# Two Thermally Insulated Tanks: Solving the Puzzle

• copitlory8
In summary, the drawing shows two thermally insulated tanks connected by a valve, initially closed. When the valve is opened, the contents of the two tanks mix and the pressure becomes constant throughout. The final temperature and pressure can be found using the ideal gas law and the conservation of energy and mass, where the amount of gas in both tanks and the final volume can be calculated using the ideal gas law. The final internal energy can be calculated by summing the initial internal energies of both tanks.
copitlory8
The drawing shows two thermally insulated tanks. drawing: http://www.webassign.net/CJ/14_26.gif
They are connected by a valve that is initially closed. Each tank contains neon gas at the pressure, temperature, and volume indicated in the drawing. When the valve is opened, the contents of the two tanks mix, and the pressure becomes constant throughout.

(a) What is the final temperature? Ignore any change in temperature of the tanks themselves.(Hint: The heat gained by the gas in one tank is equal to that lost by the other.)
_______K
(b) What is the final pressure?
_______Pa
I have stared at this picture for like 30 minutes and read the entire chapter on thermodynamics in my physics book but I can't find a solution. Please provide one, thank you.

Find quantities which are conserved during the experiment for this system of two tanks. Opening the valve will not change the overall volume. The gas does not escape. There is no exchange of energy with the surroundings...

ehild

do i use the formula that Q=cmdeltat

If you know m and c and Q... Do you know them?

ehild

i think i should answer yes, however i don't know the mass of neon gas. is it going to be the molecular mass?

You can not answer yes. In principle, the specific heat capacity is given either for constant volume or for constant pressure. If you look at the data, the gas in the tanks is at different pressure. When the valve is opened, some gas flows from one tank to the other, so the volume of the gas changes, and so does its pressure.

Use the ideal gas law to find the amount of gas in both tanks.

ehild

well the ideal gas law is pv=(m/M)RT and R=8.31 but how do i use this equation

Use the form with moles, n : pV=nRT. You know p, V and T for both tanks you can calculate the number of moles they contain.

ehild

okay so after i get the moles in each tank what do i do?

After opening the valve you have one container with volume equal to the sum of both tanks, and the amount of gas equal to the sum of the moles initially present in both tanks. You can write the idel gas law for this container, too.

You can do the same with the internal energy. It is the sum of the initial internal energies of both tanks.

ehild

now you lost me. i don't know how to calculate the internal energy give just the moles

## 1. What is the purpose of the puzzle "Two Thermally Insulated Tanks"?

The puzzle "Two Thermally Insulated Tanks" is designed to test one's understanding of the principles of thermodynamics and how heat transfer occurs in a closed system. It presents a scenario where two tanks of different temperatures are connected by a pipe and asks the player to determine how the temperatures will change over time.

## 2. Can the puzzle be solved using only basic knowledge of thermodynamics?

Yes, the puzzle can be solved using basic knowledge of thermodynamics such as the laws of thermodynamics, heat transfer equations, and the concept of thermal equilibrium. However, some critical thinking and problem-solving skills may also be necessary.

## 3. Are there multiple solutions to the puzzle?

Yes, there can be multiple solutions to the puzzle depending on the initial temperatures of the tanks and the specific parameters given in the scenario. However, there is usually one most logical and efficient solution.

## 4. How can this puzzle be applied in real-world scenarios?

The concepts and principles used in the puzzle "Two Thermally Insulated Tanks" can be applied in various real-world scenarios, such as designing and optimizing heating and cooling systems, understanding the behavior of heat transfer in different materials, and predicting temperature changes in closed systems.

## 5. What skills can be developed by solving this puzzle?

Solving the puzzle "Two Thermally Insulated Tanks" can help develop critical thinking, problem-solving, and analytical skills. It also improves one's understanding of thermodynamics and its practical application in real-world situations.

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