Which of the following represents a plot of compressibility factor (Z) versus P at room temperature for helium?

Options

A.
B.
C.
D.

Answer

To solve the question regarding the plot of compressibility factor (Z) versus pressure (P) at room temperature for helium, we will follow these steps:

### Step 1: Understand the Compressibility Factor (Z)
The compressibility factor (Z) is defined as the ratio of the molar volume of a real gas (V_real) to the molar volume of an ideal gas (V_ideal) at the same temperature and pressure. Mathematically, it is expressed as:
\[ Z = \frac{V_{\text{real}}}{V_{\text{ideal}}} \]

### Step 2: Ideal Gas Behavior
For an ideal gas, the compressibility factor (Z) is equal to 1. This means that at low pressures and high temperatures, gases behave ideally, and Z will approach 1.

### Step 3: Real Gas Behavior
For real gases, especially at high pressures, the volume of the gas deviates from the ideal gas behavior. In the case of helium, as pressure increases, the compressibility factor (Z) increases because the real volume becomes greater than the ideal volume.

### Step 4: Analyze Helium's Characteristics
Helium is a noble gas that exhibits non-ideal behavior under certain conditions. It is known for being difficult to compress and liquefy. Therefore, as pressure increases, the compressibility factor (Z) for helium will also increase.

### Step 5: Identify the Correct Plot
Given the options (A, B, C, D), we need to find the plot that shows an increasing trend of Z with increasing pressure (P). The correct plot will start at Z = 1 (ideal gas behavior) and rise above this line as pressure increases.

### Conclusion
After analyzing the characteristics of helium and the behavior of the compressibility factor, we can conclude that the correct option representing the plot of compressibility factor (Z) versus pressure (P) at room temperature for helium is **Option 1**.

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