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{:(,"List-I",,"List-II"),("(P)","Charles...

`{:(,"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):}`

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

Text Solution

AI Generated Solution

The correct Answer is:
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
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