# Conservation of energy: Change in temperature of a bucket of water after a ball falls into it...

Thread moved from a technical forum, so homework template missing.
My question:
Consider an isolated system consisted of a ball, and a bucket of water. The ball is released from height, H above a bucket of water. The initial temperature of the water-bucket system and the ball are T1 and T2 respectively. What will be the final temperature of the water after the ball is dropped? (mass of the ball = m1, mass of water = m2, mass of the bucket = m3, specific heat of ball, water and bucket are s1, s2 and s3 respectively)

The answer:
mgH = (m1S1+m2S2)T1 + m3S3T2

My problem (Conservation of energy):
We know energy cannot be created or destroyed but it can be converted from one form to another, which is known as the conservation of energy.
But why potential energy should convert into thermal energy? Again if we consider that potential energy is converted into thermal energy why the whole energy should be converted?
I mean some energy should be converted. Suppose, the amount of the converted energy is E. Then,
mgH -E= (m1S1+m2S2)T1 + m3S3T2+E
So, can you please explain the matter easily?

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## Answers and Replies

Doc Al
Mentor
But why potential energy should convert into thermal energy? Again if we consider that potential energy is converted into thermal energy why the whole energy should be converted?
Why would you think only some of the potential energy becomes thermal energy? (I assume you can ignore losses such as sound energy; I also assume that the given potential energy of the ball is with respect to its final position.)

CWatters
Science Advisor
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That last line in DocAl's post is important. The ball may float or sink so you need to be clear what you mean by the PE of the ball and what you mean by all of it.

A.T.
Science Advisor
But why potential energy should convert into thermal energy?
https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

Again if we consider that potential energy is converted into thermal energy why the whole energy should be converted?
"The whole" depends on where you place the zero potential.

haruspex
Science Advisor
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2020 Award
why potential energy should convert into thermal energy?
It doesn’t happen all at once. At first, most of the ball's KE goes into churning the water around in the bucket, and throwing some up into the air, which then falls down again. Churning water has kinetic energy since, in principle, we could harness some of that to do useful work. But it is less useful than the KE of an entire bucket of water (and before that, the entire ball) moving with a single velocity.
Over time, the water movement becomes more chaotic and less directly harnessable. This is what we call thermal energy.

hmmm27
Gold Member
But why potential energy should convert into thermal energy?

What else is it going to convert into ? There's no dimension given for the ball, so you can probably safely ignore any water displaced by sinking. As far as acoustics is concerned, it's a closed system : audio vibrations are assumed to be dampened, thus reabsorbed.

Andrew Mason
Science Advisor
Homework Helper
My question:

We know energy cannot be created or destroyed but it can be converted from one form to another, which is known as the conservation of energy.
But why potential energy should convert into thermal energy? Again if we consider that potential energy is converted into thermal energy why the whole energy should be converted?
I mean some energy should be converted. Suppose, the amount of the converted energy is E. Then,
mgH -E= (m1S1+m2S2)T1 + m3S3T2+E
So, can you please explain the matter easily?
Hi Sinan - welcome to PF!

The ball starts with gravitational potential energy - which is the ability to experience application of gravitational force through a vertical distance if allowed to fall. The gravitational force does work on the ball as it falls, converting potential energy to kinetic energy of the ball. When the ball strikes the water, its kinetic energy is transferred to kinetic energy of water molecules. Once the water reaches thermodynamic equilibrium, with all that translational kinetic energy randomly distributed throughout the water molecules, there is an increase in temperature of the water (temperature being a measure of such energy). This is similar to the original experiments by Joule showing the relationship between work and heat flow and which led to a deeper understanding of "energy".

AM