# Thermodyamics, two balls with same temperature, different elevation

• epl_manutd
In summary, two identical balls, A and B, of uniform composition and initial temperature absorb the same amount of heat before reaching their final dimensions. A, hanging from the ceiling, has a lower final temperature due to the work it does against gravity while B, resting on the floor, has a higher final temperature due to the heat primarily going towards internal energy. This is a difficult problem in elementary thermodynamics and it is advised to work on more quantitative problems.
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.

no idea

## The Attempt at a Solution

no idea

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

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

epl_manutd said:
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?)

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

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

Last edited by a moderator:
oh duh i really suck at thermodynamics

epl_manutd said:
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.

## 1. What is thermodynamics?

Thermodynamics is a branch of physics that studies the behavior and relationships between heat, energy, and work.

## 2. How do two balls with the same temperature behave at different elevations?

According to the ideal gas law, the temperature of a gas is directly proportional to its pressure. Therefore, at higher elevations where the atmospheric pressure is lower, the two balls will have a lower temperature compared to the same balls at a lower elevation.

## 3. Why do the two balls have different temperatures at different elevations?

This is due to the decrease in atmospheric pressure at higher elevations, which causes the molecules in the gas to spread out and have less frequent collisions, resulting in a lower temperature.

## 4. What is the relationship between temperature and elevation in thermodynamics?

The relationship between temperature and elevation in thermodynamics is described by the ideal gas law. As elevation increases, the temperature of a gas decreases due to the decrease in atmospheric pressure.

## 5. How does thermodynamics explain the behavior of two balls with the same temperature at different elevations?

Thermodynamics explains this behavior through the ideal gas law, which states that the pressure and temperature of a gas are directly related. As the elevation changes, the atmospheric pressure changes, causing the temperature of the gas to also change, resulting in the two balls with the same temperature having different temperatures at different elevations.

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