Are Waterfalls Hotter at the Bottom Than the Top? The Lead Shot Exp. - F-J's Physics - Video 156

So are waterfalls hotter at the bottom than the top? If the falling water's kinetic energy converts to heat and sound at the bottom then surely they should be. Join me for a practical demonstration of this that also results in the determination of the specific heat capacity of lead - the fantastic 'Lead Shot Experiment'. And do try it on your honeymoon - this is exactly what James Joule did at Cascade de Sallanches near Mont Blanc!
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Very many thanks, F-J

[@mediontevion7761]

What about the heat added to the end of the tube by holding it with your hands? You could hold the tube for the same length of time without inverting to see if there is any temperature change as a control.

[@AnthonyFrancisJones]

Good question! One of the reasons for using a cardboard/plastic plugged tube is that its thermal conductivity is very low so none of the heat in the lead shot gets out. The same is true of the heat from the hand getting in so it would be good to do a control but there would be negligible difference I think. Thanks for watching and making a good observation about the limitations of the experimental method.

[@Dealanach]

I had the exact same thought.

[@anthonyjones5711]

Very interesting video. Just a thought, how much heat is added to the lead shot as a result of friction both with the sides of the tube and the friction between the lead shot rubbing together each time it impacts at the end of the tube. Be interesting to try this again with a plastic tube and the addition of a thin lubricant. Another interesting effect is how warm a piece of metal becomes when hit with a very large hammer. I've just discovered your videos and really enjoy them. Tony

[@AnthonyFrancisJones]

Thanks - all of the heat converted by friction is from the kinetic energy of falling so that heat we need to have included in the calculations. However, heat lost to the air or the tube (which does have a high specific heat capacity but lower than most plastics) is part of the error in this determination. It is a classic 'F-J' experiment - I never liked 'accurately determine' in my teaching, rather 'show how you would' experiments! Yes, hammering does generate heat (I used to set questions on would a projectile completely melt or vaporise on impact) and of course the effect of friction on pulling out a nail too. Thanks for watching and your great comments. Keep them coming!

[@Thrustmaster64]

I wonder, talking about an actual real life waterfall, how much would evaporation cool down the water on the way down? The latent heat of vaporisation of water is absolutely massive. But then again, so is its heat capacity. And that would also depend on the temperature of the water, temperature of the air, the relative humidity of the air, wind, and exactly how the water falls (think fine droplets vs. a solid stream). If I get really bored I might try to calculate exactly what fraction of the water has to vaporise for a given waterfall to cancel out the heating from the potential energy...

[@AnthonyFrancisJones]

Good question! Yes there are lots of variables. So quick back of the envelope calculation. If 10 tonnes of water falls 10m in one second then the gain in KE is 1MJ. Assume this all turns to heat. Now, if 1kg of water vaporises on falling of the 10,000kg then that will need 2MJ of energy not taking into account the energy needed to heat up the water (SHC). Assuming this heat can be lost then it would be cooler! Thanks for taking the time to comment! F-J

[@AnthonyFrancisJones]

BTW..."And do try it on your honeymoon - this is exactly what James Joule did at Cascade de Sallanches near Mont Blanc!"

[@UnitSe7en]

Intuition tells me that yes, it should be. But intuition also tells me that in the real world, no. Not for water, due to the aerosolization and evaporatative cooling experienced during the fall. I would predict that energy loss would far exceed heat gain from kinetic energy in that case.

[@AnthonyFrancisJones]

Great question! These things are always a bit of a simplification. Here was my answer to a previous question. "Yes there are lots of variables. So quick back of the envelope calculation. If 10 tonnes of water falls 10m in one second then the gain in KE is 1MJ. Assume this all turns to heat. Now, if 1kg of water vaporises on falling of the 10,000kg then that will need 2MJ of energy not taking into account the energy needed to heat up the water (SHC). Assuming this heat can be lost then it would be cooler! Thanks for taking the time to comment! F-J"

[@AnthonyFrancisJones]

And do try it on your honeymoon - this is exactly what James Joule did at Cascade de Sallanches near Mont Blanc!

[@UnitSe7en]

@@AnthonyFrancisJones Some blokes have all the luck.

[@AnthonyFrancisJones]

@@UnitSe7en Indeed!

[@PeterGannon-x3b]

Everybody knows that more kinetic energy means higher temperatures…

[@AnthonyFrancisJones]

Thanks Peter, that's not quite the case. For example a ball rolling on a surface faster is not necessarily hotter or for that matter the lead balls getting faster as they fall down the tube. The crucial thing here is the random nature of the particles movement. I tell my students that the random translational KE of particles gives the heat to a cup of coffee on my desk but if I move the cup to the left it does not get hotter as that is all linear as it were. Hope that explains it a bit and thanks for taking the time to comment and watch the video.

[@PeterGannon-x3b]

I was thinking more along the lines of when we add heat to the atom, the atom begins to translate around. The more heat that is added, the faster the translation. If we keep adding heat, it translates faster and faster. There is more kinetic energy,so the temperature is higher.

[@AnthonyFrancisJones]

Yes, Peter, I see your point. It is very hard to get an understanding of what Temperature means by considering a single atom moving. Even Heat in this context is not easy. Better to think of Temperature as being related to the average kinetic energy of a large number of freely moving particles. We also need to consider the movement of atoms that are bonded giving extra degrees of freedom such as Nitrogen in the air which is diatomic. I am sure I bore my family many times talking about the Boltzmann's distribution and its effect on things we see around us. It is indeed facinating to consider the movement of single atoms but at this scale quantum effects dominate and that's a whole different story!

[@PeterGannon-x3b]

I can’t even begin to understand Boltzmann’s distribution.

[@AnthonyFrancisJones]

@@PeterGannon-x3b Peter, shows that in any gas (for example) there are a range of velocities of particles. Some slow and some much faster and many in between. The average velocity of the particles considering their distribution gives a idea of the temperature of the gas. BY the way, it is not too difficult a calculation to work back from the temperature of gas in a room to its average particle velocity using this fact, which is about 500m/s !