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AI-তৈরি নমুনা উত্তর

1. Van der Waals equation for $n$ moles of a real gas:
$\left( P + \frac{n^2 a}{V^2} \right) (V - nb) = nRT$
where:

• $P$ is pressure,
• $V$ is volume,
• $T$ is absolute temperature,
• $n$ is number of moles,
• $R$ is universal gas constant,
• $a$ and $b$ are Van der Waals constants.

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2. Compressibility factor ($Z_c$) at the critical point:
For $1\text{ mole}$ of a Van der Waals gas, the critical constants are:

• Critical pressure: $P_c = \frac{a}{27b^2}$
• Critical volume: $V_c = 3b$
• Critical temperature: $T_c = \frac{8a}{27Rb}$

The compressibility factor at the critical point is:
$Z_c = \frac{P_c V_c}{R T_c} = \frac{\left(\frac{a}{27b^2}\right)(3b)}{R \left(\frac{8a}{27Rb}\right)} = \frac{3}{8} = 0.375$