Question

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.

Answer 1

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.