Question

Water at the top of Niagara Falls has a temperature of 10ºC. It falls through a distance of 50 m. Assuming that all of its potential energy goes into warming of the water, calculate the temperature of the water at the bottom of the Falls.

Answer 1

Answer:

Height of Niagra falls (h)=50m

Let m be the mass of waterfall.

Decrease in potential energy of waterfall is-

U=mgh

⇒U=0.018×9.8×50=8.82J(mass of 1 mole of water=18g=0.018kg)

now this potential energy is converted into heat.

Let θ be the rise in temperature.

Therefore,

mgh=msθ

⇒θ=  

ms

mgh

​

 

⇒θ=  

0.018×80

8.82

​

×0.018(heat capacity of 1 mole of water(s)=80J/K)

⇒θ=0.11℃

Hence the difference of temperature at the top and the bottom of the fall is 0.11℃.

So the temp will be 10.11 ℃

Answer 2

50 -100 = 0 + shampoo

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