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Question

Water falls from a height of800m from a water fall. If the initial temperature of water at top of water fall is 10°C, what is its temperature at the bottom? Assume all the energy of falling water changes to heat energy.
[Take g=10ms-2and sp. heat capacity of water4200Jkg-1K-1 ]


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Solution

Step 1: Given data

height (h)=800m

acceleration due to gravity(g)=10ms-2

Sp. heat capacity(c)=4200Jkg-1K-1

m is the mass of the object

Temperature change(θR)=?

Step 2: equating the kinetic energy to the potential energy of the water

The kinetic energy of falling water=Potential energy of water at the top of water=mgh

The kinetic energy of falling water= heat produced in water

mgh=mcθRθR=ghcθR=10ms-2×800m4200Jkg-1K-1=1.9°C

So, the temperature of water at bottom=10°C+1.9°C=11.9°C

The temperature at the bottom of the water is 11.9°C.


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