Energy Analysis of Niagara Falls in Linus Pauling's "General Chemistry" I just started reading Linus Pauling's "General Chemistry" and the first example confuses me.  He writes:

Example 1-1. Niagara Falls (Horseshoe) is 160 feet high.  How much warmer is the water at the bottom than at the top, as the result of the conversion of potential energy into thermal energy? The standard acceleration of gravity is 9.80665 m s$^{-2}$.
Solution. The gravitational force on a mass of 1 kg at the earth's surface is 9.80665 N.  The change is [sic] potential energy of 1 kg over a vertical distance $h$ (in meters) is 9.80665 $\times$ $h$ J.  In this problem $h$ has the value 0.3048 $\times$ 160 = 48.77 m (conversion factor from Appendix I); hence the change in potential energy produces 9.80665 $\times$ 48.77 = 478 J to thermal energy.  The energy required to raise the temperature of 1 kg of water by 1$^{\circ}$C is given above as 1 kcal = 4.184 kJ = 4184 J. Hence the increase in temperature of the water is 478/4184 = 0.114$^{\circ}$C.

Now what I don't understand is why he doesn't account for change in kinetic energy and heat flow between the water and the environment.
If this question belongs on Chemistry.SE, feel free to move it.
 A: Most, if not all, scientific analysis of real situations involves approximations. 
If some of the kinetic energy gained from falling was converted to kinetic energy of downstream flow (like a more sliding board shaped waterfall) it could affect the calculation. 
The environment could affect the temperature of the pool of water at the bottom of the falls, especially if the volume is large compare to the flow rate.  In the winter there can be massive amounts of ice which would have a significant effect.
Gravity isn't really constant either, but changes with the position of the Sun, Moon and Earth. Gravity at the top of the falls will be less than at the bottom. Heat capacity isn't constant. Some of the water could evaporate on the way down the falls, cooling the water.  Niagara river isn't pure water. :)
For educational problems, especially if you want to do well on tests, you need to consider the spirit of the problem.   
A: The bottom of Niagara Falls is in shadow, both because points northward, both for the reflecting fog clouds. Thereafter the rock average temperature is lower there then on top, quickly cooling the fallen water. The experience of ACuriousJim should implies that this effect can be more relevant than the others mentioned above, which just reduce the temperature increment.
A: In fact, thermal energy is heat. Think about heat as atoms vibrating: The more vigorously they vibrate (i.e. the more kinetic energy they have), the hotter it gets. The relation between thermal and kinetic energy is summarized by the simple equation
$k_B T=m\langle v_x^2\rangle$, where $k_B$ is Boltzmann's constant and $\langle v_x^2\rangle $ the expectation for the velocity squared of the particles in some direction labeled $x$.
He doesnt take the heat flow between water and environment into account because, in such a short process, it is very reasonable to assume that the heat transfer is negligible. 
