The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall?
[Given 1 cal = 4.2 J and specific heat of water = 1 cal g⁻¹ °0C⁻¹]

Solution

Physics sir · 4 steps

All the potential energy the water loses on the way down turns into heat in that same water.

1. Energy balance. Take a mass m of water falling through height h. If all of its potential energy mgh heats the water, then mgh = mc Δ T.

   Δ T = gh/c

2. Units first. The mass cancels, so the answer does not depend on how much water falls. Put c in SI units: 1 cal g⁻¹ °C⁻¹ = 4.2 J g⁻¹ °C⁻¹ = 4200 J kg⁻¹ °C⁻¹.
3. Put in numbers. gh = 9.8 × 63 = 617.4 J kg⁻¹. So Δ T = 617.4/4200 = 0.147 °C.
4. So. The water at the bottom is about 0.147 °C warmer than at the top, which is option (a).

The idea to keep. For a falling liquid heating itself, Δ T = gh/c and the mass cancels. Always convert c to J kg⁻¹ °C⁻¹ before you divide.

Answer from the NTA final answer key. Solution by PrepWiser.