Question

If the specific heat capacity of water initially is
4.2×103
per kg per K and
g=10m/s2
, the difference in temperature of water between the top and bottom of a 210 m high water fall is ------

Answer 1

If the specific heat capacity of water initially is $4.2 \times 10^{3}$ per kg per K and $g = 10 \, \text{m/s}^2$, the difference in temperature of water between the top and bottom of a $210 \, \text{m}$ high water fall is ---

The energy conservation law:

$$\Delta W + \Delta Q = 0$$

where $\Delta W$ – changing of mechanical energy, $Q$ – changing of heat;

changing of mechanical energy:

$$\Delta W = m g \Delta h$$

h – high of body;

changing of heat:

$$Q = c m \Delta t$$

c – specific heat capacity, t – temperature;

Therefore:

$$m g (h - 0) = c m \Delta t$$ $$\Delta t = \frac {g h}{c} = \frac {2 1 0 m * 1 0 \frac {m}{m}}{4 2 0 0 \frac {t}{k g K}} = \frac {1}{2} = 0. 5 \text{ degrees}$$

Answer: 0.5 degrees