Match List - I with List - II.
| List - I (Partial Derivatives) |
List - II (Thermodynamic Quantity) |
||
|---|---|---|---|
| (A) | $\left(\frac{\partial \mathrm{G}}{\partial \mathrm{T}}\right)_{\mathrm{P}}$ | (I) | Cp |
| (B) | $\left(\frac{\partial \mathrm{H}}{\partial \mathrm{T}}\right)_{\mathrm{P}}$ | (II) | $-$S |
| (C) | $\left(\frac{\partial \mathrm{G}}{\partial \mathrm{P}}\right)_{\mathrm{T}}$ | (III) | Cv |
| (D) | $\left(\frac{\partial \mathrm{U}}{\partial \mathrm{T}}\right)_{\mathrm{V}}$ | (IV) | V |
Choose the correct answer from the options given below :
Solution
<p>We want to match each partial derivative in List–I to the appropriate thermodynamic quantity in List–II:</p>
<hr />
<h3>1. $\displaystyle\left(\frac{\partial G}{\partial T}\right)_{P}$</h3>
<p>A well-known thermodynamic identity is:</p>
<p>$ \left(\frac{\partial G}{\partial T}\right)_{P} \;=\; -S. $</p>
<p>Hence, </p>
<p>$ (A) \quad \longrightarrow \quad -S \quad (\text{II}). $</p>
<hr />
<h3>2. $\displaystyle\left(\frac{\partial H}{\partial T}\right)_{P}$</h3>
<p>By definition of the heat capacity at constant pressure,</p>
<p>$ \left(\frac{\partial H}{\partial T}\right)_{P} \;=\; C_P. $</p>
<p>Hence, </p>
<p>$ (B) \quad \longrightarrow \quad C_P \quad (\text{I}). $</p>
<hr />
<h3>3. $\displaystyle\left(\frac{\partial G}{\partial P}\right)_{T}$</h3>
<p>A standard thermodynamic relation (for a single‐component system) is:</p>
<p>$ \left(\frac{\partial G}{\partial P}\right)_{T} \;=\; V. $</p>
<p>Hence, </p>
<p>$ (C) \quad \longrightarrow \quad V \quad (\text{IV}). $</p>
<hr />
<h3>4. $\displaystyle\left(\frac{\partial U}{\partial T}\right)_{V}$</h3>
<p>By definition of the heat capacity at constant volume,</p>
<p>$ \left(\frac{\partial U}{\partial T}\right)_{V} \;=\; C_V. $</p>
<p>Hence, </p>
<p>$ (D) \quad \longrightarrow \quad C_V \quad (\text{III}). $</p>
<hr />
<h2>Final Matching</h2>
<p>$ (A) \to \text{(II)}, \quad (B) \to \text{(I)}, \quad (C) \to \text{(IV)}, \quad (D) \to \text{(III)}. $</p>
<p>Which corresponds to:</p>
<blockquote>
<p><strong>Option C: (A)-(II), (B)-(I), (C)-(IV), (D)-(III).</strong></p>
</blockquote>
About this question
Subject: Chemistry · Chapter: Thermodynamics · Topic: Zeroth and First Law
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