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# Thermodynamics Physics Problem?

Two thermally insulated vessels are connected by a narrow tube fitted with a valve that is initially closed. One vessel, of volume 15.2 L, contains oxygen at a temperature of 300 K and a pressure of 1.75 atm. The other vessel, of volume 22.4 L, contains oxygen at a temperature of 450 K and a pressure of 1.95 atm. When the valve is opened, the gases in the two vessels mix, and the temperature and pressure become uniform throughout.

(a) What is the final temperature? _____ K

(b) What is the final pressure? _____ atm

I honestly don't even know where to begin.... any help?

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The single most important point in solving this problem is that the total

number of moles must remain constant and the total

internal energy must remain constant before and

after opening the valve.

So, first find the number of moles in each vessel, and then find the internal energy of each vessel, then the total number of moles and energy, and consider the total volume:

V(total) = 15.2 L + 22.4 L = 37.6 L

In the first vessel, the number of moles:

n = pV/RT = 1.75(15.2) / 0.08206(300) = 1.08 mol

And in the second vessel, the number of moles:

n = pV/RT = 1.95(22.4) / 0.08206(450) = 1.183 mol

Therefore, the total # of moles:

n(total) = 1.08+1.183 = 2.263 mol

For the first vessel, the internal energy:

U = (5/2)nRT = (5/2)(1.08)(8.314)(300) = 6734 J

and for the second vessel, the internal energy:

U = (5/2)nRT = (5/2)(1.183)(8.314)450 = 11065.9 J

So that, the total energy:

U = 6734 + 11065.9 = 17800 J

Then the final temperature can be obtained by use of the

eqn for the total energy:

U(total) = (5/2)nRT = 17800.

T = (2/5)U/nR = 0.4(17800) / (2.263)(8.314)

= 378 K, and the final pressure:

P = nRT/ V = (2.263)(0.08207)(378) / 37.6 = 1.869 atm

Hth

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• Reversible technique is a technique wherein driving tension is infinitesimally smaller than the opposing tension such that reasonable strengthen in opposing tension will convey approximately substitute interior the direction of reaction.

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• i hope i am correct!!

PV =n RT

n = gram moles = PV/RT

----------------------------------

let final temp (T) & pressure be (P)

n1 + n2 = n ................ mass conserved

P1V1/RT1 + P2V2/RT2 = PV/RT

where V = V1 + V2

================= use values

you get one equation in [P,T] ---------- (1)

===================

as the system is thermally insulated, no heat enters/escapes

heat lost by hotter = heat gained by cooler

n1 c [T - 300] = n2 c [450 - T]

calculate T

use it to find P from (1)

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