Thermodynamics: Heat Sink Experiment - 3 Pots vs. 2 Pots

[dsisk559]

First off this is not a homework question that i know of. I'm not in school but I had an idea I want to flesh out but I don't have the training to come up with the answer on my own.
Scenario 1:

There are 2 pots of water the 1st at 100 degrees c and a 2nd at 0 degrees.
There is a heat sink going from the middle of the first to the middle of the second.
It takes 10 minutes to for both pots to reach 50 degrees c.

Scenario 2:
There are 3 pots of water the 1st and 2nd at 100 degrees c and the 3rd at 0 degrees.
There is a heat sink connecting all pots just like above.

The question is will it take the same, more or less time to reach 66 degrees c in all 3 pots as it did in Scenario 1.

 

[Mapes]

There's a small problem: theoretically, it should take an infinite amount of time for the pots to get to 50 and 66.6 degrees, since the rate of heat transfer decreases as the temperature difference decreases. The final temperature is approached asymptotically but is never reached. However, we can get around this problem by specifying that the temperatures get arbitrarily close to their final temperature (50.1 and 66.7 degrees, for example)

Now we can get on with solving the real question. It may be easiest to solve it numerically; that is, divide the total time into small intervals and for each interval calculate the amount of heat energy that flows through the connection and also calculate how the temperature of the pots is affected by the energy change. Then repeat for the next interval and so on until the temperature has converged satisfactorily. Does this make sense?

 

[dsisk559]

Sadly it does not make since to me because I have no training in thermodynamics and not much training in math. I'm sorry but can you just tell me weather it will take longer, the same or less time to reach near equilibrium.

Thank you for your help.

 

[Mapes]

The process is fastest when the pots are the same size (i.e., equilibrium will be reached faster in scenario 1).

 

[sardar]

I would approach this question by analyzing the thermodynamics principles involved in both scenarios. In both cases, heat is being transferred from the hot pots to the cold pot through the heat sink. This process is governed by the laws of thermodynamics, specifically the second law which states that heat will naturally flow from hot to cold objects until they reach thermal equilibrium.

In Scenario 1, there are only two pots involved, so the heat transfer process is simpler. The heat from the 100 degrees c pot will transfer directly to the 0 degrees c pot until they both reach 50 degrees c. This process takes 10 minutes, as stated in the scenario.

In Scenario 2, there are three pots involved, so the heat transfer process is more complex. The heat from the 100 degrees c pots will transfer to the 0 degrees c pot, but now there is an additional pot that is also at 100 degrees c. This means that some of the heat will also transfer to the third pot, causing it to heat up. However, since the third pot is already at 100 degrees c, it will not take as much heat as the 0 degrees c pot to reach 66 degrees c.

Therefore, in Scenario 2, it will take less time for all three pots to reach 66 degrees c compared to Scenario 1, where it took 10 minutes for two pots to reach 50 degrees c. This is because the third pot in Scenario 2 acts as an additional heat sink, absorbing some of the heat and allowing the other two pots to reach their desired temperature faster.

In conclusion, the number of pots and their initial temperatures do affect the time it takes for all pots to reach a certain temperature when connected through a heat sink. In this case, having three pots instead of two will result in a faster heating process. This can be further tested and verified through experiments to validate the theoretical explanation.