## Question

For a real gas at high pressure, the compression factor is:

A. 1

B. $$1 + \frac{Pb}{RT}$$

C. $$1 - \frac{Pb}{RT}$$

D. $$1 + \frac{RT}{Pb}$$

✨ Free AI Tools for You

Powered by Chatterbot AI

## Answer

**:**

The correct answer is **B**.

For **one mole** of a **real gas**, the Van der Waals equation is given by:

$$ \left(P + \frac{a}{V^2}\right)(V - b) = RT $$

Rewriting this, we get:

$$ PV = RT + Pb + \frac{ab}{V^2} - \frac{a}{V} $$

At **high pressure**, the Van der Waals equation simplifies to:

$$ PV = RT + Pb $$

Dividing through by $RT$, we have:

$$ \frac{PV}{RT} = 1 + \frac{Pb}{RT} $$

Thus, the **compressibility factor (Z)** is:

$$ Z = \frac{PV}{RT} = 1 + \frac{Pb}{RT} $$

Hence, the correct option is **B**.

India's 1^{st} AI Doubt Solver for CBSE, JEE, and NEET

and then it's just ₹212 a month