Match List :
`{:("Column-I","Column-II"),((A)PV^(gamma)="Constant",(p)"Expansion of ideal gas in vacuum"),((B)DeltaT=O,(q)Z=1-a/(V_mRT)),((C )"For" H_2 and He at 0^@C,(r)"Adiabatic reversible process"),((D)"At low density of gas",(s)Z=1+(pb)/(RT)):}`

Explanation

To solve the matching question, we will analyze each statement in Column I and find the corresponding statement in Column II.

### Step 1: Analyze Column I

1. **(A) PV^(γ) = Constant**:
- This equation describes an adiabatic process for an ideal gas, where γ (gamma) is the heat capacity ratio (C_p/C_v).
- **Match with (r) Adiabatic reversible process**.

2. **(B) ΔT = 0**:
- This condition indicates that there is no change in temperature, which is characteristic of free expansion, where a gas expands into a vacuum without doing work or exchanging heat.
- **Match with (p) Expansion of ideal gas in vacuum**.

3. **(C) For H₂ and He at 0°C**:
- At low temperatures, the compressibility factor (Z) for ideal gases is approximately 1. For real gases like H₂ and He, this holds true under certain conditions.
- **Match with (q) Z = 1 - a/(V_mRT)**, where 'a' is a constant related to the attractive forces between molecules.

4. **(D) At low density of gas**:
- At low densities, the behavior of real gases can be approximated by the ideal gas law, and the compressibility factor can be expressed as Z = 1 + b/(RT), where 'b' is the volume excluded due to finite size of molecules.
- **Match with (s) Z = 1 + b/(RT)**.

### Final Matches

- (A) PV^(γ) = Constant → (r) Adiabatic reversible process
- (B) ΔT = 0 → (p) Expansion of ideal gas in vacuum
- (C) For H₂ and He at 0°C → (q) Z = 1 - a/(V_mRT)
- (D) At low density of gas → (s) Z = 1 + b/(RT)

### Summary of Matches

- A → r
- B → p
- C → q
- D → s

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