Question

If $60 \%$ of the kinetic energy of water falling from $210\, m$ high water fall is converted into heat, the raise in temperature of water at the bottom of the falls is nearly _______(specific heat of water $=4.2 \times J\,kg ^{-1} K ^{-1}$)

• A. $0.6^{\circ} C$
• B. $0.3^{\circ} C$
• C. $1.2\, K$
• D. $2.4\, K$

Answer 1

Answer: (B)

Given $a , h=210\, m$
Specific heat of water, $c=4.2 \times 10^{3} J\,kg ^{-1} K^{-1}$
When water falls on the surface of earth, then its potential energy is
converted into kinetic energy.
$\therefore $ Kinetic energy = Potential energy
$K E=m g h \ldots \ldots$.(i)
According to question,
Heat produced $=60 \%$ of $K E$
[from Eq. (i)]
$\Rightarrow m c \Delta T=\frac{60}{100} \times m g h$
$\Delta T=\frac{0.6 g h}{c}=\frac{0.6 \times 10 \times 210}{4.2 \times 10^{3}}$
$=0.3^{\circ} C$