physics textbook errata - Genzer and Youngner

Anonymous Submission

Question number 14 on page 346. The book listed 1.076 degrees C/kg as the answer.

Water drops over a water fall that is 430 m high. Assuming that all of the water's PE at the top of the falls is converted into internal heat energy (rather than gross KE) what will be the temp. increase of the water at the bottom of the falls?

First of all the units are incorrect. degrees C/kg suggests that (for example) 2 kg would heat up twice as much as one kg. This is not so. The temperature increase will be proportional to the energy gained per mass, and the energy gained is proportional to the mass, so mass units cancel out. The final units should be just degrees (in C if desired).

The second problem is that the number is wrong. Depending on how many decimals are used for 'g' and the caloric equivalent, the answer obtained will be somewhere in the ballpark of 1.03 degrees C (g = 10 m/s^2, caloric equivalent = 4.18) to 1.0067 (g = 9.8 m/s^2, caloric equivalent = 4.186). In any case, the accuracy of the constants used should indicate rounding off at a lower number of decimal places.