   Chapter 11, Problem 7P

Chapter
Section
Textbook Problem

The highest recorded waterfall in the world is found at Angel Falls in Venezuela. Its longest single waterfall has a height of 807 m. If water at the top of the falls is at 15.0°C, what is the maximum temperature of the water at the bottom of the falls? Assume all the kinetic energy of the water as it reaches the bottom goes into raising the water’s temperature.

To determine
Maximumtemperature of the water at the bottom of the falls.

Explanation

Given Info: Height of the water falls is 807 m and temperature of the water at the top of the falls is at 15.0°C .

The water at top of the falls possess gravitational potential energy and it falls down the potential energy is converted in to kinetic energy. All the kinetic energy is goes into raising the water’s temperature.

Formula to calculate the change in energy is,

EP=EK

• EP is the potential energy,
• EK is the kinetic energy,

Expression for the raise in temperature when the kinetic energy is completed to heat energy is,

EK=mcΔT

• m is the mass of water,
• c is the specific heat of the water,
• ΔT is the change in temperature,

Formula to calculate the potential energy is,

EP=mgh

• g is the acceleration due to gravity,
• h is the height of the water falls,

Use mgh for EK in the equation EK=mcΔT and rearrange it in the form of ΔT .

ΔT=mghmc=ghc

Substitute 9.80m/s2 for g, 807 m for h, and 4186J/kg°C for c to find ΔT

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