Two thermally insulated tanks, calculating final temperature and final 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

 

[Hotwir3]

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!

 

[copitlory8]

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

 

[copitlory8]

actually i got the answer completely wrong

 

[copitlory8]

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

 

[Hotwir3]

Give me a minute.

 

[SiYuan]

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?

 

[copitlory8]

400k

 

[SiYuan]

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.

 

[Hotwir3]

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.

 

[copitlory8]

how do i do that

 

[ehild]

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

 

[copitlory8]

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

 

[ehild]

U=Cv*n*T

ehild

 

[copitlory8]

and what variables do i plug in?

 

[ehild]

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

ehild