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Find the final volume 
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#1
Dec2108, 03:42 PM

P: 369

1. The problem statement, all variables and given/known data
Two ideal gas (n mole A and m mole B) was separated by a piston (impermeable and diathermal) the whole setup is confine in a adiabatic walls so no heat exchange with outside. Let the piston move, at equilibrium, find the final volume. Assume the final temperature of both gas is T and the total volume is V. 2. The attempt at a solution First of all, both gas satisfy ideal gas state equation [tex] \frac{P_AV_A}{T_A} = nR, \qquad \qquad \frac{P_BV_B}{T_B} = mR [/tex] Since we know the final temperature, and at equilibrium, the pressure is the same on both compartment (otherwise, the piston will move), so assuming the final volume of A is [tex]V_A[/tex], then the final volume of B will be [tex]VV_B[/tex], we conclude that [tex] \frac{P}{T} = nRV_A = \frac{P}{T} = mR(VV_A) [/tex] We can solve for [tex]V_A[/tex] and [tex]V_B[/tex], right? 


#2
Dec2208, 03:29 AM

Sci Advisor
HW Helper
P: 4,300

Your setup looks correct, except for a mathematical error...
If [itex]\frac{P V}{T} = n R[/itex], then [itex]\frac{P}{T} = \cdots [/itex] ? By the way, once you have found the answer, it'll be nice trying to explain its physical meaning and saying something about whether you could have foreseen the outcome. 


#3
Dec2208, 12:16 PM

P: 369




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