The excluded volume of a gas will be larger, if `(T_(C))/(P_(C))` is :

Options

A. small
B. large
C. equal to 1
D. less than unity

Explanation

To solve the question regarding the excluded volume of a gas in relation to the ratio \( \frac{T_C}{P_C} \), we can follow these steps:

### Step 1: Understand the Concept of Excluded Volume
Excluded volume refers to the volume that is not available to the gas particles due to their finite size. It is an important concept in real gas behavior, especially when considering interactions between gas molecules.

### Step 2: Identify Critical Constants
The critical temperature (\( T_C \)) and critical pressure (\( P_C \)) are essential parameters in describing the behavior of gases. The critical temperature is the temperature above which a gas cannot be liquefied, and the critical pressure is the pressure required to liquefy a gas at its critical temperature.

### Step 3: Relate Excluded Volume to Critical Constants
The excluded volume (\( b \)) of a gas is related to the size of the gas molecules. According to van der Waals equation, the excluded volume is directly proportional to the parameter \( b \).

### Step 4: Analyze the Ratio \( \frac{T_C}{P_C} \)
The ratio \( \frac{T_C}{P_C} \) can give insights into the behavior of the gas. If \( T_C \) is large relative to \( P_C \), it suggests that the gas can exist at higher temperatures without liquefying, which may indicate larger molecular sizes and thus a larger excluded volume.

### Step 5: Conclusion
From the analysis, we can conclude that the excluded volume of a gas will be larger if the ratio \( \frac{T_C}{P_C} \) is larger. This is because a larger \( T_C \) relative to \( P_C \) implies that the gas molecules have a larger size, leading to a greater excluded volume.

### Final Answer
The excluded volume of a gas will be larger if \( \frac{T_C}{P_C} \) is larger.

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