Gas law and thermodynamics concept question

[newsharpie]

A 25 kg steel ball at 300 °C is held 100 m above the ground. The ball is then released and begins falling. The ball cools as it falls, and the ball continues to accelerate as it falls. Air friction is negligible. The total energy of the ball is greatest:

a. The instant it is released
b. Midway through its fall
c. Just before it hits the ground
d. After it strikes the ground
e. The energy remains constant

The answer is (a)

I found this question online when I was trying to make sure that I had all the concepts from Gas Laws and Thermodynamics down but can't figure this one out. I assumed the answer would be (c) because as the ball falls the velocity increases at a constant rate of 9.8 m/s^2 with it being highest right before it hits the ground and KE=.5mv^2. A little explanation by anyone would be great.

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[dontbeanegaton]

You're thinking too hard for this one.
The mechanical energy of the system will not change, since the potential energy is converted to kinetic energy. Total energy change due to the ball falling is 0.
The only energy that does change is the temperature. The temperature is highest at the point of release. Thus the thermal (and total) energy are highest when the ball is hottest, at t=0.

 

[cheesier]

Remember, positional energy involves both kinetic and potential energies. Right before it hits the ground its kinetic energy is equal to its potential energy at the top. Halfway down its potential energy = kinetic energy. So, at the top it has the same positional energy that it has at the bottom. That just leaves us with the energy it has from heat. More heat = more energy. It has the highest temperature at the top, so its energy (potential + kinetic (which is 0) + thermodynamic) is the highest.

 

[newsharpie]

Thank you so much

 

[LoLCareerGoals]

Completely agree with posters above, but why do you bring up gas law? Where in the problem do you see anything related to gas law?