The container shown in Fig. has two chambers, separated by a partition

1.	The container shown in Fig. has two chambers, separated by a partition, of volumes V1 = 2.0 litre and V2 = 3.0 litre. The chambers contain μ1 = 4.0 and μ2 = 5.0 moles of a gas at pressure P1 = 1.00 atm and P2 = 2.00 atm. Calculate the pressure after the partition is removed and the mixture attains equilibrium.
Answer» V₁ = 2.0 litre, V₂ = 3.0 litre μ₁ = 4.0 moles, μ₂ = 5.0 moles P₁ = 1.00 atm, P₂ = 2.00 atm P₁V₁ =μ₁RT₁, P₂V₂ = μ₂RT₂ μ = μ₁ + μ₂ V = V₁ + V₂ For 1 mole, PV = \(\frac{2}{3}\)E For μ₁ moles, P₁V₁ = \(\frac{2}{3}\)μ₁E₁ For μ₂ moles, P₂V₂ = \(\frac{2}{3}\)μ₂E₂ Total energy is (μ₁E₁ + μ₂E₂) = \(\frac{3}{2}\)(P₁V₁ + P₂V₂) PV = \(\frac{2}{3}\)E_total = \(\frac{2}{3}\) μE_{per mole} P(V₁ + V₂) = \(\frac{2}{3}\) × \(\frac{3}{2}\) (P₁V₁ + P₂V₂) \(P=\frac{P_1V_1+P_2V_2}{V_1+V_2}\) \(=(\frac{1.00\times 2.0+2.00\times 3.0}{2.0+3.0})atm\) \(=\frac{8.0}{5.0}\) = 1.60 atm. Comment : This form of Ideal gas law represented by Equation marked* becomes very useful for adiabatic changes

The container shown in Fig. has two chambers, separated by a partition, of volumes V1 = 2.0 litre and V2 = 3.0 litre. The chambers contain μ1 = 4.0 and μ2 = 5.0 moles of a gas at pressure P1 = 1.00 atm and P2 = 2.00 atm. Calculate the pressure after the partition is removed and the mixture attains equilibrium.

Answer»

V₁ = 2.0 litre,

V₂ = 3.0 litre

μ₁ = 4.0 moles,

μ₂ = 5.0 moles

P₁ = 1.00 atm,

P₂ = 2.00 atm

P₁V₁ =μ₁RT₁,

P₂V₂ = μ₂RT₂

μ = μ₁ + μ₂

V = V₁ + V₂

For 1 mole, PV = \(\frac{2}{3}\)E

For μ₁ moles, P₁V₁ = \(\frac{2}{3}\)μ₁E₁

For μ₂ moles, P₂V₂ = \(\frac{2}{3}\)μ₂E₂

Total energy is (μ₁E₁ + μ₂E₂)

= \(\frac{3}{2}\)(P₁V₁ + P₂V₂)

PV = \(\frac{2}{3}\)E_total = \(\frac{2}{3}\) μE_{per mole}

P(V₁ + V₂) = \(\frac{2}{3}\) × \(\frac{3}{2}\) (P₁V₁ + P₂V₂)

\(P=\frac{P_1V_1+P_2V_2}{V_1+V_2}\)

\(=(\frac{1.00\times 2.0+2.00\times 3.0}{2.0+3.0})atm\)

\(=\frac{8.0}{5.0}\)

= 1.60 atm.

Comment : This form of Ideal gas law represented by Equation marked* becomes very useful for adiabatic changes