Question

The water flowing over Niagara Falls drops a distance of 50 m. If all the gravitational potential energy is converted to thermal energy, by what temperature does the water rise? The specific heat of water is 4186 J/kg ∙ K.

a)0.42 C°
b)0.37 C°
c)0.12 C°
d)0.10 C°

Answer 1

Answer : (C) 0.12 C°

Explanation :

It is given that all the gravitational potential energy is converted to thermal energy.

So, the thermal energy is balanced by gravitational potential energy.

Gravitational potential energy,
`U=mgh`

And amount of heat is,
`Q=mc\Delta T`

Where, c is specific heat.

So,
`mgh=mc\Delta T`

`\Delta T=(gh)/(c)`

`\Delta T=(9.8\ m/s^2* 5\ m)/(4186\ J/kg\ K)`

`\Delta T=0.1170\ C^0}`

or
`\Delta T= 0.12\ C^0`

Hence, this is the required solution.

Correct option is (C) 0.12 C°.