Thermodyamics, two balls with same temperature, different elevation

[epl_manutd]

Homework Statement

Two identical balls, A and B, of uniform composition and initially
at the same temperature, each absorb exactly the same
amount of heat. A is hanging down from the ceiling while
B rests on the horizontal floor in the same room. Assuming
no subsequent heat loss by the balls, which of the following
statements is correct about their final temperatures, TA and
TB, once the balls have reached their final dimension?

(a) TA < TB; (b) TA > TB;
(c) TA= TB; (d) TA <= TB.

Homework Equations

no idea

The Attempt at a Solution

no idea

 

[Saketh]

Think about all the forms of energy (potential, kinetic, heat, etc.) that the balls have, and how they change when the balls are heated.

 

[epl_manutd]

i'm very bad at thermodynamics and i need a few sol'ns before i get this topic. So if you can give me the solution, that would be great. I'm not doing this for homework or anything, just preparing for a contest

 

[Saketh]

i'm very bad at thermodynamics and i need a few sol'ns before i get this topic. So if you can give me the solution, that would be great. I'm not doing this for homework or anything, just preparing for a contest

Okay, I'll tell you how to do it since this is a qualitative problem.

Both spheres expand when heated.

This is the key point: The center of mass of the ball on the floor rises, while the center of mass of the ball on the thread falls. Therefore, the potential energy of the floor ball increases, and the potential energy of the string ball decreases.

Now, the first law of thermodynamics says that the heat added goes towards work and internal energy. Both spheres have to do the same amount of work to expand against the air, so that's not the key. The important thing is that one sphere has to do work to expand against gravity, while the other just let's gravity do the work.

The heat given to the ball on the floor will go into doing work against gravity, therefore less of the heat will go towards internal energy.

The heat given to the ball on the string will go into internal energy, and gravity also contributes positive work. Because the ball on the string has a higher change in internal energy, the ball on the string has a higher temperature.

(PS: Out of curiosity, what contest are you preparing for?)

 

[epl_manutd]

So temperature increase is related to the internal energy increase right? Ok, i understand most of your sol'n, very clear thanks a lot. I'm preparing for the CAP exam which is a Canadian physics contest. I might need your help further down the road. Thanks

 

[Saketh]

Yes, temperature is related to internal energy.
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Internal energy [/URL]is often written in terms of heat capacity and temperature changes, if that rings any bells.

 

[epl_manutd]

oh duh i really suck at thermodynamics

 

[Saketh]

oh duh i really suck at thermodynamics

Everyone is bad at a subject before they learn it, so don't worry about not knowing much!

I advise, however, that you work on more quantitative problems because this one only involved a bit of physical insight. And, as reassurance, this is one of the most difficult problems in elementary thermodynamics, in my opinion.