The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall ? [Given $1 \mathrm{cal}=4.2 \mathrm{~J}$ and specific heat of water $=1 \mathrm{calg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$]

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Heat & Thermodynamics

The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall ?
[Given

1 cal = 4.2 J

and specific heat of water

= 1 calg^{- 1}^{\circ} C^{- 1}

]

(A) $0.14 7^{\circ} C$ ✓ Correct
(B) $14.7 6^{\circ} C$
(C) $1.47 6^{\circ} C$
(D) $0.01 4^{\circ} C$

Answer: (A)

Solution

All the gravitational potential energy lost by the falling water turns into heat, so

m g h = m c Δ T

and

Δ T = \frac{g h}{c} .

With

g = 9.8

m/s

^{2}

h = 63

m and

c = 1 cal g^{- 1}^{\circ} C^{- 1} = 4200 J kg^{- 1}^{\circ} C^{- 1}

Δ T = \frac{9.8 \times 63}{4200} = 0.147^{\circ} C .

The water at the bottom is warmer than at the top by

0.147^{\circ}

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Heat & Thermodynamics →

More JEE Main questions on Heat & Thermodynamics

A cylindrical tube $A B$ of length $l$ , closed at both ends contains an ideal gas of 1 mol having molecular weight $M$ . The tube is rotated in a horizontal plane with constant angular velocity $ω$ about an axis perpendicular to $A B$ and passing through the edge at end A, as s …
JEE Main 2026View solution →
Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $10 0^{\circ} C$ and $4 0^{\circ} C$ respectively. Given the thermal conductivity of rod x is three …
JEE Main 2026View solution →
The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{th}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $Δ Q = 0$ ) then identify the gas from the following options (Assuming …
JEE Main 2026View solution →
Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is …
JEE Main 2026View solution →
An insulated cylinder of volume $60 cm^{3}$ is filled with a gas at $2 7^{\circ} C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 cm^{3}$ while allowing the temperature to rise to $7 7^{\circ} C$ . The fin …
JEE Main 2026View solution →
The r.m.s speed of oxygen molecules at $4 7^{\circ} C$ is equal to that of the hydrogen molecules kept at $____$ $^{\circ} C$ . (Mass of oxygen molecule/mass of hydrogen molecule=32/2)
JEE Main 2026View solution →