calculate the increase in temperature of water which falls from a height of 100m assume that 90% of the energy due to the fall is converted into heat heat and retained by water

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Solution

Dear Student ,
Let us assume that mg amount of water falls from a height of 100 m .
$S o t h e w o r k d o n e i s, W = m g h = m \times 9 \cdot 8 \times 100 J N o w 90 % o f e n e r g y i s c o n v e r t e d i n t o h e a t a n d i t i s r e t a i n e d b y t h e w a t e r . S o t h e e t u s t a k e t h a t a f t e r t a k i n g t h i s h e a t t h e i n c r e a s e i n t e m p e r a t u r e i s t ° C . T h e r e f o r e, h e a t g e n e r a t e d = m \times 1 \times t = (m t) j o u l e N o w a c c o r d i n g t o t h e q u e s t i o n, W = J H \Rightarrow m \times 9 \cdot 8 \times 100 \times \frac{90}{100} = m t \times 4 \cdot 2 \Rightarrow t = \frac{90 \times 9 \cdot 8}{4 \cdot 2} = 210 ° C$
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