Question

water falls from a height 500 m.what is rise in temperature of water at bottom if whole energy remain in the water?​

Answer 1

By mechanical energy conservation, the energy stored in the water is equal to its potential energy when it's at a height 500 m, where it has no velocity, nor kinetic energy.

So the energy is,

$\displaystyle\longrightarrow\sf{E=mgh}$

$\displaystyle\longrightarrow\sf{E=m\times9.8\times500}$

$\displaystyle\longrightarrow\sf{E=4900m}$

The heat energy is also the same and is given by,

$\longrightarrow\sf{E=mc\,\Delta T}$

$\longrightarrow\sf{mc\,\Delta T=4900m}$

$\longrightarrow\sf{c\,\Delta T=4900}$

Specific heat capacity of water, $\sf{c=4186\ J\,kg^{-1}.}$ Then,

$\longrightarrow\sf{4186\cdot\,\Delta T=4900}$

Then, rise in temperature is,

$\longrightarrow\sf{\Delta T=\dfrac{4900}{4186}}$

$\longrightarrow\underline{\underline{\sf{\Delta T=1.17\,^oC/K}}}$