Free Expansion

The expansion of a gas against the vacuum is called free expansion.

To understand the concept of free expansion let us consider a chamber which is fully insulated. Let the chamber is divided into two parts A and B by means of a partition. Let chamber A contains a gas having properties P₁ V₁ T₁ and let chamber B is in vacuum.

Fig. Free Expansion process

Case – 1

Both chambers are considered as a system. If the partition is removed or punctured then the gases will rush into the chamber B. Therefore the total volume occupied by the gases will increase from V₁ to V2. In this process the pressure will decrease. In general we will try to find out the work done by using relation ʃ PdV but as the boundary of the system or total volume will not change so work done is zero.

Case – 2

Considering chamber A as the system. If we puncture the partition, the gases will rush into the chamber B. As the gases are crossing the system boundary therefore some work must be obtained. But as the gases are rushing into the vacuum state and we know that, work is only done when there is resistance to flow. We further know that vacuum does not offer any resistance to flow. Therefore the work done will be zero.

Points to Remember

1. As the gases rush into chamber B with very high speed so only initial and final conditions are known to us. Therefore free expansion process is irreversible process.

2. As the chamber is fully insulated from surrounding, therefore the free expansion process may be called as adiabatic process.

3. From 1st Law of Thermodynamics we know that for any process

Q₁₋₂ = dU + W₁₋₂

In case of free expansion

Q₁₋₂ = 0; W₁₋₂ = 0

⇒ dU = 0 ⇒ U₂ – U₁ = 0

⇒ U₂ = U₁

Therefore during free expansion process internal energy of the system remains constant.

4. We know that

dU = mCv ( T₂ – T₁)

as in free expansion process

dU = 0

⇒ mCv ( T₂ – T₁) = 0

Or T₂ = T₁

Therefore during free expansion process temperature will also remain constant.

5. We know that

dH = mCp (T₂ – T₁)

in free expansion process

T₂ = T₁

⇒ dH = 0

⇒ H₂ – H₁ = 0

Or H₂ = H₁

Therefore enthalpy will also remain constant during free expansion process.