# Two thermally insulated tanks, calculating final temperature and final pressure

• copitlory8
In summary: so in summary, you can solve for the temperature, pressure and volume by using the ideal gas law and the molar heat capacity of neon gas at constant pressure.
copitlory8
The drawing shows two thermally insulated tanks. drawing is located at:
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'm pretty sure this is right:

First, get:

Final Volume: Sum of the tanks
Final Pressure: Average of the tanks, because the number of molecules is constant
Final Temperature: We'll find this out now

use PV=nRT

1. Solve for n (number of molecules) in each tank.

2. Sum the number of molecules in the two tanks.

3. Use PV=nRT again using the "Final" values of Volume, Pressure, and # of molecules.

4. ?

5. Profit!

but this only solves for the finall temperature. what about the final pressure?

actually i got the answer completely wrong

please i need a real solution. i really need to pull up my physics grade

Give me a minute.

Hahaha redeem myself. O Yes I will sire.

I suppose I will give this a shot.

(a) Follow the hint, the heat gain by 1 tank = heat loss by the other. Hence the temperature should be averaged out by the two. And what's the average between 220 and 580?

400k

That's right, use this to find the number of molecules in individual tanks, then you should be able to get the answer for pressure.

I can't get this man, here what's I've got, but it doesn't come out right, maybe it will lead you somewhere.

Use PV=nRT for each tank and solve for 'n', the # of molecules.

Sum the number of molecules to get the total.

So you have
Total Volume, Total Molecules, and R, but you don't have P and T, which is what you DO need...

I'm stuck man...

Sorry.

how do i do that

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 the gas in both tanks.

The internal energy of an ideal gas is the sum of the kinetic energy of its particles.

ehild

can u write an equation for me so i can visualize this better

U=Cv*n*T

ehild

and what variables do i plug in?

T for temperature, n for number of moles and Cv for molar heat capacity of the neon gas at constant pressure .

ehild

## 1. How do I calculate the final temperature of two thermally insulated tanks?

The final temperature of two thermally insulated tanks can be calculated using the principle of thermal equilibrium, which states that the total energy of a closed system remains constant. This means that the sum of the initial energy of both tanks must equal the final energy after they reach equilibrium. By setting the initial energy of both tanks equal to the final energy, you can solve for the final temperature using the specific heat capacities and initial temperatures of each tank.

## 2. What factors affect the final temperature in this scenario?

The final temperature of two thermally insulated tanks is primarily affected by the initial temperatures and specific heat capacities of the tanks. Other factors that may have a minor impact include any heat transfer through the insulation, the volume and mass of each tank, and the type of substance contained in each tank.

## 3. How do I determine the final pressure of the tanks?

The final pressure of two thermally insulated tanks can be calculated using the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are directly proportional. By setting the initial pressure and final temperature of both tanks equal to the final pressure and temperature, respectively, you can solve for the final pressure using the initial volume and the gas constant.

## 4. Can this scenario be applied to real-life situations?

Yes, the concept of two thermally insulated tanks reaching equilibrium can be applied to various real-life situations, such as in industrial processes involving heat exchange or in the design of thermal energy storage systems.

## 5. Are there any limitations to this calculation method?

One limitation of this calculation method is that it assumes the tanks are perfectly insulated and there is no heat loss to the surroundings. In reality, there may be some heat transfer through the insulation, which can affect the final temperature and pressure. Additionally, this calculation method may not be applicable to non-ideal gases or systems with significant temperature gradients.

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