William Thomson (later to be called Lord Kelvin) enjoyed telling a story of acci

Question

William Thomson (later to be called Lord Kelvin) enjoyed telling a story of accidentally running into Joule in 1847 while he was hiking at Mt. Blanc on his honeymoon. Joule was packing a long thermometer and explained to curious hikers that he was going to "try for elevation of temperature of waterfalls". Calculate the temperature difference between the water at the top and the bottom of Niagra Falls, elevation change 167 feet. (Neglect air friction, and assume the water is insulated as it falls.)

Explanation / Answer

h = 167 feet = (167 / 3.28 m) = 50.91 m

specific heat of water c = 4186 J / kg-Co

Potential energy at the top is used up to increase the temperature of water.

mgh = cmT

T = gh/c

T = (9.8 * 50.91) / (4186)

T = 0.12o C

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