Match the column
Column-IColumn-I(i) Adiabatic bulk modulus of a gas[A] (ii) Slope of P-V curve for…

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Match the column
Column-IColumn-I(i) Adiabatic bulk modulus of a gas[A] (ii) Slope of P-V curve for isothermal process[B] (iii) Degree of freedom[C] γP(iv) Ratio of molar heat capacity    at constant pressure to R(gas constant)[D]

CGP EDU Academic Team · Accepted Answer

The correct answer is B. Step 1: Understand the definitions in Column-I.(i) Adiabatic Bulk Modulus of a Gas: In an adiabatic process, the bulk modulus (K) can be expressed as $$ K = \gamma P $$ where $ \gamma $ (gamma) is the adiabatic index and P is the pressure.(ii) Slope of P-V Curve for Isothermal Process: For an isothermal process involving an ideal gas, the slope of the P-V curve is given by $$ \frac{dP}{dV} = -\frac{nRT}{V^2} $$ which indicates how pressure changes with volume at constant temperature.(iii) Degree of Freedom: The degree of freedom of a gas is related to the number of ways in which a system can store energy. It is usually given by the equation $ f = 3N - r $, where N is the number of particles and r is the number of constraints.(iv) Ratio of Molar Heat Capacity at Constant Pressure to R: The ratio of molar heat capacity (Cp) at constant pressure to R is $ C_p/R = \gamma $, which indicates the relation of heat capacities. Step 2: Match each definition from Column-I to the expressions or values in Column-II based on the relationships described above.(i) matches with [A] since $$ K = \gamma P $$.(ii) matches with [B] as it describes the slope of the isothermal curve.(iii) matches with [C] as it relates to the definition of degrees of freedom.(iv) matches with [D] indicating the molar heat capacity ratio. Therefore, the correct matches are (i) - [A], (ii) - [B], (iii) - [C], (iv) - [D]. Hence the correct answer is [B].

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Column-I	Column-I
(i) Adiabatic bulk modulus of a gas	[A]
(ii) Slope of P-V curve for isothermal process	[B]
(iii) Degree of freedom	[C] γP
(iv) Ratio of molar heat capacity at constant pressure to R(gas constant)	[D]

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