QJEEM25Chb00d: JEE Main 2025 Chemistry - Class 11 JEEM25Chb00d Solution: Match List - I with List - II. .tg…

We want to match each partial derivative in List–I to the appropriate thermodynamic quantity in List–II:

1. $\displaystyle\left(\frac{\partial G}{\partial T}\right)_{P}$

A well-known thermodynamic identity is:

$\left(\frac{\partial G}{\partial T}\right)_{P} \;=\; -S.$

Hence,

$(A) \quad \longrightarrow \quad -S \quad (\text{II}).$

2. $\displaystyle\left(\frac{\partial H}{\partial T}\right)_{P}$

By definition of the heat capacity at constant pressure,

$\left(\frac{\partial H}{\partial T}\right)_{P} \;=\; C_P.$

Hence,

$(B) \quad \longrightarrow \quad C_P \quad (\text{I}).$

3. $\displaystyle\left(\frac{\partial G}{\partial P}\right)_{T}$

A standard thermodynamic relation (for a single‐component system) is:

$\left(\frac{\partial G}{\partial P}\right)_{T} \;=\; V.$

Hence,

$(C) \quad \longrightarrow \quad V \quad (\text{IV}).$

4. $\displaystyle\left(\frac{\partial U}{\partial T}\right)_{V}$

By definition of the heat capacity at constant volume,

$\left(\frac{\partial U}{\partial T}\right)_{V} \;=\; C_V.$

Hence,

$(D) \quad \longrightarrow \quad C_V \quad (\text{III}).$

Final Matching

$(A) \to \text{(II)}, \quad (B) \to \text{(I)}, \quad (C) \to \text{(IV)}, \quad (D) \to \text{(III)}.$

Which corresponds to:

Option C: (A)-(II), (B)-(I), (C)-(IV), (D)-(III).