Thermal Physics and Bottle Shake

In summary: That is, the bottle is not entirely full of water. So the internal energy of the water and the internal energy of the air are not the same. In summary, if you shake a bottle of water, the temperature will increase. However, if you allow heat to escape from the bottle, the temperature will decrease.
  • #1
sportcardinal
2
0

Homework Statement


If you were to shake bottle with some water in it for about ten minutes, then roughly, how much would the temperature increase?


Homework Equations



K=1/2mv^2
U=N*f*1/2*k*T


The Attempt at a Solution



I think we need to find kinetic energy and assume it all gets converted to thermal. But I don't understand how to get temperature.

Do I just find K, then assume that is U and solve for T?
 
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  • #2
Depends on whether your bottle is an insulator, like a Thermos, or whether it's conducting to the ambient, or something inbetween (which of course will be the case).

Assuming a perfect insulator, and ignoring the heat capacity of the bottle itself (imagine a very thin, perfectly insulating bottle), all the work W you do in shaking the water is tranferred to internal energy buildup of the water. You can estimate the resulting temperature buildup from dW/dT = CV where CV is heat capacity of the water (= specific heat of water, 1 cal/gm, times no. of grams m in your bottle, or CV = mCv. So for every erg of shaking you'd get 1 deg C temp. buildup divided by the no. of grams of water: ΔT = W/CV.

If you allow heat to escape from the bottle as you shake it, that of course changes the picture. If a perfect conductor there would be no change in the water temp.
 
  • #3
You are also assuming there is no change in internal energy of the air in the bottle else that would have to be included, however slight. In the problem statement the word 'some' implies the bottle is not entirely full of water.
 
  • #4
LawrenceC said:
You are also assuming there is no change in internal energy of the air in the bottle else that would have to be included, however slight. In the problem statement the word 'some' implies the bottle is not entirely full of water.

Yes, but, as you say, that's very slight. C of water = 1 cal/cc-K;
C of air at 1 at. and 20C = 0.29e-3 cal/cc-K.
 
  • #5
"imagine a very thin, perfectly insulating bottle"

If you make this assumption, you must make the other.
 

1. What is Thermal Physics?

Thermal Physics is the branch of physics that deals with the study of the thermodynamic properties of matter, such as temperature, heat, and energy. It also involves the study of how these properties affect the behavior of materials and their interactions with each other.

2. How does Thermal Physics relate to Bottle Shake?

Bottle Shake involves the transfer of thermal energy through the shaking of a bottle. When the bottle is shaken, the kinetic energy of the shaking motion is converted into thermal energy, increasing the temperature of the liquid inside the bottle. This process is governed by the principles of Thermal Physics.

3. Why does a bottle warm up when shaken?

When a bottle is shaken, the kinetic energy of the shaking motion is transferred to the liquid inside the bottle. This kinetic energy is converted into thermal energy, causing the molecules in the liquid to vibrate faster and increase the temperature of the liquid.

4. Can Thermal Physics be used to explain other everyday phenomena?

Yes, Thermal Physics is involved in many everyday phenomena, such as cooking, boiling water, and even the weather. It helps us understand how heat is transferred and how temperature affects the behavior of different materials.

5. How can Thermal Physics be applied in real-world situations?

Thermal Physics has many practical applications, such as in the design of heating and cooling systems, engines, and refrigerators. It is also used in materials science to understand the behavior of different materials at different temperatures and in chemical reactions. Additionally, Thermal Physics is important in understanding climate change and developing sustainable energy sources.

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