Thermodynamics problem. Have I answered this correctly?

[Kieran12]

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)

 

[andrewkirk]

Your answer looks right to me.