   Chapter 11, Problem 10P

Chapter
Section
Textbook Problem

A 3.00-g copper coin at 25.0°C drops 50.0 m to the ground. (a) Assuming 60.0% of the change in gravitational potential energy of the coin-Earth system goes into increasing the internal energy of the coin, determine the coin’s final temperature. (b) Does the result depend on the mass of the coin? Explain.

(a)

To determine
The coin’s final temperature.

Explanation

Given Info: The height from the ground where the copper coil fell is 50.0m , 60 % of change in gravitational potential energy goes into increasing the internal energy of the coil. The initial temperature of the coil is 25.0°C .

60 % of change in gravitational potential energy goes into increasing the internal energy of the coil. Consider the change in potential energy is positive. So,

Formula to calculate the internal energy of the coin is,

Q=60%(ΔPE)

• Q is the change in internal energy of the coin,
• |ΔPE| is the change in potential energy of the coin,

Formula to calculate the change in potential energy is,

ΔPE=mgh

• m is the mass of the coin,
• g is the acceleration due to gravity,
• h is the height,

Formula to calculate the energy required to raise the temperature of the coin,

Q=mc(TfTi)

• Q is the energy required to raise the internal temperature of the coin,
• c is the specific heat of copper,
• Ti is the initial temperature of the coin,
• Tf is the final temperature of the coin,

Use 60%mgh for Q in Q=mc(TfTi) .

60%mgh=mc(TfTi)(60100)mgh=mc(TfTi)Tf=Ti+0

(b)

To determine
Whether the result depends upon the mass of the coin.

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