`{:(,"List-I",,"List-II"),("(P)","Charles' law",(1),Vpropn),("(Q)","Boyle's law",(2),PpropT),("(R)","Avogadro's law",(3),Pprop1//V),("(S)","Gay Lussac's law",(4),VpropT):}`

Options

A. P-1, Q-3, R-2, S-4
B. P-4, Q-3, R-1, S-2
C. P-3, Q-2, R-4, S-1
D. P-2, Q-1, R-4, S-3

Answer

To solve the problem of matching the laws from List I with their corresponding properties from List II, we will analyze each law and determine its relationship with volume (V), pressure (P), and temperature (T).

### Step-by-Step Solution:

1. **Charles' Law (P)**:
- **Definition**: Charles' law states that for a fixed amount of gas at constant pressure, the volume of the gas is directly proportional to its temperature.
- **Mathematical Representation**: V ∝ T (at constant P)
- **Match**: This corresponds to option (4) in List II, which states "V prop T".

2. **Boyle's Law (Q)**:
- **Definition**: Boyle's law states that for a fixed amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume.
- **Mathematical Representation**: P ∝ 1/V (at constant T)
- **Match**: This corresponds to option (3) in List II, which states "P prop 1/V".

3. **Avogadro's Law (R)**:
- **Definition**: Avogadro's law states that at the same temperature and pressure, equal volumes of gases contain an equal number of molecules (or moles).
- **Mathematical Representation**: V ∝ n (where n is the number of moles, at constant T and P)
- **Match**: This corresponds to option (1) in List II, which states "V prop n".

4. **Gay-Lussac's Law (S)**:
- **Definition**: Gay-Lussac's law states that for a fixed amount of gas at constant volume, the pressure of the gas is directly proportional to its temperature.
- **Mathematical Representation**: P ∝ T (at constant V)
- **Match**: This corresponds to option (2) in List II, which states "P prop T".

### Final Matching:

- (P) Charles' law → (4) V prop T
- (Q) Boyle's law → (3) P prop 1/V
- (R) Avogadro's law → (1) V prop n
- (S) Gay-Lussac's law → (2) P prop T

### Summary of Matches:
- P → 4
- Q → 3
- R → 1
- S → 2