[thermodynamics] basic steady state tasks

[tomek888]

Hello,

 

Can you guys help me with these two tasks :

 

1. I have two containers one above the other. In the first one, the fluid temperature is greater then the second one (let's say T1>T2).Containers have a valve between them, when you open it, fluids will mix. In which configuration mixed fluid will reach its equlibrium faster - if T1 is in the upper container or if T2 is in the upper container ? Or it does not matter?

 

2. I have two rods that are the same material, same length but different diameter, one much larger then the other. Both are heated to lets say T1. Which one will first get to T2 (lower than T1) ?

 

I know its basic, but I will appreciate any help with those

Thank you in advance

Edited October 7, 2013 by tomek888

[studiot]

Is this homework?

 

For both of these questions more information is required.

 

1) Why will they mix if Tupper>Tlower?

 

2) What is the rate of heat input?

[tomek888]

My friend ask me these as 'what if..' and here I am looking for help.

 

1) When you open the valve the upper fluid will 'flush' in to the lower container - they are the same weight.

 

2) No more data provided on this one - lets say both were heated to 200° F and which one will reach 90° F first

[studiot]

 

1) When you open the valve the upper fluid will 'flush' in to the lower container - they are the same weight

 

No they are not, have you ever looked at your hot water tank?

 

2) No more data provided on this one - lets say both were heated to 200° F and which one will reach 90° F first

 

 

There is not enough data, what do you mean both heated to 200F? How?

 

By immersion in a blast furnace?

By heating oneend with a hair drier?

 

Come on ask a proper question to receive a proper answer.

[tomek888]

But I think that in the second one it's not important how did I heated these rods - the question is that you have both rods heated to the equal temperature and you are waiting for them to cool down - and which one is going to be first.

 

And the first one - you mean that when you open the valve and in the upper container you have hotter fluid it will stay there ?

[studiot]

 

And the first one - you mean that when you open the valve and in the upper container you have hotter fluid it will stay there

 

I don't know, there is not enough information. You stated that they would mix.

 

It is density (=specific weight), not weight that counts. If the liquids are both the same substance, then the hotter one will be less dense so if it is in the upper tank, it will not fall to the lower.

If it is in the lower tank it will rise and mix. So there is your answer.

 

 

But I think that in the second one it's not important how did I heated these rods - the question is that you have both rods heated to the equal temperature and you are waiting for them to cool down - and which one is going to be first.

 

That was not your original question and is easier to answer.

 

Newton's law of cooling says that the rate of cooling depends only on the temperature difference between a hot body and its surroundings.

So if they start at the same elevated temperature and cool freely, they will always be at the same temperature and reach room temperature at the same time.

[tomek888]

Yes you are right, now I read my post and the second task was not clear. So thank you very much for help -

 

About the first one, I can assume that if I place the hotter fluid below the colder, they will mix faster and then reach equilibrium faster than the other scenario with colder fluid below hotter?

[studiot]

If the hot liquid is placed in the upper tank it will not mix at all. Eventually the heat from the upper liquid will permeate into the lower until they reach the same temperature, but that is not the same as saying the liquids themselves will mix.

 

That is why you can draw all the hot water off a hot tank, whilst adding cold at the bottom to replace the water drawn off.

Edited October 7, 2013 by studiot

[J.C.MacSwell]

Yes you are right, now I read my post and the second task was not clear. So thank you very much for help -

 

About the first one, I can assume that if I place the hotter fluid below the colder, they will mix faster and then reach equilibrium faster than the other scenario with colder fluid below hotter?

Don't assume it if is water at 32 and 37 F. You would be wrong.