Understanding the Joule-Thompson Effect and Throttling

The question asks what happens to a gas when it is throttled and has a negative Joule-Thompson effect. Let's first understand the Joule-Thompson effect.

The Joule-Thompson effect describes the temperature change of a real gas or liquid when it expands adiabatically through a valve or porous plug from a high-pressure region to a low-pressure region, a process known as throttling. This process occurs at constant enthalpy (isenthalpic).

The key parameter for this effect is the Joule-Thompson coefficient, denoted by $\mu$. It is defined as the partial derivative of temperature with respect to pressure at constant enthalpy:

$$ \mu = \left( \frac{\partial T}{\partial P} \right)_H $$

Here, $T$ is the temperature, $P$ is the pressure, and $H$ is the enthalpy.

• If $μ > 0$: This means that when the pressure decreases ($\Delta P < 0$) during throttling, the temperature decreases ($\Delta T < 0$). The gas becomes cooler.
• If $μ < 0$: This means that when the pressure decreases ($\Delta P < 0$) during throttling, the temperature increases ($\Delta T > 0$). The gas becomes warmer.
• If $μ = 0$: This means that when the pressure decreases ($\Delta P < 0$) during throttling, the temperature remains constant ($\Delta T = 0$). There is no temperature change.

The question states that the gas has a negative Joule-Thompson effect, which means its Joule-Thompson coefficient is negative ($μ < 0$).

According to the definition of the Joule-Thompson coefficient, if $μ < 0$, then $\left( \frac{\partial T}{\partial P} \right)_H$ is negative. Since throttling involves a decrease in pressure ($\Delta P$ is negative), the change in temperature ($\Delta T$) must be positive for the ratio to be negative:

$$ \Delta T = \mu \times \Delta P $$

If $μ < 0$ and $\Delta P < 0$, then $\Delta T$ must be positive ($ ( - ) \times ( - ) = ( + ) $).

Therefore, when a gas with a negative Joule-Thompson effect is throttled, its temperature increases.

In summary:

Since the gas has a negative Joule-Thompson effect ($μ < 0$), it will become warmer when throttled.