Calculate the difference in the temperatures between the water at the top and bottom of a water fall 200 m high. Specific heat of water is 4200 J kg-1 C-1.
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Given: s = 4200 J kg-1 °C-1, h = 200 m
To find: Difference in temperatures (∆T)
Formulae:
(i) Q = ms∆T
(ii) P.E. = mgh
Calculation: From formulae (j) and (ii) When water falls from top to bottom. assuming no loss in energy, potential energy is converted into heat energy.
∴ Q = P.E.
∴ ms∆T = mgh
∴ s∆T = gh
∴ ∆T = \(\frac{gh}{s}=\frac{9.8\times200}{4200}\)
∴ ∆T = 0.467 °C
The difference in temperatures between the water at top and bottom is 0.467 °C.
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