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A falling rock has kinetic energy KE just before striking the ground and coming to rest. What is the total change in entropy of rock plus environment as a result of this collision?

Short Answer

Expert verified

The change in entropy is \(\frac{{{\rm{KE}}}}{T}\).

Step by step solution

01

Concepts

When the rock comes to rest, the total kinetic energy is converted into heat energy.

The change in entropy is\(\Delta S = \frac{Q}{T}\).

02

Given data

The kinetic energy of the rock is KE just before striking the ground.

Let T be the temperature of the environment.

03

Calculation

When the box comes to rest, the initial kinetic energy is converted into heat energy.

As the environment is at a lower temperature, the heat energy is immediately transferred to the environment. But that is energy can’t change the temperature of the environment.

Then the increase in hat energy is \(Q = {\rm{KE}}\).

Therefore the change in entropy is,

\(\begin{array}{c}\Delta S = \frac{Q}{T}\\ = \frac{{{\rm{KE}}}}{T}\end{array}\)

Hence, the change in entropy is \(\frac{{{\rm{KE}}}}{T}\).

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