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Integrated Concepts(a) What is the temperature increase of water falling 55.0 m over Niagara Falls? (b) What fraction must evaporate to keep the temperature constant?
$\begin{array}{ll}{\text { Part }(\mathrm{a}) :} & {\Delta T=0.13^{\circ} \mathrm{C}} \\ {\text { Part }(\mathrm{b}) :} & {2.22 \times 10^{-4}}\end{array}$
Physics 101 Mechanics
Chapter 14
Heat and Heat Transfer Methods
Thermal Properties of Matter
Cornell University
Hope College
University of Winnipeg
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number 74 That s what. Reading the temperature increase for water falling 55 meters. Um, so the potential energy of the water turns into heat, increasing the temperature of the water. So this is MGH. This is M C Delta T. We won't know this temperature change. Well, the master, the water falling. Zzyzx, Seimas, the master, The water increase in temperature. I don't know what that is, but I can cancel it. So G's 9.8 I was given the height was 55. See, that's a specific you'd of water. And I need to do the one in jewels because this would turn out to be in jewels on this side, um, so that it is 41 86 and I'm finding the change in temperature. So I multiply and I divide and I get that. That change in temperature is point 129 and then part B. It is what fraction of that water would have to evaporate to keep it at a constant temperature. So again, Oh, we've got the water falling. So it's p grav turning into a phase change instead. So mass times he's vaporization for evaporation. Um, so this is MGH. This is well, m times heating, vaporization. But these aren't the same masses this time. They're asking what fraction of this What are all the water falling? But not all of the water is evaporating. So I'm going to say and we call this mass total. You call this mass evaporating? We want to know what fraction So basically the mass evaporating over the total. So I'm gonna bring that to the side. So mass evaporating over mass total equal g h over the heating vaporization. And this is what I'm trying to find this reaction Come this way. So 9.8 times 55 and he did vaporization. So that's the Estrich under the chart words for it's not boiling, it's at 37 degrees. So it's on the table tells me it's 34. 30 killed Jules per kilogram and I mean that to be in jewels. I'm gonna multiply that by another 1000 e divide and I get 2.22 tame us 10 to the negative forth. That's the fraction that must evaporate toe have just a phase change and not a temperature change
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