Hot water is heavier than cold water, true or false?

It depends on what your initial conditions are, and WHEN the water is heated.

Hot water is heavier...

If you have filled with water 2 identical volume sealed containers with no added air (so no water can evaporate), and then you heat one of the containers, the hot water is actually heavier after that heating is complete.

According to Einstein Energy has mass. E=mc2.

Therefore when you add energy to something it actually gets heavier. Therefore hot water is actually heavier than cold water, all else being constant.

If you look at it this way, even though the cold water takes up less space as particles are closer together, and the hot water takes up more space, there are still the same amount of particles, and the particles weigh the same. However because you add energy, and energy has mass, the hot water will be slightly heavier.

NOTE: this "increase in mass" is exceptionally, amazingly, agonizingly small and only meaningful theoretically. It would be nearly impossible to measure such a mass difference. For any "real world" applications, hot and cold water weigh the same.

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.

http://www.thenakedscientists.com/HTML/questions/question/2946/

An interesting discussion of this topic at some Physics Forums:
https://www.physicsforums.com/threads/hot-water-is-heavier-than-cold-water.614373/

Cold Water is Heavier...

If you rephrase this experiment by STARTING OUT with two containers of equal volume water, one which is HOT, and the other which is COLD, then clearly the COLD one will be heavier because hot water is less dense and thus has smaller mass per volume. That mass loss far outweigh the relativistic effects of Em=mc^2.

Note that even this has an exception: as water cools below 4 degrees, it gets less dense again. So, there are exceptions if you're talking about water between 0 and 4 degrees. And let's not even get into ice ;)


[ Edited in some detail ]

Start from scratch. Take two separate litres of water and heat one. They will remain the same mass (= weight for most purposes down here on Earth). Now take a litre of water from the hot tap and compare the weight with a litre from GingeryNutt's water container on a Christmas campsite. The hot one weighs less because it's less dense. In the first example, the heated litre will actually expand over the one litre boundary. (In fact, GingeryNutt's water froze on the first night we were there...)

Mass can be converted to energy - and a minuscule amount of mass gives a vast amount of energy. It would take an amount of energy that would probably vaporise the water (and the experimenter) to make a difference to the mass of the water. Quote: "For example, when water is heated in a microwave oven, the oven adds about 1.11×10^−17 kg of mass for every joule of heat added to the water.". (I've inserted a ^ as the superscript -17 came through as normal -17.) That's not something you can measure on your kitchen scales, or even on your school science lab scales. 10 to the power 17 is 1 followed by 17 noughts. -17 makes it 0.000 000 000 000 000 001 (in this case 0.000 000 000 000 000 001 11 kg). The expansion of the water (and consequent reduction of density) will be a larger factor. https://en.wikipedia.org/wiki/E%3Dmc%C2%B2

OK, first off, it depends on how cold the water is. As water is cooled toward freezing, it contracts, thereby taking up less space and thereby weighing more per volume that hot water. However, at 4°C, water begins to expand when further cooled, then greatly expanding once frozen. This priciple is what allows life on Earth to flourish. If frozen water were more dense than warmer water then lakes would end up freezing from the bottom up, thereby killing all life forms in them. The frozen layter at the top of the lake allows the more dense warmer water below to stay above freezing temperatures and life to continue.

http://www.bookrags.com/research/thermal-expansion-wop/