Question

Which one of the following is true for a throttling process?

• A. A gas may have more than one inversion temperature
• B. The inversion temperature is different for different gases
• C. The inversion temperature is same for all gases
• D. The inversion temperature is the temperature at which Joule-Thomson co-efficient is infinity

Hint:

For an ideal gas, intermolecular forces are zero, which means $\mu_{\text{JT}}$ is always zero. This implies that ideal gases experience no temperature change during a throttling process.

Answer 1

The Correct Option is B

Concept: Throttling is an isenthalpic process ($H = \text{constant}$) where a fluid flows through a restriction, such as a partially closed valve or a porous plug, resulting in a pressure drop. The temperature behavior of the fluid during this process is described by the Joule-Thomson coefficient ($\mu_{\text{JT}}$): \[ \mu_{\text{JT}} = \left( \frac{\partial T}{\partial P} \right)_H \]

• If $\mu_{\text{JT}} \gt 0$, the temperature drops as pressure decreases (cooling occurs).

• If $\mu_{\text{JT}} \lt 0$, the temperature rises as pressure decreases (heating occurs).

• If $\mu_{\text{JT}} = 0$, the temperature remains constant during the expansion. This point is known as the Inversion Temperature ($T_{\text{inv}}$).

Step 1: Analyze the nature of the inversion temperature for real gases.
The inversion temperature depends directly on the intermolecular attractive and repulsive forces characteristic of a specific gas molecule. For a van der Waals gas, the inversion temperature can be approximated as: \[ T_{\text{inv}} = \frac{2a}{R b} \] where $a$ and $b$ are the specific van der Waals constants for that gas. Because these constants vary depending on the chemical structure of the molecule, the inversion temperature is different for different gases. This matches Option B.