Q. Water falls from a height 500 m. The rise in temperature of water at bottom if whole of energy remains in water, will be (specific heat of water is $c$=4.2 kJ ${kg}^{- 1}$)
A) 0.23$℃$
B) 1.16$℃$
C) 0.96$℃$
D) 1.02$℃$
Explanation
(b) When water falls from a height, it has potential energy (mgh),
this is used in heating up the water ($mc\mathrm{\Delta}\theta$).
Hence, we have
$mgh = mc\mathrm{\Delta}\theta$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathrm{\Delta}\theta = \frac{gh}{c}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{9.8 \times 500}{4.2 \times 10^{3}} = 1.16℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.