Is hot water heavier than cold water?

06 March 2011

SPLASHING-WATER

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Question

Is hot water heavier than cold water? I was wondering this while watching ice float in my drink.

Answer

Chris - Hot water is actually a little bit heavier than cold water because, as Einstein told us, E=mc2. So if E, the energy in the water, goes up because it's hotter, then mass, m, must also go up to keep the equation balanced [c, the speed of light in a vaccuum, doesn't change]. So there will be a very subtle and very tiny increase in mass of the hot water, compared to the cold water.

The reason the ice floats is actually because it's a lot less dense than the water. The ice is made of water but, because water expands when it freezes, the ice is pushing a bigger volume - and hence a bigger mass - of water out of the way than the ice itself weighs. For this reason the ice is actually feeling a bigger push "up"(called buoyancy) from the water underneath than the ice weighs itself, which makes it float.

Comments

I just found this thread after googling the topic based on a conversation with my 7yo.

My initial reaction was an appeal to E=mc², which says that since there is more energy, there would be more mass. But then I realized that the increase in mass due to energy is negligible at velocities well below light speed (think about it; to rearrange the equation for mass, you're dividing energy by the square of light speed).

Even so, there would still be an increase (however small) in mass due to the increase in energy.

*BUT*

Is that increase enough to offset the fact that there are fewer molecules in the same volume of hot water? Fewer molecules in the same volume would mean less mass.

I proposed an experiment.

Have room temperature water as a control.
Cool one pot of water to 38°F
Heat 1 pot of water to 200°F (below boiling to avoid immediate evaporation)

When the test pots are at temp, pour precisely 8oz from each into a container and weigh each. Also weigh 8oz of the control.

We will be doing this experiment as part of our home school science. If anyone is interested I will share the results.

can't somebody weigh them?

Can we write speed as time /distance

Speed = distance / time

Photons are light. Not heat.
It is well known that cold water is heavier because the molecules are more densely packed than hot water. This answer is incorrect. The correct answer is available from many sources.

If you add energy to a system then the mass increases: E=mc^2; the information provided is correct.

E does equal mc^2, but let us not confuse it’s use. You can use this formula to convert mass to energy (think atomic bomb). Adding more energy to a particle is not the same as adding more mass. Think of it this way- if a certain particle can be converted into 10 units of energy, then adding 5 units of energy to the particle simply adds to the total potential energy (but those 5 units stay as energy, they have not been converted to mass). doubling the heat...that certainly does not double the mass.

Well, instead of being theoretical about it i weighed some water at boiling point, let it cool to room temp and weighed it again (also weighed while the temperature was going down) and it went from 283g to 266g, i.e hot water definitely weighs more. I used different containers and amounts of water and even 3 different scales: same result every time.

I applaud your dedication and attempting to do the experiment; however, the mass difference you have recorded seems huge, so I am sceptical about the results. Can you provide the raw data from the experiment? For instance, you say you did the experiment multiple times with "different amounts of water", but then you only cite one pair of masses (266g vs 283g) - if you used different volumes of water the masses would be different.

Unfortunately there are a number of factors that will effect the outcome of your experiment; the water, as it cools, will still evaporate. The differential temperature between hot water and cold water is too small to measure using everyday scales; and the apparatus you would need means that it would be very difficult to perform the experiment accurately. Technically as water cools it takes up less volume (to a maximum of 4 degrees celcius) until it begins to freeze and will expand as it becomes a solid. When water is heated, it expands, caused by the transfer of heat agitating the particles at an atomic level; so the same volume of water weighs slightly more when it’s cold than when it’s hot.

Imagine a water molecule and an anti-water molecule interacting – basically a matter anti-matter interaction. Each respective water molecule would be transformed into heat (photons). Thus mass is made up of photons. So add more photons – add more mass. A hot water molecule has more mass (weight) than a cold water molecule because its electrons will absorb photons (mass) when heated.

Einstein mass energy equivalence for real objects of velocities incomparable with that of light(as is the case here) is E=mv^2.
Then, the increase in energy would be reflected as an increase in velocity.

The real answer is that cold water of the same volume is heavier than hot water as it is denser as it has lesser energy which allows closer packing of the molecules as opposed to hotter water in which molecules have a higher average kinetic energy.

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