At Boyle's temperature , compressibility factor Z for a real gas is

Options

A. 1
B. 0
C. `gt 1`
D. `lt 1`

Explanation

To solve the question regarding the compressibility factor \( Z \) for a real gas at Boyle's temperature, we can follow these steps:

### Step 1: Understand Boyle's Temperature
Boyle's temperature is a specific temperature at which a real gas behaves like an ideal gas. At this temperature, the interactions between gas molecules become negligible, and the gas follows the ideal gas law more closely.

**Hint:** Recall the definition of Boyle's temperature and its significance in the behavior of real gases.

### Step 2: Define the Compressibility Factor \( Z \)
The compressibility factor \( Z \) is defined as:
\[ Z = \frac{PV}{nRT} \]
Where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = temperature of the gas

**Hint:** Remember that \( Z \) indicates how much a real gas deviates from ideal gas behavior.

### Step 3: Analyze the Behavior of Real Gases at Boyle's Temperature
At Boyle's temperature, the behavior of real gases aligns closely with that of ideal gases. This means that the compressibility factor \( Z \) approaches 1.

**Hint:** Think about the conditions under which real gases behave like ideal gases.

### Step 4: Conclusion
Since at Boyle's temperature the compressibility factor \( Z \) is equal to 1, we can conclude that:
\[ Z = 1 \]

Thus, the answer to the question is that at Boyle's temperature, the compressibility factor \( Z \) for a real gas is 1.

**Final Answer:** The compressibility factor \( Z \) for a real gas at Boyle's temperature is 1.