Question

Match the following thermodynamic functions/equations with their expressions:

• A. A1 $\to$ B2, A2 $\to$ B4, A3 $\to$ B1, A4 $\to$ B3
• B. A1 $\to$ B4, A2 $\to$ B2, A3 $\to$ B1, A4 $\to$ B3
• C. A1 $\to$ B2, A2 $\to$ B4, A3 $\to$ B3, A4 $\to$ B1
• D. A1 $\to$ B4, A2 $\to$ B2, A3 $\to$ B3, A4 $\to$ B1

Hint:

Remember: $a = u - Ts$ (Helmholtz), $g = h - Ts$ (Gibbs), $du = Tds - Pdv$ (Tds equation), and Clapeyron equation gives slope of saturation line.

Answer 1

The Correct Option is C

Step 1: Recall Helmholtz function. \[ a = u - Ts \] But in given table, $u - Ts$ corresponds to Gibbs? Actually, by definition: - Helmholtz free energy: $a = u - Ts$ $\Rightarrow$ matches B2. - Gibbs free energy: $g = h - Ts$ $\Rightarrow$ matches B4.
Step 2: Recall $Tds$ equation. From first law: \[ du = Tds - Pdv \] Thus A3 $\to$ B3.
Step 3: Clapeyron–Clausius relation. \[ \left(\frac{d}{dT} \ln P \right)_{sat} = \frac{h_{fg}}{RT^2} \] So A4 $\to$ B1.
Step 4: Matching summary. - A1 $\to$ B2 - A2 $\to$ B4 - A3 $\to$ B3 - A4 $\to$ B1 Final Answer: \[ \boxed{\text{Option (D)}} \]