Animated Solution for Physics - Properties of Solids and Liquids: The height of victoria falls is $63\text{ m}$. What is the difference in temperature of water at the top and at the bottom of fall ? [Given, $1\text{ cal}=4.2\text{ J}$ and specific heat of water $=1{\text{ cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$]

Imagine standing at the majestic Victoria Falls. Water is plunging down from a massive height of $63\text{ m}$. As it falls, it loses gravitational potential energy. But energy doesn't just vanish; it transforms. By the law of conservation of energy, the loss in gravitational potential energy of the water is entirely converted into heat energy when it crashes at the bottom.

We can equate the potential energy lost to the heat energy gained. The potential energy is given by $mgh$, and the heat energy is given by $ms\Delta T$.

Notice how the mass $m$ cancels out from both sides. This is a beautiful realization: the temperature rise is completely independent of the amount of water falling! Whether it's a single drop or a massive waterfall, the temperature change will be exactly the same.

Now, let's set up our equation to solve for the change in temperature, $\Delta T$:

But wait, there is a catch here! The units must be consistent. The specific heat $s$ is given in calories per gram per degree Celsius ($1{\text{ cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$). We must convert it to standard SI units, Joules per kilogram per degree Celsius.

We know that $1\text{ cal}=4.2\text{ J}$, and $1\text{ g}=10^{-3}\text{ kg}$.

Let's substitute the values and get the answer. We plug in $9.8{\text{ m/s}}^2$ for $g$, $63\text{ m}$ for $H$, and $4200{\text{ J kg}}^{-1}{}^{\circ }{\text{C}}^{-1}$ for $s$.

Multiplying $9.8$ by $63$ gives us $617.4$. Dividing this by $4200$, we get exactly $0.147$.

Even a $63\text{-meter}$ drop barely raises the temperature by a fraction of a degree! This is because water has an exceptionally high specific heat capacity. It takes a massive amount of energy to raise its temperature.