes important, and in gases the density becomes more important. The object transfers momentum to a column of air it has collided with due to its own motion, not to the random bouncing of the molecules, and then the momentum from that column leaks away. The denser the air, the more momentum gets transferred in those collisions. So this drag gets bigger for denser air, and becomes bigger at lower temperature. The number of collisions with air molecules increases as the object goes faster, and so does the momentum transferred in each collision. So this drag increases as the square of the velocity.

LeeH  w. Mike W.

(published on 12/19/2007)

Follow-Up #2: do cold air car intakes work?

Cold Air Intakes are a hot thing amongst those looking to increase performance on vehicles. So my question is how much denser is cold air really? Letís say between 70 and 80 degree Fahrenheit.
- Anthony Marlette (age 23)
Manassas, VA

From the ideal gas law, we get that at fixed pressure the gas density goes as 1/T, where T is the absolute temperature. At room temperature, T ≈ 300 K. A 10°F increase in T is about 6K, or 2% of 300 K. I guess a 2% increase in density could help a bit.

Mike W.

(published on 10/02/2013)

Follow-up on this answer.