Question

Consider the following statement (I) Joule Thomson experiment is isoenthalpic as well as adiabatic (II) \(\Lambda\) negative value of \(\mu_{J \mathrm{~T}}\) (Joule Thomson coefficient) corresponds to warming of a gas on expansion (III) The temperature at which neither cooling nor heating effect is observed is known as inverson temperature Which of the above statements are correct? (1) I and II (2) I and II (3) II and III (4) I, II and III

Short answer

All three statements (I, II, and III) are correct. The answer is (4).

Step-by-step solution

Evaluating Statement I

Statement I says that the Joule-Thomson experiment is both isoenthalpic and adiabatic. The Joule-Thomson process is indeed characterized by being isoenthalpic (constant enthalpy) and nearly adiabatic (no heat exchange with the surroundings). Thus, Statement I is correct.

Evaluating Statement II

Statement II states that a negative value of the Joule-Thomson coefficient \(\mu_{JT}\) corresponds to the warming of a gas upon expansion. The Joule-Thomson coefficient \(\mu_{JT}\) is defined as the rate of change of temperature with respect to pressure at constant enthalpy. When \(\mu_{JT} < 0\), the gas warms up during expansion. Therefore, Statement II is correct.

Evaluating Statement III

Statement III states that the temperature at which neither cooling nor heating effect is observed is known as the inversion temperature. This is correct, as the inversion temperature is the point where the Joule-Thomson coefficient changes sign, and the gas does not undergo any temperature change. Therefore, Statement III is also correct.

Conclusion

Since all three statements (I, II, and III) are accurate as evaluated above, the correct answer is the option that includes all three statements.

Key concepts

Isoenthalpic Process

In thermodynamics, an isoenthalpic process is one in which the enthalpy (a measure of the total energy of a thermodynamic system) remains constant. This is a common characteristic in the Joule-Thomson effect. During the Joule-Thomson experiment, a gas expands through a porous plug or valve without exchanging heat with the surroundings, making it both isoenthalpic and adiabatic.
The constant enthalpy in an isoenthalpic process means that any reduction in pressure occurs without a change in the total heat content of the system. This principle is essential for understanding how gases can cool or warm during expansion. Understanding the isoenthalpic nature of the Joule-Thomson effect helps to predict temperatures changes in gases.

Adiabatic Process

An adiabatic process involves no heat transfer into or out of the system. In an adiabatic process, all the changes in energy are due to work done by or on the system. The Joule-Thomson experiment exemplifies an adiabatic process. As gas passes through the valve, there is no heat exchange with the environment.
This isolation is significant because it allows researchers to measure the temperature change solely due to pressure alterations, without any external heat interference.
In adiabatic processes, the system's internal energy changes can lead to cooling or heating effects purely based on expansions or compressions.

Joule-Thomson Coefficient

The Joule-Thomson coefficient, denoted by \( \mu_{JT} \), measures how the temperature of a real gas changes with pressure at constant enthalpy. It is defined mathematically as:
\( \mu_{JT} = \left( \frac{\partial T}{\partial P} \right)_{H} \).
A positive \( \mu_{JT}\ \) means the gas cools upon expansion, while a negative \( \mu_{JT} \) indicates warming. For most gases at room temperature, the Joule-Thomson coefficient is positive, leading to cooling upon expansion. Understanding \(\ \mu_{JT}\ \) is crucial for applications like gas liquefaction and refrigeration where controlled temperature changes are key.

Inversion Temperature

The inversion temperature is the point at which the Joule-Thomson coefficient changes sign. Below this temperature, a gas will cool when expanded (positive \( \mu_{JT} \)), and above it, the gas will warm when expanded (negative \( \mu_{JT} \)). This concept is essential in understanding why gases behave differently under varying thermal conditions.
At the inversion temperature, neither cooling nor heating occurs upon expansion, making it a critical reference point in processes like gas liquefaction, where maintaining or altering temperature is key. For practical applications, knowing the inversion temperature helps in designing systems that utilize the Joule-Thomson effect efficiently.