Kieran12
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Homework Statement
Two rigid containers, A and B, contain the same type of ideal gas and are connected by a thin tube which has been fitted with a valve. The initial pressures of the gases in A and B are P_1 and P_2, respectively, whilst the initial temperatures are T_1 and T_2, respectively. Container B has four times the volume of container A. The connecting valve is fully opened, and a new equilibrium is established whilst the temperature of each container is maintained at its initial value. What is the final pressure in the system?
Homework Equations
PV = nRT
The Attempt at a Solution
PV = nRT
n = PV/RT
n_1 + n_2 = n_3
=> (P1 * V1)/R * T1 + (P2 * V2)/R * T2 = (P3 * V1)/R * T1 + (P3 * V2)/R * T2
=> (P1 * V1)/ T1 + (P2 * 4V1)/ T2 = (P3 * V1)/ T1 + (P3 * 4V1)/ T2
=> All the V1's cancel
=> (P1)/ T1 + (P2 * 4)/ T2 = (P3)/ T1 + (P3 * 4)/ T2
=> (P1)/ T1 + (P2 * 4)/ T2 = (P3)(1/ T1 + 4/ T2)
=> Then just solve for P3 by dividing by (1/ T1 + 4/ T2)